Wikiversity enwikiversity https://en.wikiversity.org/wiki/Wikiversity:Main_Page MediaWiki 1.47.0-wmf.16 first-letter Media Special Talk User User talk Wikiversity Wikiversity talk File File talk MediaWiki MediaWiki talk Template Template talk Help Help talk Category Category talk School School talk Portal Portal talk Topic Topic talk Collection Collection talk Draft Draft talk TimedText TimedText talk Module Module talk Event Event talk 0 2697 2823641 2181095 2026-08-20T12:34:29Z Alexcalamaro 2169118 /* Resources */ archived link 2823641 wikitext text/x-wiki {{physics}} === Class number === This Wikiversity [[Help:Course|course]] is a guide for the traditional university course MIT 8.033. === Mathematical background === To study this material, you will need to understand basic algebra. === Study hints === The key to understanding special relativity is to master the space-time diagram and think of the metric between the points as a "weird distance." Pretty much any problem in special relativity can be solved by graphing it on a piece of graph paper. Another fundamental key when dealing with special relativity problems is remembering that when anything moves at high speed with respect to you, all its parts -along the direction of its movement- are in a different time. For example, if a mother gave birth to triplets in a train moving at a very high speed, and each one was sitting in a different rail car, for you (standing outside the train) the one in the last car would be more grown up than the one in the middle car, and this one would be more grown up than the one in the first car. The trick is that what is simultaneous for you isn't simultaneous for them. === Resources === * http://www.astro.ucla.edu/~wright/relatvty.htm *[https://web.archive.org/web/20040415204322/http://ocw.mit.edu/OcwWeb/Physics/8-033Fall2003/CourseHome/index.ht 8.033 Relativity, Fall 2003], at MIT OpenCourseWare *[http://www.modernrelativitysite.com/ Relativity], at ModernRelativitySite ===Recommended Texts=== * [[w:Edwin Taylor|Taylor]] and [[w:John Archibald Wheeler|Wheeler]]. (1992). ''Spacetime Physics'' W. H. Freeman. {{ISBN|0716723271 -}} One of the great things about this text is that it uses real problems, ie., it refers the reader to several research papers in reference to the problems given as exercises, and yet the exercises do not need anything more than a basic high school education to solve. An amazing accomplishment. * [[b:Special_relativity|Special Relativity text]]. A good introduction and orientation. [[Category:Physics]] [[Category:Science courses]] cr5myq0kb1qwwa7i7kx0bo6wzpz0wc4 2823642 2823641 2026-08-20T12:36:38Z Alexcalamaro 2169118 /* Resources */ another source 2823642 wikitext text/x-wiki {{physics}} === Class number === This Wikiversity [[Help:Course|course]] is a guide for the traditional university course MIT 8.033. === Mathematical background === To study this material, you will need to understand basic algebra. === Study hints === The key to understanding special relativity is to master the space-time diagram and think of the metric between the points as a "weird distance." Pretty much any problem in special relativity can be solved by graphing it on a piece of graph paper. Another fundamental key when dealing with special relativity problems is remembering that when anything moves at high speed with respect to you, all its parts -along the direction of its movement- are in a different time. For example, if a mother gave birth to triplets in a train moving at a very high speed, and each one was sitting in a different rail car, for you (standing outside the train) the one in the last car would be more grown up than the one in the middle car, and this one would be more grown up than the one in the first car. The trick is that what is simultaneous for you isn't simultaneous for them. === Resources === * http://www.astro.ucla.edu/~wright/relatvty.htm *[https://web.archive.org/web/20040415204322/http://ocw.mit.edu/OcwWeb/Physics/8-033Fall2003/CourseHome/index.ht 8.033 Relativity, Fall 2003], at MIT OpenCourseWare *[https://ocw.mit.edu/courses/8-033-introduction-to-relativity-and-spacetime-physics-fall-2024/ 8.033 Introduction to Relativity and Spacetime Physics, Fall 2024] *[http://www.modernrelativitysite.com/ Relativity], at ModernRelativitySite ===Recommended Texts=== * [[w:Edwin Taylor|Taylor]] and [[w:John Archibald Wheeler|Wheeler]]. (1992). ''Spacetime Physics'' W. H. Freeman. {{ISBN|0716723271 -}} One of the great things about this text is that it uses real problems, ie., it refers the reader to several research papers in reference to the problems given as exercises, and yet the exercises do not need anything more than a basic high school education to solve. An amazing accomplishment. * [[b:Special_relativity|Special Relativity text]]. A good introduction and orientation. [[Category:Physics]] [[Category:Science courses]] krksm8i3b4nyodq53ps213ppp1n9kur 102 7576 2823829 2785027 2026-08-21T04:50:29Z It-is-Truly-Meet 3089598 /* Verb Forms of the Present Active Indicative */ 2823829 wikitext text/x-wiki {{RightTOC}} == Introductory Ancient Greek Language == [[Image:Socrates Louvre.jpg|thumb|right|200px|Σωκράτης]] [[Image:Bust Athena Velletri Glyptothek Munich 213.jpg|thumb|right|200px|Ἀθηνᾶ]] Welcome to the course Introductory Ancient Greek Language. Greek was the ''lingua franca'' of the Mediterranean world from the rise of the Hellenic states after the Persian War until the rise of Rome. Its basis as the uniting factor of the Greek city-states makes knowledge of the language and its history vital to an understanding of the rise of Greek culture in the Western World. This course will prepare students to read Classical Greek texts by building a solid foundation in rudimentary grammar and vocabulary, as well as give a broad overview of its history. It will begin on a very basic level, so if you have some experience you may choose to move on to a more advanced course, or assist in lesson plans with this one. However, even a seasoned reader of Greek may benefit from a basic review. If you're coming here with no experience of the Ancient Greek Language then congratulations on your choice to begin learning it! You are in for an exciting adventure that will not only give you knowledge of a new language, but a new way of thinking. The course will be divided into several important divisions each one hopefully no longer than four lessons followed by a review. The goal is to prepare the student with a foundation in Classical Greek, on which he or she can later build a higher fluency. == Student Questions == If you happen to become stumped or just have a general question out of curiosity, then feel free to message any recent active member involved in creating this course. I intend to add much more to this page, but I don't have a huge amount of time to work on it. I am looking into adding some exercises for translation and adding some study guide outlines to later pages. == Alphabet, Breathings, Accents, Articles == After having completed these first four lessons hopefully the student will be able to read and write with Greek characters. Some vocabulary will be introduced but the goal will be to familiarize yourself with understanding the alphabet in order to begin learning the language. * [[Introductory Ancient Greek Language/Lesson 1|Lesson 1]] - Alphabet * [[Introductory Ancient Greek Language/Lesson 2|Lesson 2]] - Breathings and Accents * [[Introductory Ancient Greek Language/Lesson 3|Lesson 3]] - The Definite Article * [[Introductory Ancient Greek Language/Lesson 4|Lesson 4]] - Basic Sentences * [[Introductory Ancient Greek Language/Review|Review]] == Introduction to Verbs and Nouns == * [[Introductory Ancient Greek Language/Lesson 5|Lesson 5]] - Present, Active and Middle-Passive, Indicative * [[Introductory Ancient Greek Language/Lesson 6|Lesson 6]] - First and Second Noun Declensions * [[Introductory Ancient Greek Language/Lesson 7|Lesson 7]] - Basic Prepositions, Negation * [[Introductory Ancient Greek Language/Lesson 8|Lesson 8]] - Present Indicative of "To Be" * [[Introductory Ancient Greek Language/Review 2|Review]] == Verb Forms of the Active Indicative == * [[Introductory Ancient Greek Language/Lesson 9|Lesson 9]] - Imperfect, Active, Indicative * [[Introductory Ancient Greek Language/Lesson 10|Lesson 10]] - Future, Active, Indicative * [[Introductory Ancient Greek Language/Lesson 11|Lesson 11]] - Aorist(1st and 2nd), Active, Indicative * [[Introductory Ancient Greek Language/Lesson 12|Lesson 12]] - Perfect, Active, Indicative * [[Introductory Ancient Greek Language/Lesson 13|Lesson 13]] - Pluperfect, Active, Indicative * [[Introductory Ancient Greek Language/Review 3|Review]] This is about the middle point of this course. After this there remain the rest of the first declension, and the third, and various other syntax related concepts such as relative pronouns and compound verbs and such. The remainder of the course will be written after these first three lesson plans have been completed. Please place any questions or concerns on the discuss page for this portal or message me directly via my talk page, I only recently took up this project after finding it alone for so long, so I'd love to hear your input or address any questions you may have. [[User:Wobblywatch|Wobblywatch]] ([[User talk:Wobblywatch|discuss]] • [[Special:Contributions/Wobblywatch|contribs]]) 00:23, 8 April 2019 (UTC) == Typing Greek Text and Word List == * [[Enabling Greek Characters on Your Keyboard|Typing Greek Text]] * [[An Ancient Greek Word List]] [[Category:Language introductions]] [[Category:Ancient Greek Language]] [[el:Τμήμα:Αρχαία Ελληνικά]] 3yd5posawaas2ou4en03kfyawgg054v 0 7637 2823772 2237067 2026-08-21T01:04:25Z It-is-Truly-Meet 3089598 2823772 wikitext text/x-wiki Learning a different alphabet may seem daunting at first, but Greek characters are very similar to the Latin ones English speakers are used to. Greeks borrowed their alphabet from the {{w|Phoenicians}}, who were the first recorded civilization to create one; Latin similarly developed from Greek and other languages. The word alphabet itself comes from the words '''alpha''' and '''beta''', which come from the even older letters Aleph and Bet. It's a lot to take in at one go, so don't feel bad if you fail to remember all of these immediately. You will have plenty of time to get these characters under your belt. When you feel ready, try to convert some Greek into English and some English into Greek below. == The Letters, Greek orthography == {| class="wikitable" !Greek !!Name !!English equivalent !!Pronunciation !!Notes |- |Α α|| alpha|| a || 'a' as in 'father' || ambiguous vowel |- |Β β|| beta|| b|| 'b' as in 'book', later 'v' as in 'vase'|| |- |Γ γ || gamma|| g || 'g' as in 'graph', later as 'y' in 'yes'|| |- |Δ δ || delta || d|| 'd' as in 'dad'|| |- |Ε ε || epsilon|| ĕ|| 'ei' as in 'eight'|| |- |Ζ ζ || zeta || z || 'zd', later 'z' as in 'zoo'|| |- |Η η || eta || ē || long 'e' as in 'help', || |- |Θ θ || theta || th || 't' [tʰ] as in 'too', later 'th' as in 'thick'||<u>never</u> pronounced like 'th' in 'this' |- |Ι ι || iota || i || 'e' as in 'email'|| ambiguous vowel |- |Κ κ || kappa || k || 'k' as in 'kick'|| |- |Λ λ || lambda || l|| 'l' as in 'look'|| |- |Μ μ || mu || m|| 'm' as in 'meter'|| |- |Ν ν || nu || n|| 'n' as in 'noon'|| |- |Ξ ξ || xi || x|| 'x' as in 'axe'|| |- |Ο ο || omicron || ŏ|| 'o' as in 'oak'|| |- |Π π || pi || p|| 'p' as in 'port'|| |- |Ρ ρ || rho || r|| 'r' as in 'road'|| sometimes trilled; pronounced [[w:Voiceless dental and alveolar trills|[r̥]]] with rough-breathing |- |Σ σ, ς || sigma || s|| 's' as in 'seed'|| ' σ ' is used in the middle or beginning of a word, and ' ς ' is used at the end of a word |- |Τ τ || tau || t|| 't' as in 'touch' |- |Υ υ || upsilon || u|| 'u' [[w:Close front rounded vowel| [y]]] as in French 'tu'|| ambiguous vowel |- |Φ φ || phi || ph|| 'ph' as in 'uphold', later 'f' as in 'fit'|| |- |Χ χ || chi || kh|| 'k' as in 'kidding', later 'ch' as in 'loch'|| |- |Ψ ψ || psi || ps|| 'ps' as in 'lapse'|| |- |Ω ω || omega || ō|| long 'o' [[w:Open-mid back rounded vowel|[ɔ]]] as in 'God'|| |} == Two-Letter Combination Sounds == ===Proper Diphthongs (Two-Vowel Combinations)=== * αυ [au̯] - like 'au' in 'aural' * ευ [eu̯] - like 'eu' in 'feud' * ηυ [ɛːu̯] - like 'ew' in 'tewan' * (non-[[w:Attic Greek|Attic]]) ωυ [ɔːu̯] - like 'alw' in 'always' * υι [y] - like 'u' in 'tu' * ει [e] - like 'ai' in 'wait' * ου [uː] - like 'oo' in 'food' or like 'ou' in 'thought' * οι [ǒi̯] - like 'oi' in 'oil' * αι [ǎi̯] - like 'i' in 'hi' ===Other Combinations=== * γγ - like 'ng' in 'ding' * γκ - like 'ng' in 'ding' * μπ - like 'mp' in 'emperor' * ντ - like 'nt' in 'enter' ==Typography== [[File:Fragmentary marble inscription MET DP132672.jpg|Fragmentary_marble_inscription_MET_DP132672|thumb|200px|An {{w|Attic Greek}} inscription]] After 1981 in modern Greek, there is mostly only one accent used in publications or privately. It is known as ''tonos'' ' ΄ ' and represents the stressed syllable of a word. It may occur on one of the three ending syllables (on a vowel), but there are cases where there are two accents; one on the ending and one on the third from the word's end. Before 1981 (but also today, though not so often for practical reasons), the other accents have been used and may be seen in ancient, medieval, and most printed modern texts. These are the ὀξεῖα ' ´ ' (acute), βαρεῖα ' ` ' (grave), and περισπωμένη ' ῀ ' (circumflex). There are also two 'breathing' marks: the δασεῖα ' ῾ ' (rough; makes a ' h ' sound) and the ψιλή ' ᾽ ' (smooth; the absence of rough breathing). The breathing marks can only be used on the 1st syllable. Sometimes you also see the symbol ' ι ' under a (long) vowel, like ' ᾳ, ῃ, ῳ ' which shows a later silenced ' i ' sound (glide). In Greek, the question mark is ' ; ', the semi-colon in English. Quotations are represented with ' « ' and ' » '. However, Ancient Greek was '''never''' written with accents nor lower-case letters; this is known as {{w|scriptio continua}}. [[Category:Ancient Greek Language]] m90hzmwfgysynm8jtl39dbkqrkyngfc 0 29223 2823814 2241851 2026-08-21T04:29:05Z It-is-Truly-Meet 3089598 /* Present Indicative tense */ 2823814 wikitext text/x-wiki == Present Indicative, Active, Middle-Passive == <br /> === Active, Middle, and Passive Voice === <br /> === Indicative Mood === <br /> === Present Indicative tense === The ''athematic'' suffixes are: {| class="wikitable" border="1" cellspacing="0" cellpadding="5" | | |'''Active''' |'''Middle-Passive''' |- |'''Singular''' |'''1st Person''' | -μι | -μαι |- | |'''2nd Person''' | -ς | -σαι |- | |'''3rd Person''' | -σι(ν) | -ται |- |'''Plural''' |'''1st Person''' | -μεν | -μεθα |- | |'''2nd Person''' | -τε | -σθε |- | |'''3rd Person''' | -ασι(ν) | -νται |- |'''Infinitive''' | | -ναι | -σθαι |} The ''thematic'' suffixes are: {| class="wikitable" border="1" cellspacing="0" cellpadding="5" | | |'''Active''' |'''Middle-Passive''' |- |'''Singular''' |'''1st Person''' | -ω | -ομαι |- | |'''2nd Person''' | -εις | -ει |- | |'''3rd Person''' | -ει | -εται |- |'''Plural''' |'''1st Person''' | -ομεν | -ομεθα |- | |'''2nd Person''' | -ετε | -εσθε |- | |'''3rd Person''' | -ουσι(ν) | -ονται |- |'''Infinitive''' | | -ειν | -εσθαι |} Λύω ("to release, free"), one of the simplest verbs in Ancient Greek, is often used in charts for all tenses. {| class="wikitable" cellspacing="2" boarder="1" padding="5" |'''Greek''' |'''Pronunciation''' |- |λύω |lew-'''oh''' |- |λύεις |lew-'''eys''' |- |λύει |lew-'''ey''' |- |λύομεν |lew-'''omen''' |- |λύετε |lew-'''ete''' |- |λύουσι(ν) |lew-'''oosee'''('''n''') |} The bolded syllables indicate that, when speaking, the pitch is raised. Notice that the 3rd plural adds a 'ν'; this is known as a "'''moveable-nu''', and it is used when the verb is followed by a word that begins with a vowel or when it is the last word of a sentence. ===Translation=== In English, we have a number of ways to express actions in the present. E.g., I run, I am running, I do run. Greek does not make that distinction, so a perfectly acceptable translation for λύω can be either "I release" or "I am releasing." Another simple verb is γράφω ("to write"): * γράφω * γράφεις * γράφει * γράφομεν * γράφετε * γράφουσι(ν) [[Category:Lessons]] [[el:Κλίσεις ρημάτων/Αρχαία Ελληνικά/Οριστική Ενεργητικής/Ενεστώτας]] r1hznbnfto16iojafjg9hggs81plrbg 0 60198 2823729 2820349 2026-08-20T21:07:46Z ~2026-45454-05 3108747 /* Activities */ 2823729 wikitext text/x-wiki {{:{{BASEPAGENAME}}/Sidebar}} '''Typing''' is the process of entering or inputting text by pressing keys on a typewriter, computer keyboard, mobile phone, or calculator.<ref>[[Wikipedia: Typing]]</ref> Learners should practice typing for fifteen minutes each day until their typing speed is at least 30 words per minute. == Multimedia == * [https://www.typing.com/student/lessons Typing.com: Learn to Type] * [https://monkeytype.com/ Monkeytype] == Activities == * Complete the [https://www.typing.com/student/lessons Typing.com lessons.] * Use [https://monkeytypehub.com/ Monkeytypehub.com] , and practice typing daily until you can reach 30 words per minute consistently. == See Also == * [[Elementary Typing]] * [[Introduction_to_Computers/Input_Devices |Input Devices]] * [[Wikipedia: Typing]] == References == {{reflist}} {{subpage navbar}} {{CourseCat}} [[Category:Computer Skills]] [[Category:Typing]] [[Category:Completed resources]] ja8xx3araiwj6qgtcdgpikhv09y2yxk 14 78763 2823845 2817087 2026-08-21T08:49:36Z Digitalbrainstech 3108822 Digital Brains Tech is a trusted Digital Marketing company aiming to build a strong brand equity and business online. 2823845 wikitext text/x-wiki {{Main|Main Page}}A trusted [https://digitalbrainstech.com/ digital marketing company] aiming to build a strong brand equity and business online. We work to take your business to another level by using unique marketing strategies like PPC Campaign, SEO Services, Local SEO & Guest Posting. We envision turning your every internet-related action into the most profitable one. From conducting in-depth competitive analysis to curating outcome-based online marketing strategies, we do it all. [[Category:Wikiversity administration]] mux4cem1qm7oh9cbccut1y843kpujpn 2823847 2823845 2026-08-21T09:27:08Z Atcovi 276019 Reverted edit by [[Special:Contributions/Digitalbrainstech|Digitalbrainstech]] ([[User_talk:Digitalbrainstech|talk]]) to last version by [[User:Jtneill|Jtneill]] using [[Wikiversity:Rollback|rollback]] 2817087 wikitext text/x-wiki {{Main|Main Page}} [[Category:Wikiversity administration]] l3v254s0n9xxhozyr8m8zxqgl3ggyp4 0 98602 2823811 2818809 2026-08-21T04:27:00Z Jtneill 10242 2823811 wikitext text/x-wiki {{Motivation and emotion/Lectures|Lecture 3: Brain and physiological needs|third}} {{Motivation and emotion/Lectures/In development}} <!-- {{Motivation and emotion/Lectures/In development}} --> <!-- {{Motivation and emotion/Lectures/Complete}} --> ==Overview== [[File:WP20Symbols brain.svg|right|250px]] This lecture: * explains the role of [[Motivation and emotion/Brain structures|brain structures]], [[Motivation and emotion/Neurotransmitters|neurotransmitters]], and [[Motivation and emotion/Hormones|hormones]] in regulating motivational drives * discusses physiological needs, particularly thirst, hunger, and sexual motivation Take-home messages: * The brain is as much about motivation and emotion as it is about cognition and thinking * Biological urges are underestimated motivational forces when we are not currently experiencing them ==Outline== [[File:Hunger strike - Day 53.JPG|thumb|right|250px|Physiological needs such as breathing, drinking, urinating, eating, defecating, and sleeping are often overlooked as motivational forces until they range outside of [[w:Homeostasis|homeostasis]] and then become increasingly urgemt amd motivationally demanding. It takes extreme motivation, for example, to go on an extended hunger strike.]] ;Motivated and emotional brain * Neuroscience * Brain structures * Subcortical ** Reticular formation ** Amygdala **Reward centre **Basal ganglia **Hypothalamus * Cortical ** Insula ** Prefrontal cortex ** Orbitofrontal cortex ** Ventromedial PFC ** Dorsolateral PFC ** Anterior cingulate cortex * Bidirectional ** Neurotransmitters ** Dopamine ** Serotonin ** Norepinephrine ** Endorphins *Hormones ** Cortisol ** Oxytocin ** Testosterone ** Ghrelin (Part B) ** Leptin (Part B) ;Physiological needs * Needs * Regulatory processes * Example physiological needs ** Thirst ** Hunger ** Sexual motivation ==Focus== This lecture highlights specific brain structures and communication pathways that psychological science has identified as contributing to the subjective experience of various motivational and emotional states. ==3D brain model== * Learn about the location and function of key brain structures using [https://www.brainfacts.org/3d-brain 3d brain] (brainfacts.org) * This 3D, interactive model of the human brain shows the main structures and explains their functions. * Task: Can you find each of the brain structures mentioned in this lecture in the 3D model? ==Readings== * Chapter 3: The motivated and emotional brain ([[Motivation and emotion/Readings/Textbooks/Reeve/2024|Reeve, 2024]]) * Chapter 4: Biological needs ([[Motivation and emotion/Readings/Textbooks/Reeve/2024|Reeve, 2024]]) ==Slides== * [https://docs.google.com/presentation/d/1oI8g-0xvSxETUwYOW1TLsRJdiSq3AbVq6YMlm8D3ivc/edit?usp=sharing Motivated and emotional brain] (Google Slides) * [https://docs.google.com/presentation/d/1LgYQ9ydIaj5AJZEW7MkH1M2zVKxjWQe4vetZnOairQE/edit?usp=sharing Physiological needs] (Google Slides) <!-- ** [https://www.slideshare.net/jtneill/motivated-and-emotional-brain Motivated and emotional brain] (Slideshare) ** [https://www.slideshare.net/jtneill/physiological-needs Physiological needs] (Slideshare) --> <!-- * [http://www.slideshare.net/jtneill/brain-and-physiological-needs Lecture slides] (Slideshare) * Handouts ** [[Media:Brain and physiological needs 6 slides per page.pdf|Download 6 slides to a page]]: [[File:Brain and physiological needs 6 slides per page.pdf|100px]] ** [[Media:Brain and physiological needs 3 slides per page.pdf|Download 3 slides to a page]]:[[File:Brain and physiological needs 3 slides per page.pdf|100px]] --> ==See also== ;Wikiversity * [[/Images/]] * [[Motivation and emotion/Brain structures|Brain structures]] * [[Motivation and emotion/Hormones|Hormones]] * [[Motivation and emotion/Neurotransmitters|Neurotransmitters]] * Book chapters ** [[:Category:Motivation and emotion/Book/Brain|Brain]] (Category) ** [[:Category:Motivation and emotion/Book/Hormones|Hormones]] (Category) ** [[:Category:Motivation and emotion/Book/Neurotransmitters|Neurotransmitters]] (Category) ** [[:Category:Motivation and emotion/Book/Needs/Physiological|Physiological needs]] (Category)<!-- [[Motivation and emotion/Book/2025/Thirst regulation|Thirst regulation]] --> ;Wikipedia * [[w:Autonomic nervous system|Autonomic nervous system]] * [[w:ERG theory|ERG theory]] * [[w:Limbic system|Limbic system]] * [[w:Maslow's hierarchy of needs|Maslow's hierarchy of needs]] * [[w:Nucleus (neuroanatomy)|Nucleus (neuroanatomy)]] * [[w:Parasympathetic nervous system|Parasympathetic nervous system]] * [[w:Prefrontal cortex|Prefrontal cortex]] * [[w:Reward system|Reward system]] * [[w:Sympathetic nervous system|Sympathetic nervous system]] ;Lectures * [[{{#titleparts:{{PAGENAME}}|2}}/Historical development and assessment skills|Historical development and assessment skills]] (Previous lecture) * [[{{#titleparts:{{PAGENAME}}|2}}/Extrinsic motivation and psychological needs|Extrinsic motivation and psychological needs]] (Next lecture) ;Tutorials * [[Motivation and emotion/Tutorials/Physiological needs|Physiological needs]] <!-- ==References== {{Hanging indent|1= Australian Bureau of Statistics (2013). [http://www.abs.gov.au/ausstats/abs@.nsf/Lookup/by%20Subject/4338.0~2011-13~Main%20Features~Overweight%20and%20obesity~10007 Overweight and obesity]. ''4338.0 - Profiles of Health, Australia, 2011-13''. Eder, A. B., Elliot, A. J., & Harmon-Jones, E. (2013). [http://emr.sagepub.com/content/5/3/227 Approach and avoidance motivation: Issues and advances]. ''Emotion Review'', ''5''(3), 308-311. https://doi.org/10.1177/1754073913477990.}} --> ==Recording== * [https://au-lti.bbcollab.com/recording/54f3cdb5b30a476fbcbb77824a1b9dfb Lecture 3] (2025)<!-- * [https://au-lti.bbcollab.com/recording/b8834e9830314aa3b804d3c6c3e7a740 Lecture 3] (2024) * [https://au-lti.bbcollab.com/recording/546476bf547f4efd8ae55b05e4547efc Lecture 3] (2023) * [https://au-lti.bbcollab.com/recording/17f200f050e044da9a6571ffdf63c78c Lecture 3] (2022) * [https://au-lti.bbcollab.com/recording/d34da988d75c48b99df662329594cc9f Lecture 3] (2021) --> ==References== {{Hanging indent|1= Saper, C. B., & Lowell, B. B. (2014). The hypothalamus. ''Current Biology'', ''24''(23), R1111–R1116. https://doi.org/10.1016/j.cub.2014.10.023 }} ==External links== * [https://fs.blog/knowledge-project-podcast/anna-lembke/ Between pleasure and pain] (Dr. Anna Lembke, The Knowledge Project Ep. #159) * [https://www.iheart.com/podcast/105-stuff-you-should-know-26940277/episode/short-stuff-hangry-102038598/ Hangry] (Stuff You Should Know, Podcast, 12:30 mins) * [https://www.youtube.com/watch?v=tZ4YnYUJnOQ&list=PL9JAHwJN4qyArhEyLUgU_MoGddk2PVTeb Hormones of hunger: Leptin and ghrelin] (Corporis, 2019, YouTube, 9:33 mins) - how leptin and ghrelin work together to modulate hunger<!-- As you watch the video, consider: What causes hunger and eating? --> * [https://www.ted.com/playlists/1/how_does_my_brain_work How does my brain work?] (TED Talks playlist) * [https://www.youtube.com/watch?v=Qymp_VaFo9M Let's talk about sex] (Crash Course Psychology #27; YouTube 11:35 mins) * [https://www.ted.com/talks/david_anderson_your_brain_is_more_than_a_bag_of_chemicals Your brain is more than a bag of chemicals] (David Anderson, 2013, TED talk, 16 mins) - neuroscientific research into motivation and emotion using a basic animal model (fruit fly)<!-- As you watch the video, some questions to think about: 1. Do animals experience emotions? If so, which emotions - and why? 2. What might pharmacological treatment of psychological disorders look like in 20, 50, 100 years? --> {{Motivation and emotion/Lectures/Navigation}} [[Category:Motivation and emotion/Lectures/Brain and physiological needs]] h67xa0vi13vl88wwb4t9iczyq14gdb9 2823828 2823811 2026-08-21T04:50:27Z Jtneill 10242 2823828 wikitext text/x-wiki {{Motivation and emotion/Lectures|Lecture 3: Brain and physiological needs|third}} {{Motivation and emotion/Lectures/In development}} <!-- {{Motivation and emotion/Lectures/In development}} --> <!-- {{Motivation and emotion/Lectures/Complete}} --> ==Overview== [[File:WP20Symbols brain.svg|right|250px]] This lecture: * highlights specific [[Motivation and emotion/Brain structures|brain structures]] and communication pathways involving [[Motivation and emotion/Neurotransmitters|neurotransmitters]] and [[Motivation and emotion/Hormones|hormones]] that psychological science has identified as contributing to the subjective experience of various motivational and emotional states * discusses physiological needs, particularly thirst, hunger, and sexual motivation Take-home messages: * The brain is as much about motivation and emotion as it is about cognition and thinking * Biological urges are underestimated motivational forces when we are not currently experiencing them ==Outline== [[File:Hunger strike - Day 53.JPG|thumb|right|250px|Physiological needs such as breathing, drinking, urinating, eating, defecating, and sleeping are often overlooked as motivational forces until they range outside of [[w:Homeostasis|homeostasis]] and then become increasingly urgemt amd motivationally demanding. It takes extreme motivation, for example, to go on an extended hunger strike.]] ;Motivated and emotional brain * Neuroscience * Brain structures * Subcortical ** Reticular formation ** Amygdala **Reward centre **Basal ganglia **Hypothalamus * Cortical ** Insula ** Prefrontal cortex ** Orbitofrontal cortex ** Ventromedial PFC ** Dorsolateral PFC ** Anterior cingulate cortex * Bidirectional ** Neurotransmitters ** Dopamine ** Serotonin ** Norepinephrine ** Endorphins *Hormones ** Cortisol ** Oxytocin ** Testosterone ** Ghrelin (Part B) ** Leptin (Part B) ;Physiological needs * Needs * Regulatory processes * Example physiological needs ** Thirst ** Hunger ** Sexual motivation ==3D brain model== * Learn about the location and function of key brain structures using [https://www.brainfacts.org/3d-brain 3d brain] (brainfacts.org) * This 3D, interactive model of the human brain shows the main structures and explains their functions. * Task: Can you find each of the brain structures mentioned in this lecture in the 3D model? ==Readings== * Chapter 3: The motivated and emotional brain ([[Motivation and emotion/Readings/Textbooks/Reeve/2024|Reeve, 2024]]) * Chapter 4: Biological needs ([[Motivation and emotion/Readings/Textbooks/Reeve/2024|Reeve, 2024]]) ==Slides== * [https://docs.google.com/presentation/d/1oI8g-0xvSxETUwYOW1TLsRJdiSq3AbVq6YMlm8D3ivc/edit?usp=sharing Motivated and emotional brain] (Google Slides) * [https://docs.google.com/presentation/d/1LgYQ9ydIaj5AJZEW7MkH1M2zVKxjWQe4vetZnOairQE/edit?usp=sharing Physiological needs] (Google Slides) <!-- ** [https://www.slideshare.net/jtneill/motivated-and-emotional-brain Motivated and emotional brain] (Slideshare) ** [https://www.slideshare.net/jtneill/physiological-needs Physiological needs] (Slideshare) --> <!-- * [http://www.slideshare.net/jtneill/brain-and-physiological-needs Lecture slides] (Slideshare) * Handouts ** [[Media:Brain and physiological needs 6 slides per page.pdf|Download 6 slides to a page]]: [[File:Brain and physiological needs 6 slides per page.pdf|100px]] ** [[Media:Brain and physiological needs 3 slides per page.pdf|Download 3 slides to a page]]:[[File:Brain and physiological needs 3 slides per page.pdf|100px]] --> ==See also== ;Wikiversity * [[/Images/]] * [[Motivation and emotion/Brain structures|Brain structures]] * [[Motivation and emotion/Hormones|Hormones]] * [[Motivation and emotion/Neurotransmitters|Neurotransmitters]] * Book chapters ** [[:Category:Motivation and emotion/Book/Brain|Brain]] (Category) ** [[:Category:Motivation and emotion/Book/Hormones|Hormones]] (Category) ** [[:Category:Motivation and emotion/Book/Neurotransmitters|Neurotransmitters]] (Category) ** [[:Category:Motivation and emotion/Book/Needs/Physiological|Physiological needs]] (Category)<!-- [[Motivation and emotion/Book/2025/Thirst regulation|Thirst regulation]] --> ;Wikipedia * [[w:Autonomic nervous system|Autonomic nervous system]] * [[w:ERG theory|ERG theory]] * [[w:Limbic system|Limbic system]] * [[w:Maslow's hierarchy of needs|Maslow's hierarchy of needs]] * [[w:Nucleus (neuroanatomy)|Nucleus (neuroanatomy)]] * [[w:Parasympathetic nervous system|Parasympathetic nervous system]] * [[w:Prefrontal cortex|Prefrontal cortex]] * [[w:Reward system|Reward system]] * [[w:Sympathetic nervous system|Sympathetic nervous system]] ;Lectures * [[{{#titleparts:{{PAGENAME}}|2}}/Historical development and assessment skills|Historical development and assessment skills]] (Previous lecture) * [[{{#titleparts:{{PAGENAME}}|2}}/Extrinsic motivation and psychological needs|Extrinsic motivation and psychological needs]] (Next lecture) ;Tutorials * [[Motivation and emotion/Tutorials/Physiological needs|Physiological needs]] <!-- ==References== {{Hanging indent|1= Australian Bureau of Statistics (2013). [http://www.abs.gov.au/ausstats/abs@.nsf/Lookup/by%20Subject/4338.0~2011-13~Main%20Features~Overweight%20and%20obesity~10007 Overweight and obesity]. ''4338.0 - Profiles of Health, Australia, 2011-13''. Eder, A. B., Elliot, A. J., & Harmon-Jones, E. (2013). [http://emr.sagepub.com/content/5/3/227 Approach and avoidance motivation: Issues and advances]. ''Emotion Review'', ''5''(3), 308-311. https://doi.org/10.1177/1754073913477990.}} --> ==Recording== * [https://au-lti.bbcollab.com/recording/54f3cdb5b30a476fbcbb77824a1b9dfb Lecture 3] (2025)<!-- * [https://au-lti.bbcollab.com/recording/b8834e9830314aa3b804d3c6c3e7a740 Lecture 3] (2024) * [https://au-lti.bbcollab.com/recording/546476bf547f4efd8ae55b05e4547efc Lecture 3] (2023) * [https://au-lti.bbcollab.com/recording/17f200f050e044da9a6571ffdf63c78c Lecture 3] (2022) * [https://au-lti.bbcollab.com/recording/d34da988d75c48b99df662329594cc9f Lecture 3] (2021) --> ==References== {{Hanging indent|1= Saper, C. B., & Lowell, B. B. (2014). The hypothalamus. ''Current Biology'', ''24''(23), R1111–R1116. https://doi.org/10.1016/j.cub.2014.10.023 }} ==External links== * [https://fs.blog/knowledge-project-podcast/anna-lembke/ Between pleasure and pain] (Dr. Anna Lembke, The Knowledge Project Ep. #159) * [https://www.iheart.com/podcast/105-stuff-you-should-know-26940277/episode/short-stuff-hangry-102038598/ Hangry] (Stuff You Should Know, Podcast, 12:30 mins) * [https://www.youtube.com/watch?v=tZ4YnYUJnOQ&list=PL9JAHwJN4qyArhEyLUgU_MoGddk2PVTeb Hormones of hunger: Leptin and ghrelin] (Corporis, 2019, YouTube, 9:33 mins) - how leptin and ghrelin work together to modulate hunger<!-- As you watch the video, consider: What causes hunger and eating? --> * [https://www.ted.com/playlists/1/how_does_my_brain_work How does my brain work?] (TED Talks playlist) * [https://www.youtube.com/watch?v=Qymp_VaFo9M Let's talk about sex] (Crash Course Psychology #27; YouTube 11:35 mins) * [https://www.ted.com/talks/david_anderson_your_brain_is_more_than_a_bag_of_chemicals Your brain is more than a bag of chemicals] (David Anderson, 2013, TED talk, 16 mins) - neuroscientific research into motivation and emotion using a basic animal model (fruit fly)<!-- As you watch the video, some questions to think about: 1. Do animals experience emotions? If so, which emotions - and why? 2. What might pharmacological treatment of psychological disorders look like in 20, 50, 100 years? --> {{Motivation and emotion/Lectures/Navigation}} [[Category:Motivation and emotion/Lectures/Brain and physiological needs]] 16ftdfyohhcjjc5850xpzshp251bjgs 10 98655 2823812 2817167 2026-08-21T04:28:17Z Jtneill 10242 2823812 wikitext text/x-wiki <noinclude>{{center top}}{{tl|Motivation and emotion/Lectures/Navigation}}{{center bottom}}</noinclude> {{Navbox | name = Motivation and emotion/Lectures/Navigation | title = [[Motivation and emotion/Lectures|Lectures]] | list1 = <div> [[Motivation and emotion/Lectures/Introduction|1 Intro]] <nowiki>|</nowiki> [[Motivation and emotion/Lectures/Historical development and assessment skills|2 History & assessment]] <nowiki>|</nowiki> [[Motivation and emotion/Lectures/Brain and physiological needs|3 Brain & phys needs]] <nowiki>|</nowiki> [[Motivation and emotion/Lectures/Extrinsic motivation and psychological needs|4 Extrinsic motiv & psych needs]] <nowiki>|</nowiki> [[Motivation and emotion/Lectures/Goals and mindsets|5 Goals and mindsets]] <nowiki>|</nowiki> [[Motivation and emotion/Lectures/Personal control and the self|6 Personal control & the self]] <nowiki>|</nowiki> [[Motivation and emotion/Lectures/Nature of emotion|7 Nature of emotion]] <nowiki>|</nowiki> [[Motivation and emotion/Lectures/Aspects of emotion|8 Aspects of emotion]] <nowiki>|</nowiki> [[Motivation and emotion/Lectures/Individual emotions|9 Individual emotions]] <nowiki>|</nowiki> [[Motivation and emotion/Lectures/Unconscious motivation|10 Unconscious motivation]] <nowiki>|</nowiki> [[Motivation and emotion/Lectures/Growth psychology|11 Growth psych]] <nowiki>|</nowiki> [[Motivation and emotion/Lectures/Interventions and review|12 Interventions & review]] </div> }}<noinclude> [[Category:Motivation and emotion/Lectures]] [[Category:Motivation and emotion/Templates]] </noinclude> irym9n6ej32sgzvuca2u2xoz80toppw 0 139384 2823649 2823144 2026-08-20T13:55:25Z Young1lim 21186 /* Adder */ 2823649 wikitext text/x-wiki == Adder == * Binary Adder Architecture Exploration ( [[Media:Adder.20131113.pdf|pdf]] ) {| class="wikitable" |- ! Adder type !! Overview !! Analysis !! VHDL Level Design !! CMOS Level Design |- | '''1. Ripple Carry Adder''' || [[Media:VLSI.Arith.1A.RCA.20250522.pdf|A]]|| || [[Media:Adder.rca.20140313.pdf|pdf]] || [[Media:VLSI.Arith.1D.RCA.CMOS.20211108.pdf|pdf]] |- | '''2. Carry Lookahead Adder''' || [[Media:VLSI.Arith.2A.CLA.20260722.pdf|A]], [[Media:VLSI.Arith.2B.CLA.20260820.pdf|B]], [[Media:VLSI.Arith.2C.CLA.20260820.pdf|C]], [[Media:VLSI.Arith.2D.CLA.20260720.pdf|D]] || || [[Media:Adder.cla.20140313.pdf|pdf]]|| |- | '''3. Carry Save Adder''' || [[Media:VLSI.Arith.1.A.CSave.20151209.pdf|A]]|| || || |- || '''4. Carry Select Adder''' || [[Media:VLSI.Arith.1.A.CSelA.20191002.pdf|A]]|| || || |- || '''5. Carry Skip Adder''' || [[Media:VLSI.Arith.5A.CSkip.20250405.pdf|A]]|| || || [[Media:VLSI.Arith.5D.CSkip.CMOS.20211108.pdf|pdf]] |- || '''6. Carry Chain Adder''' || [[Media:VLSI.Arith.6A.CCA.20211109.pdf|A]]|| || [[Media:VLSI.Arith.6C.CCA.VHDL.20211109.pdf|pdf]], [[Media:Adder.cca.20140313.pdf|pdf]] || [[Media:VLSI.Arith.6D.CCA.CMOS.20211109.pdf|pdf]] |- || '''7. Kogge-Stone Adder''' || [[Media:VLSI.Arith.1.A.KSA.20140315.pdf|A]]|| || [[Media:Adder.ksa.20140409.pdf|pdf]]|| |- || '''8. Prefix Adder''' || [[Media:VLSI.Arith.1.A.PFA.20140314.pdf|A]]|| || || |- || '''9.1 Variable Block Adder''' || [[Media:VLSI.Arith.1A.VBA.20221110.pdf|A]], [[Media:VLSI.Arith.1B.VBA.20230911.pdf|B]], [[Media:VLSI.Arith.1C.VBA.20240622.pdf|C]], [[Media:VLSI.Arith.1C.VBA.20250218.pdf|D]]|| || || |- || '''9.2 Multi-Level Variable Block Adder''' || [[Media:VLSI.Arith.1.A.VBA-Multi.20221031.pdf|A]]|| || || |} </br> === Adder Architectures Suitable for FPGA === * FPGA Carry-Chain Adder ([[Media:VLSI.Arith.1.A.FPGA-CCA.20210421.pdf|pdf]]) * FPGA Carry Select Adder ([[Media:VLSI.Arith.1.B.FPGA-CarrySelect.20210522.pdf|pdf]]) * FPGA Variable Block Adder ([[Media:VLSI.Arith.1.C.FPGA-VariableBlock.20220125.pdf|pdf]]) * FPGA Carry Lookahead Adder ([[Media:VLSI.Arith.1.D.FPGA-CLookahead.20210304.pdf|pdf]]) * Carry-Skip Adder </br> == Barrel Shifter == * Barrel Shifter Architecture Exploration ([[Media:Bshift.20131105.pdf|bshfit.vhdl]], [[Media:Bshift.makefile.20131109.pdf|bshfit.makefile]]) </br> '''Mux Based Barrel Shifter''' * Analysis ([[Media:Arith.BShfiter.20151207.pdf|pdf]]) * Implementation </br> == Multiplier == === Array Multipliers === * Analysis ([[Media:VLSI.Arith.1.A.Mult.20151209.pdf|pdf]]) </br> === Tree Mulltipliers === * Lattice Multiplication ([[Media:VLSI.Arith.LatticeMult.20170204.pdf|pdf]]) * Wallace Tree ([[Media:VLSI.Arith.WallaceTree.20170204.pdf|pdf]]) * Dadda Tree ([[Media:VLSI.Arith.DaddaTree.20170701.pdf|pdf]]) </br> === Booth Multipliers === * [[Media:RNS4.BoothEncode.20161005.pdf|Booth Encoding Note]] * Booth Multiplier Note ([[Media:BoothMult.20160929.pdf|H1.pdf]]) </br> == Divider == * Binary Divider ([[Media:VLSI.Arith.1.A.Divider.20131217.pdf|pdf]])</br> </br> </br> go to [ [[Electrical_%26_Computer_Engineering_Studies]] ] [[Category:Digital Circuit Design]] [[Category:FPGA]] lc2s3f2hu35gn20e65uf3hjdffw2lh1 10 148360 2823841 2822249 2026-08-21T06:21:45Z Jtneill 10242 Revise 2823841 wikitext text/x-wiki <noinclude> {{:Motivation and emotion/Assessment/Topic/Quickstarttip}} <hr> </noinclude>{{title|Title goes here:<br>Subtitle goes here?}} <div align=center>Edit the wording (and [[w:Stylistic or specialised usage|casing]]) above so that it matches the [[Motivation and emotion/Book/Current|topic list]].<br>[[Motivation and emotion/About/Staff|Seek approval]] for any changes.<br>Do not add your name; authorship is recorded in the [[Special:History/{{PAGENAME}}|page history]]).</div> __TOC__ ==Overview== {{RoundBoxTop|theme=3}} [[File:A picture is worth a thousand words.jpg|right|thumb|150px|'''Figure 1'''. Use a captioned image to illustrate the scenario]] ; Imagine this ... or Scenario ... or Case study or ... ?) Start with an engaging [[#Scenarios|scenario, example, or case study]] which illustrates the problem and engages reader interest. Present the scenario in a [[#Feature box|feature box]]. To change the box colour: # Edit source # Change "theme=3" to another number Include an image and cite it (e.g., see Figure 1). {{RoundBoxBottom}} The Overview section should provide: # '''Scenario''': A short, engaging case study or real-world example in a feature box, with an accompanying image (see above) # '''Explanation of the problem, issue, or topc''': Briefly explain the problem, why it is important, and outline how psychological science can help # '''Focus questions''': Unpack the sub-title into focus questions in a feature box Recommended length: 180 to 330 words. This template provides key headings, examples, and tips for each section. Gradually remove this generic information as the chapter develops. It is OK to retain some template material for the topic development, but it should all be removed from the book chapter. Key resources: * [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] explains how to edit * [[Motivation and emotion/Assessment/Topic|Topic development guidelines]] * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] {{RoundBoxTop|theme=3}} '''Focus questions''' Break the sub-title down into three to five [[Motivation and emotion/Assessment/Chapter/Focus questions|focus questions]]. Align the top-level headings with these focus questions. * What is the first focus question? * What is the second focus question? * What is the third focus question? Ask [[w:Open-ended question|open-ended]] questions. For example: {{cross}} Is there a relationship between weather and criminal behaviour? (closed-ended)<br>{{tick}} What is the relationship between weather and criminal behaviour? (open-ended) {{RoundBoxBottom}} ==Headings== Use this heading structure: * [[#Overview|Overview]] * 3 to 6 major headings tailored to the topic; can have sub-headings: ** avoid sections with only one sub-heading (use 0 or 2+ sub-headings) ** provide an introductory paragraph before breaking into sub-sections * [[#Conclusion|Conclusion]] * [[#See also|See also]] * [[#References|References]] * [[#External links|External links]] ==Key points== * For the topic development, provide at least three bullet-points for each heading and sub-heading, including the Overview and Conclusion * Include key citations ==Figures== [[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]] * For the book chapter, use several figures to illustrate concepts, add interest, and to serve as examples * For the topic development, use at least one figure (even if not ideal) to show that you know how to embed, caption, and cite a figure * Figures can show any kind of media such as photos, diagrams, graphs, video, audio, and so on * Embed figures throughout the chapter, starting with the scenario in the Overview section * Provide descriptive figure captions (use '''Figure #''' and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== Learning features help to bring book chapters to life and can be embedded throughout the chapter. Here are some options: {{anchor|Scenarios}} ;Scenarios * Scenarios, case studies, or examples that illustrate concepts in action * Present using [[#Feature boxes|feature boxes]]; can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Can be real or fictional; if real, provide citation(s) {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted '''Table 1''' A Descriptive Caption Explains The Table Contents and its Relevance to the Text e.g., The 2 x 2 Johari Window Model Showing the Relationship Between Known/Unknown and Self/Other {| class="wikitable" style="margin: auto; |- ! !! Known to self !! Not known to self |- | '''Known to others''' || Open area || Blind spot |- | '''Not known to others''' || Hidden area || Unknown |} ;Quizzes * One or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as the take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] Example simple quiz questions. Choose your answers and click "Submit": <quiz display=simple> {The purpose of quizzes is to provide an interactive learning feature: |type="()"} + True - False {Long and complex quiz questions are recommended: |type="()"} - True + False </quiz> ==Conclusion== * Arguably the most important section * Provide at least three bullet-points for this section even at the topic development stage, based on preliminary thinking * For the book chapter, develop clear take-home message(s) that address the focus questions based on psychological theory and research * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing this problem * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== [[Help:Contents/Links#Interwiki_links|Internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) * [[w:Self determination theory|Self determination theory]] (Wikipedia) {{tip|Suggestions for this section: * Link to the most relevant internal resources about the topic * Include the source in parentheses }} ==References== Provide the references for all citations in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. Alternatively, you can use wiki style (as used on Wikipedia), as long as the information is complete and the formatting is consistent. APA style example: {{Hanging indent|1= Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091 Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper & Row. }} {{tip|Suggestions for this section: * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) ** Hanging indent: Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: *** Use "Edit source" *** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== [[Help:Contents/Links#External_links|External links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Link to the most relevant external resources about the topic * Include the source in parentheses after the link }}<includeonly> [[Category:{{#titleparts:{{PAGENAME}}|3}}]]</includeonly><noinclude> [[Category:Motivation and emotion/Book]]</noinclude> qp3esak2f81xivhrpcpp4g8ldt5key8 2823843 2823841 2026-08-21T06:22:20Z Jtneill 10242 2823843 wikitext text/x-wiki <noinclude> {{:Motivation and emotion/Assessment/Topic/Quickstarttip}} <hr> </noinclude>{{title|Title goes here:<br>Subtitle goes here?}} <div align=center>Edit the wording (and [[w:Stylistic or specialised usage|casing]]) above so that it matches the [[Motivation and emotion/Book/Current|topic list]].<br>[[Motivation and emotion/About/Staff|Seek approval]] for any changes.<br>Do not add your name; authorship is shown in the [[Special:History/{{PAGENAME}}|page history]].</div> __TOC__ ==Overview== {{RoundBoxTop|theme=3}} [[File:A picture is worth a thousand words.jpg|right|thumb|150px|'''Figure 1'''. Use a captioned image to illustrate the scenario]] ; Imagine this ... or Scenario ... or Case study or ... ?) Start with an engaging [[#Scenarios|scenario, example, or case study]] which illustrates the problem and engages reader interest. Present the scenario in a [[#Feature box|feature box]]. To change the box colour: # Edit source # Change "theme=3" to another number Include an image and cite it (e.g., see Figure 1). {{RoundBoxBottom}} The Overview section should provide: # '''Scenario''': A short, engaging case study or real-world example in a feature box, with an accompanying image (see above) # '''Explanation of the problem, issue, or topc''': Briefly explain the problem, why it is important, and outline how psychological science can help # '''Focus questions''': Unpack the sub-title into focus questions in a feature box Recommended length: 180 to 330 words. This template provides key headings, examples, and tips for each section. Gradually remove this generic information as the chapter develops. It is OK to retain some template material for the topic development, but it should all be removed from the book chapter. Key resources: * [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] explains how to edit * [[Motivation and emotion/Assessment/Topic|Topic development guidelines]] * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] {{RoundBoxTop|theme=3}} '''Focus questions''' Break the sub-title down into three to five [[Motivation and emotion/Assessment/Chapter/Focus questions|focus questions]]. Align the top-level headings with these focus questions. * What is the first focus question? * What is the second focus question? * What is the third focus question? Ask [[w:Open-ended question|open-ended]] questions. For example: {{cross}} Is there a relationship between weather and criminal behaviour? (closed-ended)<br>{{tick}} What is the relationship between weather and criminal behaviour? (open-ended) {{RoundBoxBottom}} ==Headings== Use this heading structure: * [[#Overview|Overview]] * 3 to 6 major headings tailored to the topic; can have sub-headings: ** avoid sections with only one sub-heading (use 0 or 2+ sub-headings) ** provide an introductory paragraph before breaking into sub-sections * [[#Conclusion|Conclusion]] * [[#See also|See also]] * [[#References|References]] * [[#External links|External links]] ==Key points== * For the topic development, provide at least three bullet-points for each heading and sub-heading, including the Overview and Conclusion * Include key citations ==Figures== [[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]] * For the book chapter, use several figures to illustrate concepts, add interest, and to serve as examples * For the topic development, use at least one figure (even if not ideal) to show that you know how to embed, caption, and cite a figure * Figures can show any kind of media such as photos, diagrams, graphs, video, audio, and so on * Embed figures throughout the chapter, starting with the scenario in the Overview section * Provide descriptive figure captions (use '''Figure #''' and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== Learning features help to bring book chapters to life and can be embedded throughout the chapter. Here are some options: {{anchor|Scenarios}} ;Scenarios * Scenarios, case studies, or examples that illustrate concepts in action * Present using [[#Feature boxes|feature boxes]]; can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Can be real or fictional; if real, provide citation(s) {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted '''Table 1''' A Descriptive Caption Explains The Table Contents and its Relevance to the Text e.g., The 2 x 2 Johari Window Model Showing the Relationship Between Known/Unknown and Self/Other {| class="wikitable" style="margin: auto; |- ! !! Known to self !! Not known to self |- | '''Known to others''' || Open area || Blind spot |- | '''Not known to others''' || Hidden area || Unknown |} ;Quizzes * One or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as the take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] Example simple quiz questions. Choose your answers and click "Submit": <quiz display=simple> {The purpose of quizzes is to provide an interactive learning feature: |type="()"} + True - False {Long and complex quiz questions are recommended: |type="()"} - True + False </quiz> ==Conclusion== * Arguably the most important section * Provide at least three bullet-points for this section even at the topic development stage, based on preliminary thinking * For the book chapter, develop clear take-home message(s) that address the focus questions based on psychological theory and research * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing this problem * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== [[Help:Contents/Links#Interwiki_links|Internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) * [[w:Self determination theory|Self determination theory]] (Wikipedia) {{tip|Suggestions for this section: * Link to the most relevant internal resources about the topic * Include the source in parentheses }} ==References== Provide the references for all citations in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. Alternatively, you can use wiki style (as used on Wikipedia), as long as the information is complete and the formatting is consistent. APA style example: {{Hanging indent|1= Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091 Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper & Row. }} {{tip|Suggestions for this section: * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) ** Hanging indent: Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: *** Use "Edit source" *** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== [[Help:Contents/Links#External_links|External links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Link to the most relevant external resources about the topic * Include the source in parentheses after the link }}<includeonly> [[Category:{{#titleparts:{{PAGENAME}}|3}}]]</includeonly><noinclude> [[Category:Motivation and emotion/Book]]</noinclude> 2h3e2oeao2x08n2obs5zatjfcu79qn2 0 171005 2823656 2823150 2026-08-20T14:25:30Z Young1lim 21186 /* Geometric Series Examples */ 2823656 wikitext text/x-wiki Many of the functions that arise naturally in mathematics and real world applications can be extended to and regarded as complex functions, meaning the input, as well as the output, can be complex numbers <math>x+iy</math>, where <math>i=\sqrt{-1}</math>, in such a way that it is a more natural object to study. '''Complex analysis''', which used to be known as '''function theory''' or '''theory of functions of a single complex variable''', is a sub-field of analysis that studies such functions (more specifically, '''holomorphic''' functions) on the complex plane, or part (domain) or extension (Riemann surface) thereof. It notably has great importance in number theory, e.g. the [[Riemann zeta function]] (for the distribution of primes) and other <math>L</math>-functions, modular forms, elliptic functions, etc. <blockquote>The shortest path between two truths in the real domain passes through the complex domain. — [[wikipedia:Jacques_Hadamard|Jacques Hadamard]]</blockquote>In a certain sense, the essence of complex functions is captured by the principle of [[analytic continuation]].{{mathematics}} ==''' Complex Functions '''== * Complex Functions ([[Media:CAnal.1.A.CFunction.20140222.Basic.pdf|1.A.pdf]], [[Media:CAnal.1.B.CFunction.20140111.Octave.pdf|1.B.pdf]], [[Media:CAnal.1.C.CFunction.20140111.Extend.pdf|1.C.pdf]]) * Complex Exponential and Logarithm ([[Media:CAnal.5.A.CLog.20131017.pdf|5.A.pdf]], [[Media:CAnal.5.A.Octave.pdf|5.B.pdf]]) * Complex Trigonometric and Hyperbolic ([[Media:CAnal.7.A.CTrigHyper..pdf|7.A.pdf]], [[Media:CAnal.7.A.Octave..pdf|7.B.pdf]]) '''Complex Function Note''' : 1. Exp and Log Function Note ([[Media:ComplexExp.29160721.pdf|H1.pdf]]) : 2. Trig and TrigH Function Note ([[Media:CAnal.Trig-H.29160901.pdf|H1.pdf]]) : 3. Inverse Trig and TrigH Functions Note ([[Media:CAnal.Hyper.29160829.pdf|H1.pdf]]) ==''' Complex Integrals '''== * Complex Integrals ([[Media:CAnal.2.A.CIntegral.20140224.Basic.pdf|2.A.pdf]], [[Media:CAnal.2.B.CIntegral.20140117.Octave.pdf|2.B.pdf]], [[Media:CAnal.2.C.CIntegral.20140117.Extend.pdf|2.C.pdf]]) ==''' Complex Series '''== * Complex Series ([[Media:CPX.Series.20150226.2.Basic.pdf|3.A.pdf]], [[Media:CAnal.3.B.CSeries.20140121.Octave.pdf|3.B.pdf]], [[Media:CAnal.3.C.CSeries.20140303.Extend.pdf|3.C.pdf]]) ==''' Residue Integrals '''== * Residue Integrals ([[Media:CAnal.4.A.Residue.20140227.Basic.pdf|4.A.pdf]], [[Media:CAnal.4.B.pdf|4.B.pdf]], [[Media:CAnal.4.C.Residue.20140423.Extend.pdf|4.C.pdf]]) ==='''Residue Integrals Note'''=== * Laurent Series with the Residue Theorem Note ([[Media:Laurent.1.Residue.20170713.pdf|H1.pdf]]) * Laurent Series with Applications Note ([[Media:Laurent.2.Applications.20170327.pdf|H1.pdf]]) * Laurent Series and the z-Transform Note ([[Media:Laurent.3.z-Trans.20170831.pdf|H1.pdf]]) * Laurent Series as a Geometric Series Note ([[Media:Laurent.4.GSeries.20170802.pdf|H1.pdf]]) === Laurent Series and the z-Transform Example Note === * Overview ([[Media:Laurent.4.z-Example.20170926.pdf|H1.pdf]]) ====Geometric Series Examples==== * Causality ([[Media:Laurent.5.Causality.1.A.20191026n.pdf|A.pdf]], [[Media:Laurent.5.Causality.1.B.20191026.pdf|B.pdf]]) * Time Shift ([[Media:Laurent.5.TimeShift.2.A.20191028.pdf|A.pdf]], [[Media:Laurent.5.TimeShift.2.B.20191029.pdf|B.pdf]]) * Reciprocity ([[Media:Laurent.5.Reciprocity.3A.20191030.pdf|A.pdf]], [[Media:Laurent.5.Reciprocity.3B.20191031.pdf|B.pdf]]) * Combinations ([[Media:Laurent.5.Combination.4A.20200702.pdf|A.pdf]], [[Media:Laurent.5.Combination.4B.20201002.pdf|B.pdf]]) * Properties ([[Media:Laurent.5.Property.5A.20220105.pdf|A.pdf]], [[Media:Laurent.5.Property.5B.20220126.pdf|B.pdf]]) * Permutations ([[Media:Laurent.6.Permutation.6A.20230711.pdf|A.pdf]], [[Media:Laurent.5.Permutation.6B.20251225.pdf|B.pdf]], [[Media:Laurent.5.Permutation.6C.20260819.pdf|C.pdf]], [[Media:Laurent.5.Permutation.6C.20240528.pdf|D.pdf]]) * Applications ([[Media:Laurent.5.Application.6B.20220723.pdf|A.pdf]]) * Double Pole Case :- Examples ([[Media:Laurent.5.DPoleEx.7A.20220722.pdf|A.pdf]], [[Media:Laurent.5.DPoleEx.7B.20220720.pdf|B.pdf]]) :- Properties ([[Media:Laurent.5.DPoleProp.5A.20190226.pdf|A.pdf]], [[Media:Laurent.5.DPoleProp.5B.20190228.pdf|B.pdf]]) ====The Case Examples==== * Example Overview : ([[Media:Laurent.4.Example.0.A.20171208.pdf|0A.pdf]], [[Media:Laurent.6.CaseExample.0.B.20180205.pdf|0B.pdf]]) * Example Case 1 : ([[Media:Laurent.4.Example.1.A.20171107.pdf|1A.pdf]], [[Media:Laurent.4.Example.1.B.20171227.pdf|1B.pdf]]) * Example Case 2 : ([[Media:Laurent.4.Example.2.A.20171107.pdf|2A.pdf]], [[Media:Laurent.4.Example.2.B.20171227.pdf|2B.pdf]]) * Example Case 3 : ([[Media:Laurent.4.Example.3.A.20171017.pdf|3A.pdf]], [[Media:Laurent.4.Example.3.B.20171226.pdf|3B.pdf]]) * Example Case 4 : ([[Media:Laurent.4.Example.4.A.20171017.pdf|4A.pdf]], [[Media:Laurent.4.Example.4.B.20171228.pdf|4B.pdf]]) * Example Summary : ([[Media:Laurent.4.Example.5.A.20171212.pdf|5A.pdf]], [[Media:Laurent.4.Example.5.B.20171230.pdf|5B.pdf]]) ==''' Conformal Mapping '''== * Conformal Mapping ([[Media:CAnal.6.A.Conformal.20131224.pdf|6.A.pdf]], [[Media:CAnal.6.A.Octave..pdf|6.B.pdf]]) go to [ [[Electrical_%26_Computer_Engineering_Studies]] ] [[Category:Complex analysis]] 1pwbgtirx9igbknigqoamdcb6ekxq94 2823658 2823656 2026-08-20T14:33:13Z Young1lim 21186 /* Geometric Series Examples */ 2823658 wikitext text/x-wiki Many of the functions that arise naturally in mathematics and real world applications can be extended to and regarded as complex functions, meaning the input, as well as the output, can be complex numbers <math>x+iy</math>, where <math>i=\sqrt{-1}</math>, in such a way that it is a more natural object to study. '''Complex analysis''', which used to be known as '''function theory''' or '''theory of functions of a single complex variable''', is a sub-field of analysis that studies such functions (more specifically, '''holomorphic''' functions) on the complex plane, or part (domain) or extension (Riemann surface) thereof. It notably has great importance in number theory, e.g. the [[Riemann zeta function]] (for the distribution of primes) and other <math>L</math>-functions, modular forms, elliptic functions, etc. <blockquote>The shortest path between two truths in the real domain passes through the complex domain. — [[wikipedia:Jacques_Hadamard|Jacques Hadamard]]</blockquote>In a certain sense, the essence of complex functions is captured by the principle of [[analytic continuation]].{{mathematics}} ==''' Complex Functions '''== * Complex Functions ([[Media:CAnal.1.A.CFunction.20140222.Basic.pdf|1.A.pdf]], [[Media:CAnal.1.B.CFunction.20140111.Octave.pdf|1.B.pdf]], [[Media:CAnal.1.C.CFunction.20140111.Extend.pdf|1.C.pdf]]) * Complex Exponential and Logarithm ([[Media:CAnal.5.A.CLog.20131017.pdf|5.A.pdf]], [[Media:CAnal.5.A.Octave.pdf|5.B.pdf]]) * Complex Trigonometric and Hyperbolic ([[Media:CAnal.7.A.CTrigHyper..pdf|7.A.pdf]], [[Media:CAnal.7.A.Octave..pdf|7.B.pdf]]) '''Complex Function Note''' : 1. Exp and Log Function Note ([[Media:ComplexExp.29160721.pdf|H1.pdf]]) : 2. Trig and TrigH Function Note ([[Media:CAnal.Trig-H.29160901.pdf|H1.pdf]]) : 3. Inverse Trig and TrigH Functions Note ([[Media:CAnal.Hyper.29160829.pdf|H1.pdf]]) ==''' Complex Integrals '''== * Complex Integrals ([[Media:CAnal.2.A.CIntegral.20140224.Basic.pdf|2.A.pdf]], [[Media:CAnal.2.B.CIntegral.20140117.Octave.pdf|2.B.pdf]], [[Media:CAnal.2.C.CIntegral.20140117.Extend.pdf|2.C.pdf]]) ==''' Complex Series '''== * Complex Series ([[Media:CPX.Series.20150226.2.Basic.pdf|3.A.pdf]], [[Media:CAnal.3.B.CSeries.20140121.Octave.pdf|3.B.pdf]], [[Media:CAnal.3.C.CSeries.20140303.Extend.pdf|3.C.pdf]]) ==''' Residue Integrals '''== * Residue Integrals ([[Media:CAnal.4.A.Residue.20140227.Basic.pdf|4.A.pdf]], [[Media:CAnal.4.B.pdf|4.B.pdf]], [[Media:CAnal.4.C.Residue.20140423.Extend.pdf|4.C.pdf]]) ==='''Residue Integrals Note'''=== * Laurent Series with the Residue Theorem Note ([[Media:Laurent.1.Residue.20170713.pdf|H1.pdf]]) * Laurent Series with Applications Note ([[Media:Laurent.2.Applications.20170327.pdf|H1.pdf]]) * Laurent Series and the z-Transform Note ([[Media:Laurent.3.z-Trans.20170831.pdf|H1.pdf]]) * Laurent Series as a Geometric Series Note ([[Media:Laurent.4.GSeries.20170802.pdf|H1.pdf]]) === Laurent Series and the z-Transform Example Note === * Overview ([[Media:Laurent.4.z-Example.20170926.pdf|H1.pdf]]) ====Geometric Series Examples==== * Causality ([[Media:Laurent.5.Causality.1.A.20191026n.pdf|A.pdf]], [[Media:Laurent.5.Causality.1.B.20191026.pdf|B.pdf]]) * Time Shift ([[Media:Laurent.5.TimeShift.2.A.20191028.pdf|A.pdf]], [[Media:Laurent.5.TimeShift.2.B.20191029.pdf|B.pdf]]) * Reciprocity ([[Media:Laurent.5.Reciprocity.3A.20191030.pdf|A.pdf]], [[Media:Laurent.5.Reciprocity.3B.20191031.pdf|B.pdf]]) * Combinations ([[Media:Laurent.5.Combination.4A.20200702.pdf|A.pdf]], [[Media:Laurent.5.Combination.4B.20201002.pdf|B.pdf]]) * Properties ([[Media:Laurent.5.Property.5A.20220105.pdf|A.pdf]], [[Media:Laurent.5.Property.5B.20220126.pdf|B.pdf]]) * Permutations ([[Media:Laurent.6.Permutation.6A.20230711.pdf|A.pdf]], [[Media:Laurent.5.Permutation.6B.20251225.pdf|B.pdf]], [[Media:Laurent.5.Permutation.6C.20260820.pdf|C.pdf]], [[Media:Laurent.5.Permutation.6C.20240528.pdf|D.pdf]]) * Applications ([[Media:Laurent.5.Application.6B.20220723.pdf|A.pdf]]) * Double Pole Case :- Examples ([[Media:Laurent.5.DPoleEx.7A.20220722.pdf|A.pdf]], [[Media:Laurent.5.DPoleEx.7B.20220720.pdf|B.pdf]]) :- Properties ([[Media:Laurent.5.DPoleProp.5A.20190226.pdf|A.pdf]], [[Media:Laurent.5.DPoleProp.5B.20190228.pdf|B.pdf]]) ====The Case Examples==== * Example Overview : ([[Media:Laurent.4.Example.0.A.20171208.pdf|0A.pdf]], [[Media:Laurent.6.CaseExample.0.B.20180205.pdf|0B.pdf]]) * Example Case 1 : ([[Media:Laurent.4.Example.1.A.20171107.pdf|1A.pdf]], [[Media:Laurent.4.Example.1.B.20171227.pdf|1B.pdf]]) * Example Case 2 : ([[Media:Laurent.4.Example.2.A.20171107.pdf|2A.pdf]], [[Media:Laurent.4.Example.2.B.20171227.pdf|2B.pdf]]) * Example Case 3 : ([[Media:Laurent.4.Example.3.A.20171017.pdf|3A.pdf]], [[Media:Laurent.4.Example.3.B.20171226.pdf|3B.pdf]]) * Example Case 4 : ([[Media:Laurent.4.Example.4.A.20171017.pdf|4A.pdf]], [[Media:Laurent.4.Example.4.B.20171228.pdf|4B.pdf]]) * Example Summary : ([[Media:Laurent.4.Example.5.A.20171212.pdf|5A.pdf]], [[Media:Laurent.4.Example.5.B.20171230.pdf|5B.pdf]]) ==''' Conformal Mapping '''== * Conformal Mapping ([[Media:CAnal.6.A.Conformal.20131224.pdf|6.A.pdf]], [[Media:CAnal.6.A.Octave..pdf|6.B.pdf]]) go to [ [[Electrical_%26_Computer_Engineering_Studies]] ] [[Category:Complex analysis]] go0yibfajdsgyhduwi1ywk5u70vnyaf 0 214027 2823791 2673864 2026-08-21T02:21:31Z U3275992 3106315 /* People at risk */ Added 'of age' after years for clarity purposes. 2823791 wikitext text/x-wiki {{title|Anorexia nervosa and extrinsic motivation:<br> What extrinsic motivational factors contribute to anorexia nervosa?}} {{MECR3|1=https://www.youtube.com/watch?v=E2OCBl0QqDk}} __TOC__ == Overview == {{RoundBoxTop|theme=2}} When Debra was 19 years old, she was admitted to a mental health centre. She weighed 29 kilos. Her liver, pancreas and kidneys were damaged, and she spent almost 2 months in hospital recovering. During this time, Debra received psychotherapy that helped her understand why her eating behaviour had become dangerous. She also engaged in a behaviour modification program that rewarded her with privileges for each kilo she gained. Slowly, she began to gain weight and through therapy began to understand why her eating behaviour had become dangerous. When she left the hospital, she weighed 48 kilos, and two years later, was maintaining a steady weight (Steele, 1977). {{RoundBoxBottom}} Debra's experience highlights the burden of anorexia, a debilitating eating disorder that leads to diminished quality of life, and serious adverse health effects. It is a complex disorder and has been the focus of research attempting to determine contributing factors and effective treatments. It also lends itself to many questions: What motivates an individual to engage in damaging eating habits? Are internal or external motivations responsible? This chapter examines the external motivational factors that contribute to the development of anorexia. It will also attempt to answer some of the questions above, and hopefully answer your own questions; so if you have any, keep them in mind while you read. {{RoundBoxTop|theme=2}} '''Focus question''' 1. What extrinsic motivational factors contribute to anorexia nervosa?{{RoundBoxBottom}} == Eating disorders == Eating disorders are characterised by persistent disturbance surrounding eating or eating-related behaviours, leading to significant psychological distress and impaired functioning, and in some cases, death (APA, 2013). It is estimated that approximately 4% of the Australian population has an eating disorder (Butterfly foundation, 2016), with at least 15% of women experiencing an eating disorder at some point in their life (NEDC, 2016). Some common eating disorders are listed in Table 1. Eating disorders are diagnosed in Australia through the Diagnostic and Statistical Manual, fifth edition, a clinical tool that lists currently recognised mental disorders, and includes various information about the different sub-types, causes and prevalence of these disorders (APA, 2013). [[File:Many Hands (16859686419).jpg|thumb|212x212px|''Figure 2.'' Australia has a network of eating disorder support groups.]] Table 1. Summary of common eating disorders (National Institute of Mental Health (2017) {| class="wikitable" | |'''Common symptoms''' |- |'''Anorexia nervosa''' |Extreme restriction of food intake, accompanied by excessive exercise and at times purging behaviours. (Vancampfort et al., 2014) |- |'''Bulimia nervosa''' |Bingeing on sweet or high-caloric foods, and then purging through vomiting, or diuretic use. (Vancampfort et al., 2014) |- |'''Binge Eating Disorder''' |Out of control consumption of large quantities of foods (usually within 2 hours) and is accompanied by feelings of guilt or distress after eating (Giel et al., 2022) |} {{RoundBoxTop|theme=10}} Note: An individual may have problems or issues surrounding eating and eating behaviours, but these will only fall under the definition of "eating disorder", if they cause significant impairment in that individual's life. For example, Eddie may be very focused on eating only vegetables and doing at least two hours of exercise every day, but until these behaviours start to interfere with other aspects of Eddie's life, he would not be diagnosed with an eating disorder (APA, 2013). {{RoundBoxBottom}} == Anorexia nervosa == [[File:Person looking at a green apple.jpg|thumb|352x352px|''Figure 3''. Restricted food intake is a common feature of anorexia]] Anorexia is a serious eating disorder, clinically named ''Anorexia Nervosa''. Anorexia can be identified by changes in an individual's thoughts, feelings and behaviour to lose weight. Common behavioural changes include excessively restricting food intake and engaging in regular, intense periods of physical activity (APA, 2013). Physical changes such as dizziness, disruptions of the menstrual cycle (in women), and the appearance of fine hair across the body, are also often present (NEDC, 2016). Psychological changes include a preoccupation with eating, intense fear of gaining weight, and a distorted body image (NEDC, 2016). Other symptoms include frequently checking weight, and measuring body parts (APA, 2013). Often, individuals with anorexia will see losing weight as extraordinary self-control and determination; gaining weight is seen as an unacceptable failure (APA, 2013). === People at risk === Anorexia usually develops in adolescence or young adulthood, between 15 and 19 years of age (Bulik, Reba, Siega-Riz, & Reichborn-Kjennerud, 2005). Statistics from the United States show that in 2007, the lifetime prevalence of anorexia was affecting 0.6% of the adult population, with lifetime prevalence rates for females at 0.9%, and 0.3% for males (Hudson, Hiripi, Pope, & Kessler, 2007). Other statistics suggest that anorexia is ten times more common among females than males (Rieger, 2014). However, the incidence of anorexia among males is increasing (Wooldridge, & Lytle, 2012). === Possible causes === Anorexia has no one single cause, although there are minor predispositions and precipitations that may be necessary for its development, they are not entirely sufficient for all cases of the development of the disorder (Morris & Taddle, 2007). ==== Biology ==== Although not entirely understood, biological factors, such as an inherited disposition or genetic abnormality may predispose an individual to developing anorexia. Research shows that families of individuals suffering from anorexia will likely present traits such as a disposition towards leanness, or a family history of obsessive-compulsive personalities, or mood disorders, all of which may have a genetic basis (Rieger, 2014). In fact, the risk for individuals who have an immediate family member diagnosed with anorexia is approximately seven to twelve times higher than for other individuals (Herpertz-Dahlmann, Seitz, & Konrad, 2011). ==== Psychology ==== [[File:Diagram showing a double helix of a chromosome CRUK 065.svg|thumb|286x286px|''Figure 4''. Genetics likely plays a role in the development of anorexia.]] Psychological factors such as dysfunctional thoughts have been identified as other possible factors that lead to anorexia. A European study in 2012 interviewed eight adolescents between the age of 13 and 17 years, to try and determine what psychological factors are present at the onset of anorexia. Results showed that a variety of overwhelming emotions, such as frustration, guilt and fear were present in participants before the onset of anorexia (Koruth, Nevison, & Schwannauer, 2012). Obsessiveness, perfectionism and competitive traits have also been found to be present in adolescents and adults with anorexia (Morris & Taddle, 2007). Furthermore, anorexia has also been found to occur in individuals who were well-behaved, hard-working and successful as children (Bruch, 1985, as cited in Herpertz-Dahlmann, Seitz, & Konrad, 2011). ==== Society ==== There are social implications associated with having eating disorders. Machado, Goncalves, Martins, Hoek, & Machado (2014) examined the possible social causes of anorexia, by comparing 86 women diagnosed with anorexia with two matched groups of either healthy individuals, or individuals with other mental disorders. Analysis revealed that the women with anorexia reported receiving negative or critical comments about their body shape, or weight, in the year preceding their diagnosis (Machado, Goncalves, Martins, Hoek, & Machado, 2014). Social favouring of certain body types may be a contributory factor; a study conducted in 1995 and 1998 examined the incidence of eating disorder symptoms among young Fijian women before, and after the introduction of television to their province. Results revealed that a greater percentage of women scored in the clinical range on an eating disorder questionnaire after exposure to television, compared to women who had not been exposed (Becker, Burwell, Gilman, Herzog, & Hamburg, 2002, as cited in Rieger, 2014). === Co-morbid disorders === Individuals with anorexia are often diagnosed with other mental disorders. Anxiety disorders are one of the most frequently reported disorders to co-occur with anorexia (Herpertz-Dahlmann, Seitz, & Konrad, 2011). Other co-occurring disorders include mood disorders, such as major depressive disorder, and personality disorders, such as obsessive-compulsive personality disorder (Rieger, 2014). A 2015 study of patients with severe anxiety disorders in Denmark found that individuals diagnosed with obsessive-compulsive disorder presented the greatest risk for anorexia (Meier, Bulik,Thornton, Mattheisen, Mortensen, & Peterson, 2015). === Treatment === {{expand}} Medical treatment. If undernourishment or starvation has started to break down your body, medical treatment will be the first priority. A GP will treat the medical conditions that have been caused by anorexia, such as, heart problems, or depression. ==== Setting ==== In this chapter's opening case study, Debra visited a mental health centre and a hospital (Steele, 1977). Recently, the treatment setting for individuals with anorexia has changed; rather than long-term hospital admittance, the individual will likely engage in a short-term hospital stay, followed by returning to a treatment centre several times a week. The individual may also remain at home and see a therapist several times a week (Rieger, 2014). ==== Psychotherapy ==== Psychological treatments involve a clinical psychologist, who helps the client understand their disorder and treat it. Individuals with anorexia often seen the disorder as a channel for achievement, with the result that some individuals do not want to change (Rieger, 2014). ''Motivational enhancement therapy'' aims to alter the client's motivation to change (Rieger, 2014). ''Cognitive Behavioural Therapy'' (CBT), is useful in cases where the client has motivation to treat their disorder, and is conducted over three phases, summarised below (Rieger, 2014). ''Interpersonal psychotherapy'', deals with how the client relates to other people, and ''family therapy'' attempts to draw the focus of the client's family from the client's eating disorder, to relationships (Rieger, 2014). Currently, evidence supports the effectiveness of motivational enhancement therapy, CBT and family therapy in treating anorexia (Rieger, 2014). Interpersonal psychotherapy has also been supported for its long-term benefits in focusing on the client's relationship to others (Zipfel, et al., 2014, as cited in Bulik, 2014). Table 2. Summary of the three phases of CBT in treating anorexia {| class="wikitable" !Phase !Action |- !1 |Establishes the therapeutic relationships between the client and the psychologist, and creates meal plans with a dietitian. |- !2 |Identifies the client's dysfunctional thoughts about their weight and eating, examining evidence for and against these thoughts, and replacing them with more realistic beliefs. |- !3 |Concludes treatment and provides the client with strategies to prevent relapse. |} == Quick quiz == If you like, complete the following quiz to see if you recognise the basic causes, symptoms, and treatments for anorexia, before reading the rest of the chapter: <quiz display="simple"> {What is a common symptom of anorexia? |type="()"} + Disturbed body image. - Narcissism. - Over-eating. {Has the cause of anorexia been proven? |type="()"} - Yes, genetic factors are the cause. + No, but it is likely caused by a range of interacting factors - No, but it is likely caused psychological factors. {Choose a common co-morbid disorder of anorexia from the list below: |type="()"} + Anxiety disorders. - Psychotic disorders. - There are no co-morbid disorders of anorexia. {What is a common treatment for anorexia? |type="()"} - Encourage the client to eat more. - Sporadic change therapy. + Motivational enhancement therapy. </quiz> == Introduction to motivation: basic definitions == [[File:Concentrate - Tulane University baseball batter, 2008.jpg|thumb|241x241px|''Figure 5.'' If this batter is playing baseball because he loves the game, he is intrinsically motivated.]] The rest of this chapter focuses on extrinsic motivations and anorexia; however, it is first important to understand some basic definitions of motivational concepts. ''Motivation:'' an organism is moved to do something, implying a level of energy and direction in that movement; it is divided into two categories, intrinsic and extrinsic motivation (Ryan, & Deci, 2000c). ''Extrinsic motivation'': <blockquote>"''An incentive to do something that arises from factors outside the individual, such as rewards or penalties''" (Law, 2016).</blockquote>''Intrinsic motivation'':<blockquote>"''An incentive to do something that arises from factors within the individual, such as a need to feel useful or to seek self-actualization''" (Law, 2016).</blockquote>The distinction between extrinsic and intrinsic motivation is whether an incentive originates externally or internally, and is associated with losses and gains, or interest, respectively. Furthermore, an individual can be intrinsically motivated even if a task is difficult. Research has shown that greater levels of motivation are associated with intrinsic motivators, rather than extrinsic motivators (Reeve, 2015). While extrinsic motivation seems undesirable, research has also shown positive sides to extrinsic motivation, which we will discuss further. {{RoundBoxTop|theme=6}} Which one is extrinsic motivation? Which one is intrinsic motivation? # Brendan does his homework because he doesn't want to fail his class. # Sarah does her difficult guitar lessons because she really wants to learn a song she likes. {{RoundBoxBottom}} == Self-determination theory == Several theories that focus on understanding how different types of motivation effect human behaviour have been proposed by researchers; the following is a short overview of a motivational theory that explores different facets of motivation, including extrinsic motivation. Self-determination theory suggests that there are three basic psychological needs, competence, autonomy and relatedness, which lead to increased motivation and enhanced welfare (Ryan, & Deci, 2000a). ''Competence'' refers to the individual's need to feel control in their life. ''Autonomy'' refers to the individual's need to feel that one's behaviours and thoughts are guided from within, rather than exerted by external forces. ''Relatedness'' refers to the individual's need to experience a sense of connection to other individuals (Ryan, & Deci, 2000a). This theory suggests that these are fulfilled primarily through intrinsic motivation. This theory also acknowledges positive multidimensional aspects of extrinsic motivation, defining four types of extrinsic motivation, ranging from a state of ''amotivation'' (no motivation) to intrinsic motivation (Reeve, 2015). Self-determination theory also distinguishes between ''autonomous'' and ''controlled motivation; autonomous motivation'' describes a combination of intrinsic and extrinsic motivations, where behaviour is influenced by free incorporation of useful extrinsic motivators into one's identity. ''Controlled motivation'' is a combination of extrinsic motivational types that control an individual's behaviour through external pressures such as approval, or shame avoidance (Deci, & Ryan, 2008). == Understanding the relationship between anorexia and extrinsic motivations == [[File:Dog clicker training.jpg|thumb|''Figure 6''. Obedience training is an example of externally regulated behaviour.]] Now, with an understanding of anorexia and some motivational concepts, we can discuss the relationship between extrinsic motivation and anorexia. The following is the final component of this chapter, and looks at the four types of extrinsic motivation and specific motivators that may play a role in the development of anorexia. === Levels of extrinsic motivation === Self-determination theory proposes several levels of extrinsic motivation, summarised in the table below (Deci, & Ryan, 2000b; Vallerand, 1997). Table 3. Summary of the four levels of extrinsic motivation. {| class="wikitable" !Level !Effect on behaviour |- |External regulation |Behaviour is strictly controlled by consequences. |- |Introjected regulation |Behaviour is performed because of self-imposed pressures. |- |Identified regulation |Behaviour is personally identified with. |- |Integrated regulation |Behaviour is freely chosen & organised into the individual's identity |} These levels distinguish between the influence of external pressures and free choice on behaviour (Vallerand, 1997), and may also explain anorexia development. Several different levels of extrinsic motivation are identifiable in anorexic behaviours. For example, anorexic eating behaviour is controlled by consequential weight-loss and is therefore externally regulated. A study in 2007 examined the role of extrinsic motivations in relation to exercise, body image and need satisfaction among a group of 149 aerobic instructors. Results found that introjected regulation demonstrated a negative relationship with body image and self-worth, suggesting that self-imposed pressures to exercise in order to achieve a desired body type, may have a negative effect on self-esteem, in turn possibly leading to anorexia (Thogersen-Ntoumani, & Ntoumanis, 2007). Identified regulation is also implicated; in a qualitative recovery study, anorexia survivors cited personally identifying with their disorder until it became a "way of life" (Weaver, Wuest, & Ciliska, 2005). Together, this research suggests that these different levels of extrinsic motivation may influence the development of anorexia. As well as these levels, specific extrinsic motivators may also contribute to the disorder. Provide more in-text references === Two specific extrinsic motivators === {{expand}} ==== Body image ==== The promotion of certain body types may act as a powerful extrinsic motivator that contributes to the development of anorexia. Current media promotes an ultra-thin female body type that for many women is unattainable (Attie, & Brooks-Gun, 1989, as cited in, Hawkins, Richards, Granley, & Stein, 2004). As many young women are exposed to media daily, research has focused on the role that exposure to promotion of these body types has on anorexia development. In a revealing study, researchers exposed a mixed group of 145 women from the Ohio State University campus to images from popular magazines that were either neutral, or promoted an ultra-thin body type. Results revealed that women who were exposed to the ultra-thin images experienced greater body dissatisfaction, decreased self-esteem, increased negative mood and eating disorder symptoms (Hawkins, Richards, Granley, & Stein, 2004). Although limited by self-report measures (Hawkins, Richards, Granley, & Stein, 2004), this study presents that promotion of certain unattainable body-types may act as an extrinsic motivator for anorexia. A qualitative study discussing 28 women's battles with anorexia also highlighted the extrinsic motivational power of promoted body-types; while not blaming the media for the development of their disorder, participants acknowledged the influence of fashion magazine models (Thomsen, McCoy, & Williams, 2001). In the words of one participant: <blockquote> ''"On my wall, I would cut out all the pictures of the models...I'd cut them and pin them up on my wall just like a motivator...I'd think, "Those are the legs I want. Those are the arms I want." And I just filled up my room with that and that was my goal"'' (Thomsen, McCoy, Williams, 2001). </blockquote> Another study explored the relationship between associating underweight models with positive attributes, and eating disorder symptoms (Ahern, Bennett, & Hetherington, 2008). A sample of 99 female undergraduate students completed an implicit association test on weight, and a self-report measure assessing eating disorder symptoms and body dissatisfaction. Results revealed that participants associating being underweight with positive attributes, also presented elevated eating disorder symptoms (Ahern, Bennett, & Hetherington, 2008). While limited by possible sample bias (Ahern, Bennett, & Hetherington, 2008), this study also presents the importance of recognising the promotion of thin body types as an extrinsic motivator for anorexia. {{RoundBoxTop|theme=2}} Next time you're browsing the internet, count the number of times you see an attractive model who is very thin. Compare this with the number of times a model is a healthy weight. {{RoundBoxBottom}} ==== Control ==== Another extrinsic motivator that has links to anorexia, is control. Attempting to gain control of life situations has been examined as a contributory extrinsic motivator of anorexia. The aforementioned qualitative study by Thomsen, McCoy and Williams (2001), found participants often described living in difficult family dynamics, which led to a desire to gain control, before developing anorexia. These familial situations often included parenting younger siblings and protecting mothers from abusive partners (Thomsen McCoy, & Williams, 2001). As one participant stated: <blockquote>''"I didn't want to be the cause of another problem ... it was easier for me to just worry about my body and exercise and food."'' (Thomsen, McCoy, & Williams, 2001).</blockquote> [[File:Waist measurement.jpg|thumb|266x266px|''Figure 8''. For individuals with anorexia, weight-loss can be seen as gaining control, or achieving. ]] Research with anorexia survivors also shows that experience of difficult life circumstances, such as parental unemployment or divorce, contribute to a desire to take control (Weaver, Wuest, & Ciliska, 2005). One anorexia survivor pin-pointed the stress of moving house, and hearing that her parent's marriage was in trouble, as precursory events that led to anorexia (National health scheme, 2016). Another qualitative study of 12 female anorexia survivors found that participants saw the feeling of "taking control" by engaging anorexic behaviours, as a "lure" to engage in further anorexic behaviours (Weaver, Wuest, & Ciliska, 2005). Participants described feeling greater personal control and effectiveness when experiencing events such as a "running high" and lack of appetite after exercise; this encouraged the progression of anorexic behaviours, to the long-term development of anorexia (Weaver, Wuest, & Ciliska, 2005). Interestingly, this desire to take control is connected to a desire to "achieve something"; anorexia survivors often note that they wanted to feel better about themselves before engaging in anorexic behaviours. One anorexia survivor found that dieting led to immediate feelings of achievement. <blockquote>''"As I began to lose weight, I started to feel that life was worth living. At last I seemed to be achieving something."'' (National health scheme, 2016).</blockquote> Another survivor's desire to achieve strongly motivated here to be constantly busy because she didn't want her friends and family to think she was "lazy" (Eating Disorders Victoria, 2016). Individuals who develop anorexia often present a strong drive for achievement (Weaver, Wuest, & Ciliska, 2005); it is no surprise that signs of immediate achievement such as weight-loss, are a major factor in anorexia. Although these studies rely on self-report, they present evidence that seeking to gain control of difficult life situations and to a desire to achieve, may act as extrinsic motivational factors that lead to and support anorexia. ==Conclusion== This chapter has provided a brief overview of the factors that contribute to anorexia. We have explored eating disorders and anorexia, defined the different types of motivation, and examined how extrinsic motivations are related to anorexia. However, this chapter has only discussed two specific motivators; it is likely that individuals not yet included in research could define other extrinsic factors related to anorexia, a possible future direction for motivational research. During your journey through this chapter you have also been asked questions; perhaps you managed to answer these, perhaps you did not. However, hopefully this chapter has encouraged you to think on some challenging concepts, and overall, has left you with a more complete understanding of motivation. Thank you for reading. ==See also== * [[Motivation and emotion/Book/2013/Extrinsic motivation|Extrinsic motivation]] (Book Chapter, 2013). * [[Motivation and emotion/Book/2013/Workplace motivation|Self-determination theory in the workplace]] (Book Chapter, 2013). * [[Motivation and emotion/Book/2014/Eating disorder recovery and motivation|Eating disorder recovery]] (Book Chapter, 2014). * [[Motivation and emotion/Book/2015/Workplace motivation and autonomy|Autonomy]]<nowiki/> (Book Chapter, 2015). ==References== {{Hanging indent|1= Ahern, A. L., Bennett, K. M., & Hetherington, M. M. (2008). Internalization of the ultra-thin ideal: positive implicit associations with underweight fashion models are associated with drive for thinness in young women. ''Eating Disorders, 16'', 294-307. doi: 10.1080/10640260802115852. American Psychiatric Association. (2013). ''Diagnostic and statistical manual of mental disorders'' (5th ed.). Arlington, VA: American Psychiatric Publishing. Bulik, C. M., Reba, L., Siega-Riz, A., & Reichborn-Kjennerud, T. (2005). Anorexia Nervosa: Definition, Epidemiology, and Cycle of Risk. ''Psychopathology, 37'', 2-9. doi: 10.1002/eat.20107 Bulik, C. (2014). The challenges of treating anorexia nervosa. ''The Lancet, 383'', 105-106. doi: 10.1016/S0140-6736(13)61940-6 Butterfly Foundation for Eating Disorders. (2016). ''Understanding Eating Disorders & Body Image Issues''. Retrieved from the Butterfly Foundation for Eating Disorders: https://thebutterflyfoundation.org.au/understand-eating-disorders/ Deci, E. L., & Ryan, R. M. (2008). Self-Determination Theory: A Macrotheory of Human Motivation, Development, and Health. ''Canadian Psychology, 49'', 182-185. doi: 10.1037/a0012801 Eating Disorders Victoria (2016). '' Lauren's Recovery From Anorexia''. Retrieved from Eating Disorders Victoria https://www.eatingdisorders.org.au Hawkins, N., Richards, P. S., Granley, H. M., & Stein, D. M. (2004). The impact of exposure to the thin-ideal media image on women. ''Eating Disorders, 12'', 35-50. doi: 10.1080/10640260490267751 headspace: the National Youth Mental Health Foundation. (2016). ''Who we are''. Retrieved from headspace the National Youth Mental Health Foundation https://www.headspace.org.au/about-us/who-we-are/ Herpertz-Dahlmann, B., Seitz, J., & Konrad, K. (2011). Aetiology of anorexia nervosa: from a "psychosomatic family model" to a neuropsychiatric disorder?. ''European Archives of Psychology and Clinical Neuroscience, 261'', 177-181. doi: 10.1007/s00406-011-0246-y Hudson, J. I, Hiripi,. E, Pope, H. G, & Kessler, R.C (2007). The prevalence and correlates of eating disorders in the National Comorbidity Survey Replication. ''Biological Psychiatry, 61'', 348-58. doi:10.1007/s00406-011-0246-y Koruth, N., Nevison, C., & Schwannauer, M. (2012). A grounded theory exploration of the onset of anorexia in adolescence. ''European Eating Disorders Review, 20'', 257-264. doi:10.1002/erv.1135 Law, J. (2016). A Dictionary of Business and Management (6th. ed.). Retrieved from http://www.oxfordreference.com.ezproxy.canberra.edu.au/view/10.1093/acref/9780199684984.001.0001/acref-9780199684984-e-2403 Machado, B. C., Goncalves, S. F., Machado, P. P., Martins, C., & Hoek, H. W. (2014). Risk factors and antecedent life events in the development of anorexia nervosa: A portuguese case-control study. ''European Eating Disorders Review, 22'', 243-251. doi:10.1002/erv.2286 Morris, J., & Twaddle, S. (2007). Anorexia nervosa. BMJ (Clinical research ed.), 334(7599), 894–898. https://doi.org/10.1136/bmj.39171.616840.BE National Eating Disorders Collaboration. (2016). ''What is an eating disorder?'' Retrieved from National Eating Disorders Collaboration: http://www.nedc.com.au/ National Health Scheme (2016). ''Anorexia nervosa - Katie's story'' Retrieved from National Health Scheme: http://www.nhs.uk/ Reeve, J. (2015). Extrinsic Motivation. In C, Johnson (Eds.), Understanding Motivation and Emotion (pp. 116-151). Hoboken, NJ: Wiley. Rieger, E. (2014). Abnormal Psychology: Leading Researcher Perspectives (3rd. ed.). North Ryde, NSW: McGraw-Hill Ryan, R. M., & Deci, E. L. (2000c). Intrinsic and Extrinsic Motivations: Classic Definitions and New Directions. ''Contemporary Educational Psychology, 25'', 54-67. doi: 10.1006/ceps.1999.1020 Ryan, R. M., & Deci, E. L. (2000b). Self-determination theory and the facilitation of intrinsic motivation, social development and well-being. ''American Psychologist, 55'', 68-78. doi: 10.1037110003-066X.55.1.68 Ryan. M., & Deci, E. L. (2000a). The "What" and "Why" of Goal Pursuits: Human Needs and the Self-Determination of Behavior. '' Psychological Inquiry, 11'', 227-268. doi: 10.1207/S15327965PLI1104_01 Steele, R. L. (1977). Anorexia nervosa: a case study. ''Psychotherapy and Psychosomatics, 27'', 47-53. Thaler, L., Israel, M., Antunes, J. M., Sarin, S., Zuroff, D., & Steiger, H. (2016). An examination of the role of autonomous versus controlled motivation in predicting inpatient treatment outcome for anorexia nervosa. ''International Journal of Eating Disorders, 49'', 626-629. doi: 10.1002/eat.22510 Thogersen-Ntoumani, C., & Ntoumanis, N. (2007). A Self-Determination Theory Approach to the Study of Body Image Concerns, Self-presentation and Self-perceptions in a sample of Aerobic Instructors. ''Journal of Health Psychology, 12'', 301-315. doi: 10.1177/1359105307074267 Thomsen, S. R., McCoy, J. K., & Williams, M. (2001). Internalizing the impossible: anorexic outpatients' experiences with women's beauty and fashion magazines. ''Eating Disorders, 9'', 49-64. doi: 10.1080/106402601300187731 Vallerand, R. J. (1997). Toward a Hierarchical Model of Intrinsic and Extrinsic Motivation. ''Advances in Experimental and Social Psychology, 29'', 271-360. doi: 10.1016/S0065-2601(08)60019-2 Weaver, K., Wuest, J., & Ciliska, D. (2005). Understanding women's journey of recovering from anorexia nervosa. ''Qualitative Health Research, 15'', 188-206. doi: 10.1177/1049732304270819 Wooldridge, T., & Lytle, P. (2012). An overview of anorexia nervosa in males. ''Eating Disorders, 20'', 368. doi:10.1080/10640266.2012.715515 }} ==External links== * [https://www.headspace.org.au/ headspace: National Youth Mental Health Foundation] * [http://www.helpguide.org/articles/eating-disorders/anorexia-nervosa.htm Helpguide.org] * DSM-V FAQ's http://www.dsm5.org/about/Pages/faq.aspx * The Butterfly Foundation https://thebutterflyfoundation.org.au/understand-eating-disorders/ * Life Without Anorexia [http://www.lifewithoutanorexia.com/] * The pro-anorexia [http://www.webmd.com/mental-health/eating-disorders/anorexia-nervosa/features/pro-anorexia-web-sites-thin-web-line phenomenon] [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Eating]] [[Category:Motivation and emotion/Book/Extrinsic motivation]] [[Category:Motivation and emotion/Book/Hunger]] bzufwycmw5asy52stuuzhtc9dibq77x 0 223496 2823846 2535140 2026-08-21T08:54:48Z CommonsDelinker 9184 Replacing Cathédrale_Saint-Ètienne,_Sens-6998.jpg with [[File:Cathédrale_Saint-Étienne,_Sens-6998.jpg]] (by [[:c:User:CommonsDelinker|CommonsDelinker]] because: [[:c:COM:FR|File renamed]]:). 2823846 wikitext text/x-wiki =Task 1= Name architectural elements. Sometimes more answers are possible. <quiz display=simple> {[[Image:Amiens_cathedral_002.JPG|150px]] [[Image:Cathédrale_Saint-Étienne,Toulouse_Rosace.jpg|145px]] | type="{}" } { rose window } {[[Image:Coupe.transversale.nef.cathedrale.Reims.png|150px]] [[Image:Notre_Dame_buttress.jpg|180px]] | type="{}" } { flying buttress|flying buttresses } {[[Image:Pinnacle_(PSF).png|60px]] [[Image:Reims,_Cathédrale_Notre-Dame-PM_13975.jpg|150px]] | type="{}" } { pinnacle|pinnacles } {[[Image:Ablis_-_voutes.jpg|180px]] | type="{}" } { quadripartite cross-ribbed vault|1uadripartite vault } </quiz> =Task 2= Look at plans and pictures of Gothic cathedrals. For each group decide if they represent English, French or Italian Gothic architecture. <quiz display=simple> {[[Image:Plan.cathedrale.Bourges.png|150px]] [[Image:Dehio_361_Soissons_Cathedrale.jpg|150px]] [[Image:Dehio_361_Noyon_Cathedrale.jpg|150px]] [[Image:Plan.cathedrale.Limoges.png|150px]] |type="()"} + French - English - Italian {[[Image:EB_1911_Plan_of_Ely_Cathedral.png|150px]] [[Image:LincCathplanDehio.jpg|150px]] [[Image:PeterPlanDehio.jpg|150px]] [[Image:YorkMinsterPlanDehio_vert.jpg|150px]] |type="()"} - French + English - Italian {[[Image:Orvieto_kathedrale_1.jpg|180px]] [[Image:Santa_Maria_Novella_Florence_façade.jpg|150px]] [[Image:20110724_Milan_Cathedral_5260.jpg|150px]] [[Image:Abbazia_di_Fossanova_(2008).jpg|180px]] [[Image:ITA_Firenze_Basilica_di_Santa_Croce_2.jpg|180px]] |type="()"} - French - English + Italian {[[Image:Westminster_Abbey_2008.jpg|150px]] [[Image:Selby_Abbey_-_geograph.org.uk_-_1508435.jpg|150px]] [[Image:Rochester_Cathedral.jpg|150px]] [[Image:Lincoln_Cathedral_from_the_Castle.jpg|180px]] [[Image:Gloucester_Cathedral_-_2004-11-02.jpg|180px]] |type="()"} - French + English - Italian {[[Image:Cathédrale Saint-Étienne, Sens-6998.jpg|150px]] [[Image:Reims_Kathedrale.jpg|180px]] [[Image:Cathédrale_de_Noyon_straight.JPG|180px]] [[Image:Cathédrale_Saint-Pierre-et-Saint-Paul,_Troyes,_West_view_20140509_1.jpg|180px]] [[Image:Vendome-église-de-l'abbaye-de-la-Trinité-dpt-Loir-et-Cher-DSC_0545.jpg|180px]] |type="()"} + French - English - Italian </quiz> {{CourseCat}} [[Category:Gothic architecture]] g1iw2i0sgfk5yjlx3cqixlmxz18plun 0 243861 2823810 2462590 2026-08-21T04:24:50Z It-is-Truly-Meet 3089598 2823810 wikitext text/x-wiki == Present indicative of "to be" == It is worth noting that "to be" is a highly irregular verb in Greek as well as in English. The verb stem of ''εἰμί'' is ἐσ-. Recall the ''athematic'' personal endings of the present active indicative, and note the spelling changes that occured: {| class="wikitable" |'''Number''' |'''Person''' |'''Greek''' |'''English''' |- |'''Singular''' |1st |εἰμί |I am |- | |2nd |εἶ |You are |- | |3rd |ἐστί |He/she/it is |- |'''Plural''' |1st |ἐσμέν |We are |- | |2nd |ἐστέ |You are |- | |3rd |εἰσίν |They are |- |'''Infinitive''' | - |εἶναι |To be |} [[Category:Ancient Greek Language]] 48mz9wjvqzdnuoqu6xz5ht22jqhbssb 5 247450 2823764 2793078 2026-08-21T00:05:52Z Codename Noreste 2969951 /* Split "Requests for Undeletion" from this page? */ new section 2823764 wikitext text/x-wiki Please see the [[/Archive]] for past discussions. == Course clean-ups == I wonder whether we are in favour of course clean-ups. It means someone is updating a course, which is actually a multipage resource, and they decide they no longer need some pages. Do we encourage them to keep it and improve it, or do we allow them to delete it? If so, it's pretty tough for custodians, as tools for mass deletion aren't installed on en.wv. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 14:36, 18 February 2026 (UTC) == Split "Requests for Undeletion" from this page? == Currently, this page is for both deletion and undeletion requests, but I would like to propose splitting a new page ([[Wikiversity:Requests for Undeletion]]) solely to better handle undeletion requests using a separate, dedicated page instead of using this page. [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:05, 21 August 2026 (UTC) ikewiax889d9k9y1dv0u7v5moyhu6vl 2823823 2823764 2026-08-21T04:40:43Z Jtneill 10242 /* Split "Requests for Undeletion" from this page? */ reply: Makes sense to me (-) ([[mw:c:Special:MyLanguage/User:JWBTH/CD|CD]]) 2823823 wikitext text/x-wiki Please see the [[/Archive]] for past discussions. == Course clean-ups == I wonder whether we are in favour of course clean-ups. It means someone is updating a course, which is actually a multipage resource, and they decide they no longer need some pages. Do we encourage them to keep it and improve it, or do we allow them to delete it? If so, it's pretty tough for custodians, as tools for mass deletion aren't installed on en.wv. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 14:36, 18 February 2026 (UTC) == Split "Requests for Undeletion" from this page? == Currently, this page is for both deletion and undeletion requests, but I would like to propose splitting a new page ([[Wikiversity:Requests for Undeletion]]) solely to better handle undeletion requests using a separate, dedicated page instead of using this page. [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:05, 21 August 2026 (UTC) : Makes sense to me -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 04:40, 21 August 2026 (UTC) 7caelec2w4rlq7kx0emuowqzl66sfa8 2823831 2823823 2026-08-21T05:23:41Z Atcovi 276019 /* Split "Requests for Undeletion" from this page? */ Reply 2823831 wikitext text/x-wiki Please see the [[/Archive]] for past discussions. == Course clean-ups == I wonder whether we are in favour of course clean-ups. It means someone is updating a course, which is actually a multipage resource, and they decide they no longer need some pages. Do we encourage them to keep it and improve it, or do we allow them to delete it? If so, it's pretty tough for custodians, as tools for mass deletion aren't installed on en.wv. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 14:36, 18 February 2026 (UTC) == Split "Requests for Undeletion" from this page? == Currently, this page is for both deletion and undeletion requests, but I would like to propose splitting a new page ([[Wikiversity:Requests for Undeletion]]) solely to better handle undeletion requests using a separate, dedicated page instead of using this page. [[User:Codename Noreste|<span style="color: blue">Codename Noreste</span>]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:05, 21 August 2026 (UTC) : Makes sense to me -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 04:40, 21 August 2026 (UTC) :+1 —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 05:23, 21 August 2026 (UTC) 46424vta3w8gcbudf30min9954p1nsp 0 261500 2823862 2821755 2026-08-21T10:52:59Z Cmglee 291664 Add [[File:Galilean_moon_Laplace_resonance_animation_2.svg]] 2823862 wikitext text/x-wiki [[File:Magnetic field element (Biot-Savart Law) r1r2.svg|thumb|Shows differential for integrating Biot-Savart Law|175px]] [[File:Rail gun.jpg|thumb|File:Rail gun.jpg|175px]] [[File:Electromagnetic momentum archery analogy.svg|thumb|Electromagnetic momentum archery analogy|175px]] [[File:Fala plaska 3d.gif|thumb|175px]] [[File:International System of Units Logo.png|thumb|175px]] [[File:Divergence theorem example.svg|thumb|175px]] [[File:Fourier Series Square Wave.svg|thumb|The first four terms of the Fourier series of a square wave, <math>\psi(x) = \frac 4 \pi \sin(\pi x)</math> <math>+\frac 4 {3\pi} \sin(3\pi x)</math> <math>+\frac 4 {5\pi} \sin(5\pi x)</math> <math>+\frac 4 {7\pi} \sin(7\pi x) +\ldots</math><math>=\sum_{\text{odd }n=1}^\infty \frac 4 {n\pi} \sin(n\pi x)</math>. |175px]] [[File:String wave linear lumped mass spring.svg|thumb|Figure for calculating wave equation for transverse string waves|175px]] [[File:Shannon entropy 5 coin illustration.svg|thumb|Five fair coins to illustrate the additive property of Shannon's information entropy|175px]] [[File:Entropy wheel of fortune.svg|thumb|Shannon's entropy for unfair coin|175px]] [[File:3-el permutation counting decisions.svg|thumb|Establishes that 3 items have 3!=6 permutations.|175px]] [[File:5-take-3 Crows-A.svg|thumb|5 choose 3 versus permutation of ordered set of five objects.|175px]] <noinclude>{{:User:Guy vandegrift/T/Title}}</noinclude> <gallery> Lens and wavefronts.gif|Lens and wavefronts.gif Partial transmittance.gif|Partial transmittance.gif Snells law wavefronts.gif|Snells law wavefronts.gif Two sources interference.gif|Two sources interference.gif Wave equation 1D fixed endpoints.gif|Wave equation 1D fixed endpoints.gif Exp series.gif|Exp series.gif Atomic-orbital-clouds spd m0.png|Atomic-orbital-clouds spd m0.png Bohr atom model (mul).svg|Bohr atom model (mul).svg Hydrogen Density Plots.png|Hydrogen Density Plots.png AirShower.svg|AirShower.svg Aurore australe - Aurora australis.jpg|Aurore australe - Aurora australis.jpg Alfa beta gamma radiation penetration.svg|Alfa beta gamma radiation penetration.svg Rays_of_light_through_a_different_medium_(labelled).svg|Rays_of_light_through_a_different_medium_(labelled).svg Coupled oscillators.gif|Coupled oscillators.gif Mode Shape of a Tuning Fork at Eigenfrequency 440.09 Hz.gif|Mode Shape of a Tuning Fork at Eigenfrequency 440.09 Hz.gif Simple harmonic motion animation 1.gif|Simple harmonic motion animation 1.gif Heisenberg microscope with wavefronts and electron scatter.svg|Heisenberg microscope with wavefronts and electron scatter.svg Wave-particle duality.gif|Wave-particle duality.gif Circlestrafing animation.gif|Circlestrafing animation.gif Rolling Racers - Moment of inertia.gif|Rolling Racers - Moment of inertia.gif Model of the initiation of termination of a Rayleigh-Taylor instability in 2D.gif|Model of the initiation of termination of a Rayleigh-Taylor instability in 2D.gif Karman Vortex street ani.gif|Karman Vortex street ani.gif Mars Loop.gif|Mars Loop.gif Zirkumpolar ani.gif|Zirkumpolar ani.gif Tuned circuit animation 3 400ms.gif|Tuned circuit animation 3 400ms.gif Dipole.gif|Dipole.gif Brachistochrone.gif|Brachistochrone.gif Halley's Comet animation.gif|Halley's Comet animation.gif Galilean moon Laplace resonance animation 2.gif|Galilean moon Laplace resonance animation 2.gif Galilean_moon_Laplace_resonance_animation_2.svg|Plot of vertical position ''y'' vs time ''t'' of animation above Surface chemical diffusion.gif|Surface chemical diffusion.gif InfiniteSquareWellAnimation.gif|InfiniteSquareWellAnimation.gif Karman trefftz.gif|Karman trefftz.gif Mouvement dans une vague en eau peu profonde.gif|Propagation du tsunami en profondeur variable.gif Propagation du tsunami en profondeur variable.gif|Propagation du tsunami en profondeur variable.gif Vortex-street-animation.gif|Vortex-street-animation.gif Maxwell's demon.svg|Maxwell's demon.svg Ergodic hypothesis w reflecting rays.svg|Ergodic hypothesis w reflecting rays.svg Proving Carnot Theorem.svg|Proving Carnot Theorem.svg Fizeau experiment schematic.svg|Fizeau experiment schematic.svg Stellar aberration illustration.svg|Stellar aberration illustration.svg Entropy flip 2 coins.jpg|Entropy flip 2 coins.jpg Earth-moon-field.svg|Earth-moon-field.svg Van de graaf generator.svg|Van de graaf generator.svg WestinghouseAtomSmasher.jpg|WestinghouseAtomSmasher.jpg Electric Bell animation.gif|Electric Bell animation.gif Faraday cage.gif|Faraday cage.gif Leaderlightnig.gif|Leaderlightnig.gif Stages of how a photocopier works.png|[[wikibooks: Electronics/Photocopier]] File:Simple harmonic motion animation 2.gif|File:Simple harmonic motion animation 2.gif File:Fourier series and transform.gif </gallery> [[Category:MyOpenMath]] jokt4hy5u67prrckjn648ozqsyus0t8 0 264724 2823684 2823224 2026-08-20T16:41:47Z Scogdill 1331941 2823684 wikitext text/x-wiki {{Short description|Dress worn by Queen Victoria at her wedding to Prince Albert in 1840}} = Sandbox = Page to draft revisions for Wikipedia articles. For Gwladys Robinson, see Gwladys Lowther Robinson, [[Social Victorians/People/Ripon|Marchioness of Ripon]] and, earlier, [[Social Victorians/People/Lowther|Countess of Lonsdale]] ==References== {{reflist|2}} [[Category:1840 works]] [[Category:Royal wedding dresses|Victoria Queen]] [[Category:1840s fashion]] [[Category:British royal attire]] [[Category:Dresses in the Royal Collection of the United Kingdom|Victoria, Wedding]] [[Category:Diamond Jubilee of Queen Victoria]] = Victorian fashion = '''Victorian fashion''' consists of the various fashions and trends in [[Culture of the United Kingdom|British culture]] that emerged and developed in the [[United Kingdom of Great Britain and Ireland|United Kingdom]] and the [[British Empire]] throughout the [[Victorian era]], roughly from the 1830s through the 1890s. The period saw many changes in fashion, including changes in styles, fashion technology and the methods of distribution. Various movements in architecture, literature, and the [[decorative arts|decorative]] and [[visual arts]] as well as a changing perception of [[gender roles]] also influenced fashion. Under [[Queen Victoria]]'s reign, England enjoyed a period of growth along with technological advancement. [[Mass production]] of sewing machines in the 1850s as well as the advent of synthetic dyes introduced major changes in fashion.<ref name=":3">{{Cite book|title=The Culture of Fashion|last=Breward|first=Christopher|publisher=Manchester University Press|year=1995|pages=145–180}}</ref> Clothing could be made more quickly and cheaply. Fashion made more extreme and more rapid changes than it had in prior centuries. Advancement in printing and proliferation of fashion magazines allowed the masses to participate in the evolving trends of high fashion, opening the market of mass consumption and advertising. By 1905, clothing was increasingly factory made and often sold in large, fixed-price department stores, spurring an age of consumerism with the rising middle classes, who benefited from the [[Industrial Revolution|industrial revolution]].<ref name=":3" /> ==Women's fashions== [[File:Fashions.jpg|thumb|upright|Illustration depicting fashions throughout the 19th century]]During the [[Victorian era|Victorian Era]], women generally inhabited the private, domestic sphere.<ref>{{Cite web|url=https://www.bl.uk/romantics-and-victorians/articles/gender-roles-in-the-19th-century|title=Gender roles in the 19th century|website=The British Library|access-date=2016-10-21|archive-date=8 July 2022|archive-url=https://web.archive.org/web/20220708075142/https://www.bl.uk/romantics-and-victorians/articles/gender-roles-in-the-19th-century|url-status=dead}}</ref> Unlike in earlier centuries when women labored with their husbands and brothers or worked in family businesses, during the nineteenth century, gender roles became more rigidly defined. Farm labourers was no longer in such a high demand after the [[Industrial Revolution]], and women were more likely to perform domestic work or, if married, give up paid work entirely. Dress reflected these new lifestyles, and was, for the middle and upper classes, less utilitarian.<p> Clothes were seen as an expression of women's place in society<ref>{{Cite book|title=Victorian and Edwardian Fashion - A Photographic Survey|last=Gernsheim|first=Alison|publisher=Dover Publications Inc.|year=1963|location=New York|pages=26}}</ref> and were differentiated by [[social class]]. Most women wore a [[corset]] over a [[chemise]], followed by a gown or [[skirt]] paired with a [[bodice]], [[blouse]], or [[chemisette]]. The shape of the skirt would be supported by layers of petticoats or, later in the period, structured support such as cage crinolines or bustles. The clothing of [[Upper class|upper-class women]], who generally did not do paid labor, was often elaborately decorated with more layers and [[Trim (sewing)|trims]]. [[Middle class|Middle-class women]] wore less complex dress styles with less expensive trim. [[Working class|Working-class]] clothing was simpler still, with less expensive fabric, fewer layers still and little trim. Including the undergarments, the amount of fabric in women's clothing made it much heavier and the construction made it much more restrictive than ours, especially in the waist (due to the boning in the corset) and the shoulders (due to the popularity of dropped shoulder seams). The amount, quality and type of fabric were displays of wealth and status.<p> Throughout the 19th century, journalism targeting women increased enormously and addressed an increasingly more class-diverse audience. According to the ''Dictionary of Nineteenth-Century Journalism'',<blockquote><p> The closely allied fashion and women's journals can be divided into three phases: titles such as the ''Lady's Magazine'' continued eighteenth-century models, addressing readers as "ladies" and catering to a leisured, fashionable elite; a more domesticated format by the 1840s, targeting middle-class women with instructive and entertaining content including dressmaking and etiquette articles ...; finally, from the 1870s, a livelier, more engaging style of fashion reporting influenced by the New Journalism was integrated with an increased amount of imagery, including better quality fashion plates ....<ref>{{Cite book|title=Dictionary of Nineteenth-Century Journalism In Great Britain and Ireland|last=Beetham|first=Margaret Rachel|last2=A|first2=R|publisher=Academia Press and the British Library|year=2009|editor-last=Brake|editor-first=Laurel, and Marysa Demoor|location=Gent|pages=215a–c|chapter=Fashion Journals}}</ref></blockquote>By the end of the century, women's periodicals were including patterns for dressmaking in their pages, reflecting the presence of middle- and working-class readers as well as technological change like sewing machines for home use and mass-produced fabrics and trim.[[File:1837 Dress.jpg|alt=This dress features a low waistline, and the bodice is worn over the hips to further emphasise the silhouette|thumb|upright|An undressed woman In 1837, featuring a fashionable hairstyle, busked corset, and layers of petticoats.]]It is important not to oversimplify the fashion of the Victorian age. The rate of change in fashion accelerated in the 19th century to the point that styles were distinctly different from one decade to the next (see "When Was That Dress in Fashion?", above right). The styles of Elizabethan England, in contrast, changed much less extremely over the course of a century. The most important characteristics for the analysis of 19th-century fashion include silhouette or line, corsets or stays, the neckline and the sleeves. The silhouette in particular but also the color, the variety of available fabrics and the distribution of information and opinion about fashion were the result of [[Social Victorians/People/Gwladys Robinson#Technological advancement|technological changes]] made throughout the century, but centering in the 1850s.[[File:The Engageants sleeves.jpg|thumb|Engageants, worn to fill open sleeves, were made of light fabrics like lace, linen, lawn or cambric.]] * '''Silhouette''': Silhouette changed over time supported by the evolution of the foundation garments. In fact the line or silhouette of garments changed about every ten years. Just as outer clothing changed, foundation garments were also modified to give the wearer a different silhouette. Over the course of the century most Europeans and some in their colonies wore the same kinds of undergarments and similar outer garments. For example, wide skirts were supported by layers of petticoats that used woven horsehair to stiffen them.<ref>{{Cite web |title=Corsets, crinolines and bustles: fashionable Victorian underwear · V&A |url=https://www.vam.ac.uk/articles/corsets-crinolines-and-bustles-fashionable-victorian-underwear |access-date=2025-10-27 |website=Victoria and Albert Museum |language=en}}</ref> By 1856 the [[Crinoline|cage crinoline]] (a domed structure using steel bands and wires) replaced the petticoats, making the skirts lighter in weight and easier to walk in. The line of the outer garments was influenced by how full the skirt was, how small the waist was and its location relative to the natural waistline, how the sleeves were shaped, and how deep the neckline went. * '''Corsets''': [[Corset]]s or stays were ubiquitous, providing adjustable bust and posture support, helping to shape the body into the fashionable silhouette and preventing horizontal creasing in the bodice. Foundation garments were constantly evolving throughout the century. Over the course of the century, almost all women and some men wore corsets. After the late 1850s, an individual could lace a corset without help.<ref name=":24">{{Cite book|title=Victorian Fashions for Women|last=Kay|first=Fiona|last2=Storey|first2=Neil R.|publisher=Pen & Sword History|year=2022|isbn=978 1 39900 416 9|location=Yorkshire and Philadelphia|pages=30-31}}</ref> Most corsets were constructed with a busk, "(a flat length of whalebone, wood or steel) inserted in a channel down the centre to smooth out the front of the dress."<ref>{{Cite book|title=Victorian Fashions for Women|last=Kay|first=Fiona|publisher=Storey|year=Neil R.|isbn=978 1 39900 416 9|location=Yorkshire and Philadelphia|pages=13}}</ref> The drawing of an undressed woman (above right) shows a self-laced corset with what may be a split busk. * '''Neckline''': Necklines changed over the course of the century as bodices and sleeves evolved. The less formal daywear had a higher neckline, regardless of class and decade. For formal wear, which varied widely by class and kind of event, the neckline was often lower and off the shoulder and finished with a [[Collar (clothing)|bertha]] (lace collar or flounce) or multiple bands of fabric pleats. This [[décolletage|décolleté evening style]] popularized shawls or [[cape]]lets and required a [[Corsets|corset]] without shoulder straps. The fashion was for dressmakers to produce two bodices with each skirt, one closed décolletage for day and one décolleté for evening. * '''Sleeves''': Over the course of the century, styles in sleeves changed radically and more than one sleeve style was fashionable at the same time. Some of the most popular styles included gigot, pagoda, ''engageants'' (see right), bishop and leg-of-mutton sleeves. The changes were in the [[armscye]], the wrist treatment, and the fullness at the shoulder, elbow and wrist. For example, as [[crinoline]]s began to appear in the 1850s, sleeves were shaped like large bells known as pagoda sleeves. [[Engageante]]s, or false sleeves, were stitched inside full or open sleeves like pagoda sleeves. They were easy to remove, launder and restitch into position. Even though the changes in fashion over the century were sometimes rapid and extreme, they were also evolutionary.[[File:Dress - MET 1971.47.3a–e.jpg|thumb|English day dress, c. 1836, with bow details and puffed sleeves]] === 1830s dress style === [[File:Princess Victoria and Dash by George Hayter.jpg|alt=Old portrait of a teenage girl in a white formal dress, with a dog|thumb|Princess Victoria and her dog Dash, 1833|left]]During the beginning of Queen Victoria's reign in 1837, the fashionable silhouette was an hourglass shape with wide shoulders, emphasized by puffed [[gigot sleeves]], a full skirt, and a slim waist. Corsets were extended over the abdomen and down towards the hips, and worn with a busk.<ref name=":0">{{Cite book|title=From Queen to Empress - Victorian Dress 1837-1877|last=Goldthorpe|first=Caroline|publisher=The Metropolitan Museum of Art|year=1988|location=New York|pages=23–24}}</ref> A chemise was worn under the corset and cut relatively low in the neck so that it could not be seen. Over the corset was a tight-fitting bodice featuring a high, straight waistline. Under the ankle-length skirt were layers of petticoats<ref name=":0" /> stiffened with horsehair. (Skirts would not be extremely full for another two decades.) To contrast with the narrow waist, necklines were low and wide. Queen Victoria's 1833 white dress (left) shows an off-the-shoulder neckline, a higher waist and an ankle-length skirt held out by horsehair. The c. 1836 yellow day dress (right) shows gigot sleeves, a higher neckline and a skirt held out by petticoats. Always a mark of wealth and status, Princess Victoria's white dress shows that she is formally dressed, perhaps for court, although the pose itself suggests some informality as well. === 1840s dress style === The 1840s saw an increase in domestic magazines targeting women, along with new varieties in the weave of ready-made fabrics as well as new and much more vibrant colors because of the invention of aniline dyes. And the industrial revolution supplied women with more varieties of color and weave in ready-made fabrics. Cotton replaced silk as a basic fabric, especially among middle-class women because silk was expensive, limiting who could afford it. The elements of fashion changed rapidly during this transitional decade.[[File:Magasin för konst, nyheter och moder 1844, illustration nr 8.jpg|thumb|1844 [[fashion plate]] depicting fashionable clothing for men and women, including illustrations of a [[glove]], a fanchon, and [[Bonnet (headgear)|bonnets]]]]At the beginning of the 1840s, skirts began to widen and become dome shaped (because the skirt pieces changed from rectangles to gores, which are wider at the bottom). The waistline lowered with a point formed at the bottom of both the bodice and corset, which gave a rather rigid look to the silhouette. During this decade, the amount of trim decreased in general, although trim was still plentiful. In addition to the flowers, feathers, and ribbons many of the decorations on the dress were made of the fabric of the dress (tucks and pleats, flounces, ruffles). At the end of the decades waists rose to the natural waistline.[[File:Woman's_Dress_LACMA_M.2007.211.744_(1_of_7).jpg|left|thumb|English silk day dress of the second half of the 1840s, with dropped shoulder seams, tight sleeves, and a pointed waist.]]Although corsets narrowed the bodices and gave them a point in the early 1840s, by the end of the decade, they returned to the natural waistline. Corsets lost their straps by the end of the decade.  Busks in the front of the corset were split by Jean Julien Joselin in 1829, () but the corset wouldn’t stay closed until 1848 when Joseph Cooper patented the "slot and stud" which is still in use today.<ref name=":24" /> (75 [of 298]) Necklines remained wide with further use of lace berthas to frame the upper body. At the end of the decade, necklines were raised and remained high. Dresses were stiffer due to boning in the bodice as well as the corset. Skirts lengthened, while in 1847 widths increased with the introduction of the [http://3.bp.blogspot.com/-bOuPyjWzwT8/TuKx-x1R12I/AAAAAAAAAF0/oRs6AyGH0gw/s1600/CI53.51.15_B1870Amer.Horsehair.jpg horsehair crinoline], which was stiffened with horsehair and starch. The petticoats were numerous and became bulky and heavy and sometimes entangled the feet. Petticoats had another disadvantage: the number of waistbands increased with each additional petticoat. Skirts often had one or two flounces at the bottom that increased the look of fullness (see, for example, the 1844 fashion plate, right). To achieve the narrow waist, skirts were attached to bodices using very tight organ [[pleat]]s secured at each fold.<ref name=":1">{{Cite book |last=Goldthorpe |first=Caroline |title=From Queen to Empress - Victorian Dress 1837-1877 |publisher=The Metropolitan Museum of Art |year=1988 |location=New York |pages=32}}</ref> . Sleeves narrowed with smaller decorative additions (see, for example, the English silk day dress, left). They eventually widened at the wrists into open pagoda-type sleeves requiring engageants to cover the forearms. Shawls were used to convert a simple dress into a more formal outfit. The popularity of shawls grew because of the very soft and beautifully dyed and woven cashmere shawls from India with a paisley design (after the Scottish town that manufactured shawls).<ref name=":24" /> (48 [of 298]) Head coverings were ''de regeur'', dominated by poke bonnets.<ref name=":24" /> (51 [of 298]) (The mannequin in the English silk day dress, above left, is wearing a poke bonnet.) Cosmetics became more popular, with instructions The Handbook of the Toilette (anonymous, many editions beginning in 1839. Unfortunately many contained toxic elements like calcium oxide (or quicklime) found hair dye that was recommended to stay in the hair for 3 to 8 hours.<ref name=":24" /> (47 [of 298]) By the end of the 1840s skirts were more dome shaped, necklines were higher and wider and sleeves broadened at the bottom. === 1850s dress style === The 1850s saw revolutionary [[Social Victorians/People/Gwladys Robinson#Technological advancement|changes in technologies]] affecting the manufacture and consumption of clothing, especially * the mass production of fabrics * the invention of synthetic dyes * the manufacture of inexpensive, flexible and lightweight steel * the invention of a sewing machine that could be used in the home * the spread of fashion journalism and journalism for women According to the ''Dictionary of Nineteenth-Century Journalism'', "The 1850s and 1860s saw the eclipse of the older ladies' journals [that began in the 18th century and targeted upper-class women] and the emergence of the magazine for middle-class ... women."<ref>{{Cite book|title=Dictionary of Nineteenth-Century Journalism In Great Britain and Ireland.|last=Beetham|first=Margaret Rachel|publisher=Academia Press and the British Library|year=2009|editor-last=Brake|editor-first=Laurel, and Marysa Demoor|location=Gent|pages=683–684|chapter=Women's Periodicals}}</ref> (684) Nine fashion magazines were being published in London by 1850 and fourteen by 1859 as part of the burgeoning collection of magazines for women, both domestic magazines aimed at middle-class women and journalism focused mostly on fashion.<ref name=":24" /> (63 [of 298]) The journalism aimed at middle-class women introduced haute couture, making the styles, names of couturiers and fashion houses familiar to them for the first time. These technological changes were revolutionary because of the impact they had on fashion over the course of the rest of the century. Their impact on fashion arises largely because most women were taught a wide range of seamstress skills and, due to reforms in education over the century, more women could read.[[File:Ensemble_MET_DT6845.jpg|thumb|A day ensemble c. 1855, featuring tiers of ruffles and pagoda style sleeves.]] ==== Silhouette ==== The 1850s are considered a transitional decade in 19th-century fashion because little changed in the silhouette and appearance of clothing, but technological changes would make increasingly important structural differences in what was available for people to wear. Skirts widened with the disappearance of the many layers of petticoats but did not change their basic shape. Beyond the silhouette, the design elements of the dress (like sleeves, neckline, or skirt) were barely changed as they evolved from the 1840s to the 1860s. While the silhouette and elements of design did not change significantly, the effect of the technological changes related to the manufacture and consumption of clothing was to give individual (and especially middle-class women) more agency over how their dresses got made and who made them, what fabrics their dresses were made of, how broad a range of options they could choose from and how easy it was to move in their dresses. The number of flounces and ruffles on the skirt increased, making the skirt look wider (see the c. 1855 day ensemble, right). ==== Neckline ==== [[File:1850's Evening Dress.jpg|thumb|1850s evening dress with a bertha|left]] With trim and a front closure in the corset and the bodice, the bodice emphasized a distinct V-shape. Necklines of day dresses were sometimes cut into a V-shape, causing a need to cover the bust area with a chemisette. For evening, a wide, low neckline was popular, often with a [[Collar (clothing)|bertha]] (see the 1850s even dress with a bertha, left).<ref name="h608">{{cite book |last=Arnold |first=Janet |title=Patterns of fashion. 2: Englishwomen's dresses and their construction: 1860 - 1940 |date=1993 |publisher=MacMillan |isbn=978-0-89676-027-1 |publication-place=London |page=}}</ref> ==== Sleeves ==== Pagoda sleeves and under sleeves (''engageants'') continued to be popular for most of the decade. ==== Foundations ==== [[File:1856 Cage Crinoline.jpg|alt=1st patented cage crinoline.Fullness of the skirt is even further emphasised.|thumb|1850s fashionable silhouette and the cage crinoline needed to support it.]] In 1856, the invention of the first [[Crinoline|cage crinoline]] allowed for even wider skirts. The cage crinoline was constructed by joining thin metal strips together with wires to form a circular cage-like structure that could support a very wide skirt (see 1950s silhouette and cage crinoline, right). Although often ridiculed by journalists and cartoonists of the time as the crinoline swelled in size, this innovation freed women from the heavy weight of petticoats.<ref name=":4">{{Cite book |last=Steele |first=Valerie |url=https://archive.org/details/fashioneroticism0000stee |title=Victorian Fashion. Fashion and Eroticism: Ideals of Feminine Beauty from the Victorian Era to the Jazz Age |publisher=Oxford University Press |year=1985 |isbn=978-0-19-503530-8 |pages=[https://archive.org/details/fashioneroticism0000stee/page/51 51]–84 |url-access=registration}}</ref> For a description of the [[Social Victorians/People/Gwladys Robinson#Technological advancement|technological advancement]] that made cage crinolines possible, see below.) Not visible on the outside garment, the cage crinoline was the foundation for the huge dome-shaped skirts that dominated the decade. It was safer and easier to walk in a cage because the hoops held the skirt away from the feet and legs of the wearer. Without the innumerable petticoats more women began to wear drawers or "pantalettes" for modesty and warmth. The dome shape made possibly by the cage foundation changed the way skirts were cut. Instead of rectangles, gores were cut with one end of the skirt piece wider than the other end,<ref name="w586">{{cite book |last=Arnold |first=Janet |title=Patterns of fashion. 2: Englishwomen's dresses and their construction: 1860 - 1940 |date=1993 |publisher=MacMillan |isbn=0-333-13607-1 |publication-place=London |page=}}</ref> preventing bulkiness at the waist from gathered fabric and created a skirt bottom much wider than the top. Bloomers, designed by Amelia Jenks Bloomer,  introduced bifurcated garments for women. These were essentially trousers or pants with a seam between the legs. Even in pantalettes there was no seam between the legs; it was simply left open. This experiment failed and women didn’t wear pants until the 20th century. The 1850s saw two other developments that permanently changed the clothing available to Victorian women (and men). Created in 1856, the first synthetic dyes were much more vivid and vibrant than natural dyes and resisted fading.<ref name=":24" /> (92 [of 298]) Because Victorian photography was black and white, we do not typically see the gaudy and saturated colours that many Victorians loved.<ref name=":3" /> Also, although sewing machines had already been invented, changing the accessibility and value of individual articles of clothing, it was the invention of and widespread sale of "lightweight domestic machines" for home sewing that affected large numbers of women.<ref name=":24" /> (91 [of 298]) Cage crinolines remained popular for perhaps 5 years among the fashion forward and perhaps 10 years for the less adventurous.[[File:Woman's_silk_taffeta_dress_c._1865.jpg|thumb|An 1865 English silk morning dress.]] [[File:Mrs_Ellinor_Guthrie_by_Frederic_Leighton.jpg|thumb|English dress, 1864, with simple trim.]] === 1860s dress style === ==== Foundations ==== The cage crenoline reached the peak of its width during the 1860s. Photographs show that the fashion-forward Empress Eugénie of France, Empress Elisabeth of Austria and Countess Pauline von Metternich had stopped wearing the very large crinoline cages as early as 1862, but most middle- and upper-class women (including Queen Victoria) wore them for much of the rest of the decade. During the first half of the 1860s, crinolines began decreasing in size at the top, while retaining their volume at the bottom, creating a more pyramidal shape.<ref name=":2">{{Cite book|title=From Queen to Empress - Victorian Dress 1837-1877|last=Goldthorpe|first=Caroline|publisher=The Metropolitan Museum of Art|year=1988|location=New York|pages=26}}</ref> Then the fullness began to move to the back while the front became flat and close to the body. As the back fullness increased, skirts sometimes lengthened into trains. (The 1865 English silk dress, above right, shows the flattening of the front at the waist and the development of the train). In order to emphasize the back, the train was gathered together to form soft folds and [[Drapery|draperies]].<ref>{{Cite book|title=Making Victorian Costumes for Women|last=Audin|first=Heather|publisher=Crowood|year=2015|pages=45}}</ref> This line or silhouette would eventually evolve into a bustle in the next decade. Decoration or trim often appeared only at the bottom of the skirt (see English dress, 1864, below right). Flounces and ruffles diminished as geometric designs in trim began to be quite popular.<ref name=":24" /> (102 [of 298]) Skirts were also decorated with overskirts of the same fabric or a different shade of the same color. Waistlines were pointed in front below the natural waistline. By mid-century the waist was seated at the natural waistline often with a wide belt and large decorative buckle.   ==== Bodices and Sleeves ==== Bodices often had buttons down the front as both the corset and the bodice opened in the front. Necklines were generally high and rounded. Some dresses were cut without separating the bodice and skirt so it could be buttoned from the neck to the bottom of the skirt. It became popular for dresses to be made as one skirt and two bodices, one for day wear and one for formal wear.<ref name=":0" /> (43) Sleeves narrowed but remained loose on the arms and went down to the wrist. Sometimes there might be more fullness at the shoulder but not very puffed. Dresses were made to accommodate the more active life women had in sports, walking and even riding bicycles. ==== General Trends ==== Even more fabrics were available and the richer middle class was striving for acceptance among the aristocracy. Silk was still essential in the dress of wealthy middle- and upper-class women. What was new about clothing construction during this transitional decade was how clothing was cut and pieced together, which gave the wearer more freedom of movement. The trends that began in the 1860s continued through the 1870s and into the 1880s; change was evolutionary.[[File:Black_net_ball_dress_1874.png|thumb|A black net ball dress, 1874]] === 1870s dress style === ==== Silhouette ==== The silhouette was not consistent during the 1870s because of the shape of the bustle, the addition of an overskirt and the layers of the polonaise. Foundation garments changed very little. Perhaps the greatest change came in corsets. In 1870 women were wearing corsets that came to just below the waist with a pointed center front. By 1879 corsets were being built using ‘princess’ seams to support the tailoring of the smooth, straight dresses so popular among the women who followed the fashion set by Paris. In 1877, dresses moulded to fit the figure,<ref name=":2" /> as increasingly slimmer silhouettes were favored. Although dress styles took on a more natural form, corsetry was still required and the train was often supported with a cage. The armscye, for the first time in the period, moved from a dropped position up to the shoulders and would remain there for the rest of the era. ==== Skirts ==== [[File:Woman's_Polonaise_Dress_LACMA_M.2007.211.777a-f_(1_of_4).jpg|left|thumb|An c. 1875 English polonaise]]The trend for broad skirts slowly disappeared during the 1870s, as women started to prefer a slimmer silhouette. Skirts went from their most extreme width to their most narrow, waists went to a natural level and the backside took the point of interest in the ensemble. The back of the dress became the focal point of the design. The skirt began the decade rather flat in front with most of the fabric pulled to the back. At first it was simply gathered and draped toward the backside. It evolved into bunching the extra fabric to placing a pad on the hips for supporting the extra fabric to inventing a tournure or bustle in order to keep in place the elaborate draping of the back of the skirt and train. Extra fabric was gathered together behind in pleats, thus creating a narrower but longer tiered, draped train too. Due to the longer trains, petticoats had to be worn underneath in order to keep the dress clean. (The bustle on the 1874 black net ball dress, right, has been gathered and bunched and would require padding to keep the draping in place. It also has an overskirt.) [[overskirt|Overskirts]] became extremely popular, often tied up into an apron effect at the front with a [[Polonaise (clothing)|polonaise]] or puffed draperies at the back.<ref name="g4223">{{cite book |last=Cunnington |first=Cecil Willett |title=English Women's Clothing in the Nineteenth Century |date=1990-05-01 |publisher=Courier Corporation |isbn=0-486-26323-1 |publication-place=New York |page=}}</ref> A polonaise is a garment featuring both an overskirt and bodice often of the same fabric (see c. 1875 English polonaise, below left). Over time, the overskirt shortened into a detached [[Basque (clothing)|basque]], resulting in an elongation of the bodice over the hips. The [[tournure]] was also introduced, and along with the polonaise, it created an illusion of an exaggerated rear end. (The early 1870s fashion plate, below right, shows an assortment of ways overskirts were worn, including one for a girl.)[[File:1870's Dress.jpg|alt=Dresses featuring the Bustle & Polonaise|thumb|An early 1870s fashion plate]] ==== Neckline ==== Necklines were high and lines were sleek and fitted. Sewing a curved seam from the shoulder to the skirt bottom was the ‘princess line’ tailoring technique that was named after the new wife of the Prince of Wales, Princess Alexandra. Since Queen Victoria had been in mourning for so long, the princess was expected to lead in the haute couture of the day. She set a trend for tailored dresses that was quickly picked up by all classes.   ==== Sleeves ==== Pagoda sleeves began to lose their three-decade popularity in 1875,<ref name=":24" /> (102 [of 298]) but most sleeve treatments had narrowed the sleeves, which came to the wrist. Fringe became one of the most used decorative elements along with ribbon, braid, ball fringe, ruching, epaulettes, pieces of the same fabric in a lighter or darker shade, pieces of a different-textured fabric like velvet or velveteen, etc. ==== General Trends ==== An unusual trend occurred during the 1870s in hairstyles. Hairstyles grew to a very large placement of braids, buns, coils, poufs, and strands. Although women had been supplementing their own hair with someone else’s hair, the human hair market erupted. The elaborate hairstyles required multiple hair pieces and the tiny, over-decorated hats perched almost vertically on the head. The practice of constructing two bodices (one for day and one for evening wear) and one skirt for a dress continued from the 1860s. === 1880s dress style === [[File:1885 Bustle.jpg|alt=Horizontal protrusion at the back.|thumb|The lobster tail bustle of around 1885.]] The saw the growing popularity of austere, menswear inspired tailoring.<ref name=":4" /> Some credited the change in silhouette to the [[Victorian dress reform]], which consisted of a few movements including the [[Artistic Dress movement|Aesthetic Costume]] Movement and the [[Victorian dress reform|Rational Dress Movement]] in the mid-to-late Victorian Era advocating for a natural silhouette and lightweight underwear, and rejecting [[tightlacing]]. However, these movements did not gain widespread support. Others noted the growth in cycling and tennis as acceptable feminine pursuits that demanded a greater ease of movement in women's clothing.<ref name=":3" /> Still others argued that the growing popularity of tailored semi-masculine suits was simply a fashionable style, and indicated neither advanced views nor the need for practical clothes.<ref name=":4" /> [[File:Edward_Hughes_-_Juliette_Gordon_Low_-_Google_Art_Project.jpg|left|thumb|An 1887 portrait of English evening dress with higher shoulder placement, simple trims, and a V-shaped neckline.]] After a period of slim, train-less skirts with heavy decoration, the bustle made a re-appearance in 1883, and it featured a further exaggerated horizontal protrusion at the back. Due to the additional fullness, drapery moved towards the sides or front panel of the skirt instead. Bodices shortened, now ending above the hips. Skirts were much less full than the last time the bustle was in fashion in the 1870s and instead focused on a slim front with a shelf-like back protrusion. Sleeves of bodices were thinner and tighter, while necklines became higher again, with a high collar being ubiquitous for daytime, a trend that would continue into the 1890s. For the evening, the bertha fell out of favor, replaced by V-shaped necklines or draped styles due to the new higher shoulder.<ref name="g4223"/> Sleeves tightened again during the [[1880s in Western fashion|1880s]] and the armscye moved back up the shoulders.<ref name="y040">{{cite book |last=Severa |first=Joan L. |title=Dressed for the Photographer |date=1995 |publisher=Kent State University Press |isbn=0-87338-512-8 |publication-place=Kent, Ohio |page=}}</ref> === 1890s dress style === [[File:Lady_Beatrice_Pole-Carew.jpg|thumb|English socialite Lady Beatrice Pole-Carew in the mid-1890s, with puffed sleeves.]] By 1890, the crinoline and bustle were fully abandoned, and skirts flared in an A-line. Necklines were high, while sleeves of bodices initially peaked at the shoulders, but increased in size in the middle of the decade to a puffed [[Sleeve|leg-of-mutton]] style.The sleeves grew to a volume rivaling the 1830s and even sometimes required a cushion to retain their fullness. This sleeve style narrowed down towards the end of the decade. Women also adopted the style of the tailored jacket during this period, with menswear influences such as necktie inspired neckwear continuing from the previous decade. == Hats and headwear == [[File:Ford.madox.brown.last.emma.study.jpg|thumb|''Emma Hill'' by [[Ford Madox Brown]] (1853), a woman wearing a later version of the [[poke bonnet]]]] [[File:Hoed,_objectnr_KA_1237.tif|left|thumb|Perched bonnet style of the early 1870s.]] Hats were crucial to a respectable appearance for both men and women. To go bareheaded was simply not proper. The top hat, for example, was standard formal wear for upper- and middle-class men.<ref name=":4" /> For women, the styles of hats changed over time and were designed to match their outfits. During the early Victorian decades, hats were modest in size and design, straw and fabric bonnets being the popular choice. [[Poke bonnet]]s, which had been worn during the late [[Regency period]], had high, small crowns and brims that grew larger until the 1830s, when the face of a woman wearing a poke bonnet could only be seen directly from the front. They had rounded brims, echoing the rounded form of the bell-shaped hoop skirts. Bonnets shrunk at the end of the 1860s and moved to a perched position in the early 1870s as hairstyles grew in scale and intricacy. This led to the popularization of hats, which became the headwear of choice for the remainder of the Victorian era.<ref name="g4223"/> [[File:The_London_and_Paris_ladies'_magazine_(Apr_1885)_03.png|thumb|Flower pot style hat of 1885.]] The 1880s saw a hat inspired by the top hat for women known as the flowerpot hat, and the 1890s saw the popularity of the boater. The hats of the late Victorian era were covered with elaborate creations of silk flowers, ribbons, and above all, exotic plumes; hats sometimes included entire exotic birds that had been stuffed. Many of these plumes came from birds in the Florida everglades, which were nearly made entirely extinct by overhunting. By 1899, early environmentalists like [[Adeline Knapp]] were engaged in efforts to curtail the hunting for plumes. By 1900, more than five million birds a year were being slaughtered, and nearly 95 per cent of Florida's shore birds had been killed by [[Plume hunting|plume hunter]]s.<ref>{{cite web|title=Everglades National Park|url=https://www.pbs.org/nationalparks/parks/everglades/|archive-url=https://web.archive.org/web/20090927085907/http://www.pbs.org/nationalparks/parks/everglades/|url-status=dead|archive-date=27 September 2009|publisher=PBS|access-date=7 November 2011}}</ref> == Shoes == The women's shoes of the early Victorian period were narrow and heelless, in black or white satin. By 1850s and 1860s, they were slightly broader with a low heel and made of leather or cloth. Ankle-length laced or buttoned boots were also popular. From the 1870s to the twentieth century, heels grew higher and toes more pointed. Low-cut pumps were worn for the evening.<ref name=":4" /> == Cosmetics == [[Victorian-era cosmetics]] were typically minimal, as makeup was associated by the middle classes with promiscuity. However, small amounts of pale face powder or powdered blush were more widely used.<ref>{{Cite book |last=Goodman |first=Ruth |title=How to be a Victorian |date=2014 |publisher=Penguin Books |isbn=978-0-670-92136-2 |location=London}}</ref> Some cosmetics contained toxic or caustic ingredients like lead, mercury, ammonia, and arsenic {{Citation needed|date=October 2025}}. Hair color == Men's fashion == [[File:Mens Coats 1872 Fashion Plate.jpg|thumb|upright|Drawing of Victorian men 1870s]] During the [[1840s in fashion|1840s]], men wore tight-fitting, calf length [[frock coat]]s and a [[waistcoat]] or vest. Sleeves were full at the top and waists were tight, creating an hourglass form. Waistcoats were single- or double-breasted, with shawl or notched collars, and might be finished in double points at the lowered waist. For more formal occasions, a cutaway morning coat was worn with light trousers during the daytime, and a dark tail coat and trousers was worn in the evening. Shirts were made of linen or cotton with low collars, occasionally turned down, and were worn with wide [[Cravat (early)|cravat]]s or neck ties. Trousers had fly fronts, and [[breeches]] were used for formal functions and when horseback riding. Men wore [[top hat]]s, with wide brims in sunny weather. During the [[1850s in fashion|1850s]], men started wearing shirts with high upstanding or turnover [[collar (clothing)|collars]] and [[necktie#Four-in-hand|four-in-hand necktie]]s tied in a bow, or tied in a knot with the pointed ends sticking out like "wings". The upper-class continued to wear top hats, and [[bowler hat]]s were worn by the working class. In the [[1860s in fashion|1860s]], men started wearing wider neckties that were tied in a bow or looped into a loose knot and fastened with a stickpin. Frock coats were shortened to knee-length and were worn for business, while the mid-thigh length [[sack coat]] slowly displaced the frock coat for less-formal occasions, with the overall effect of a looser silhouette. Top hats briefly became the very tall "stovepipe" shape, but a variety of other hat shapes were popular. During the [[1870s in fashion|1870s]], three-piece suits grew in popularity along with patterned fabrics for shirts. Neckties were the four-in-hand and, later, the [[Ascot tie]]s. A narrow ribbon tie was an alternative for tropical climates, especially in the Americas. Both frock coats and sack coats became shorter and more form fitting. Flat straw boaters were worn when boating. During the [[1880s in fashion|1880s]], formal evening dress remained a dark tail coat and trousers with a dark waistcoat, a white bow tie, and a shirt with a winged collar. In mid-decade, the dinner jacket or [[tuxedo]], was used in more relaxed formal occasions. The [[Norfolk jacket]] and tweed or woolen breeches were used for rugged outdoor pursuits such as shooting. Knee-length topcoats, often with contrasting velvet or fur collars, and calf-length overcoats were worn in winter. Men's shoes had higher heels and a narrow toe. Starting from the [[1890s in fashion|1890s]], the [[blazer]] was introduced, and was worn for sports, sailing, and other casual activities.<ref>{{cite web|last=Landow|first=George|url=http://www.victorianweb.org/art/costume/90s/2.html|title=Men's informal sporting dress, late 1880s and '90s}}</ref> Throughout much of the Victorian era most men wore fairly short hair. This was often accompanied by various forms of facial hair including moustaches, side-burns, and full beards. A clean-shaven face did not come back into fashion until the end of the 1880s and early 1890s.<ref>{{cite web|url=http://www.victorianweb.org/art/costume/nunn21.html|title=Victorian Men's Fashions, 1850–1900: Hair}}</ref> Distinguishing what men really wore from what was marketed to them in periodicals and advertisements is difficult, as reliable records do not exist.<ref name="shannon597">{{cite journal|last=Shannon|first=Brent|title=Refashioning Men: Fashion, Masculinity, and the Cultivation of the Male Consumer in Britain, 1860–1914|journal=Victorian Studies|year=2004|volume=46|issue=4|pages=597–630|doi=10.1353/vic.2005.0022}}</ref> Influence of Bertie, Albert Edward, Prince of Wales ==Mourning black== {{See also |Mourning stationery}} [[File:The royal children in mourning Mar 1862.jpg|thumb|Victoria's five daughters (Alice, Helena, Beatrice, Victoria and Louise), photographed wearing mourning black beneath a bust of their late father, Prince Albert (1862)]] [[File:Mourning dress MET 50.40.3a-b front CP4.jpg|alt=Black Victorian mourning dress|thumb|Mourning Dress, 1894–95]] In Britain, black is the colour traditionally associated with mourning for the dead. The customs and etiquette expected of men, and especially women, were rigid during much of the Victorian era. The expectations depended on a complex hierarchy of close or distant relationship with the deceased. The closer the relationship, the longer the mourning period and the wearing of black. The wearing of full black was known as First Mourning, which had its own expected attire, including fabrics, and an expected duration of 4 to 18 months. Following the initial period of First Mourning, the mourner would progress to Second Mourning, a transition period of wearing less black, which was followed by Ordinary Mourning, and then Half-mourning. Some of these stages of mourning were shortened or skipped completely if the mourner's relationship to the deceased was more distant. Half-mourning was a transition period when black was replaced by acceptable colours such as lavender and mauve, possibly considered acceptable transition colours because of the tradition of [[Church of England]] (and [[Catholic Church|Catholic]]) clergy wearing lavender or mauve [[Stole (vestment)|stoles]] for funeral services, to represent the [[Passion (Christianity)|Passion of Christ]].<ref>{{cite web|title=The Colors of the Church Year|url=http://fullhomelydivinity.org/articles/colors.htm|publisher=Consortium of Country Churches|access-date=6 November 2011|archive-date=13 November 2011|archive-url=https://web.archive.org/web/20111113075214/http://fullhomelydivinity.org/articles/colors.htm|url-status=dead}}</ref> The mourning dress on the right was worn by Queen Victoria, "it shows the traditional touches of mourning attire, which she wore from the death of her husband, Prince Albert (1819–1861), until her own death."<ref>{{Cite web|url=https://www.metmuseum.org/art/collection/search/155839?&searchField=All&sortBy=Relevance&deptids=8&ft=queen+victoria&offset=0&rpp=20&amp;pos=2|title=Mourning Dress, 1894–95|last=The Metropolitan Museum of Art|date=7 September 2019|website=The Metropolitan Museum of Art|access-date=7 September 2019}}</ref> === Norms for mourning=== ''Manners and Rules of Good Society, or, Solecisms to be Avoided'' (London, Frederick Warne & Co., 1887) gives clear instructions, such as the following:<ref>{{cite book|last=Flanders|first=Judith|title=The Victorian House|year=2003|publisher=Harper Perennial|location=London|isbn=0-00-713189-5|pages=378–83}}</ref> {| class="wikitable" |- ! Relationship to deceased !! First mourning !! Second mourning !! Ordinary mourning !! Half-mourning |- | Wife for husband || 1-year, 1-month; [[bombazine]] fabric covered with [[Crape|crepe]]; [[widow's cap]], [[lawn cuff]]s, collars || 6 months: less crepe || 6 months: no crepe, silk or wool replaces bombazine; in last 3 months jet jewellery and ribbons can be added || 6 months: colours permitted are grey, lavender, mauve, and black-and-grey |- | Daughter for parent || 6 months: black with black or white crepe (for young girls); no linen cuffs and collars; no jewellery for first 2 months || 4 months: less crepe || – || 2 months as above |- | Wife for husband's parents || 18 months in black bombazine with crepe || – || 3 months in black || 3 months as above |- | Parent for son- or daughter-in-law's parent || – Black armband in representation of someone lost || – || 1-month black || – |- | Second wife for parent of a first wife || – || – || 3 months black || – |} The complexity of these etiquette rules extends to specific mourning periods and attire for siblings, step-parents, aunts and uncles distinguished by blood and by marriage, nieces, nephews, first and second cousins, children, infants, and "connections" (who were entitled to ordinary mourning for a period of "1–3 weeks, depending on level of intimacy"). Men were expected to wear mourning black to a lesser extent than women, and for a shorter mourning period. After the mid-19th century, men would wear a black hatband and black suit, but for only half the prescribed period of mourning expected of women. Widowers were expected to mourn for a mere three months, whereas the proper mourning period expected for widows was up to four years.<ref>{{cite book|last=Flanders|first=Judith|title=The Victorian House|year=2003|publisher=Harper Perennial|location=London|isbn=0-00-713189-5|pages=378–9}}</ref> Women who mourned in black for longer periods were accorded great respect in public for their devotion to the departed, the most prominent example being Queen Victoria herself. Women with lesser financial means tried to keep up with the example being set by the middle and upper classes by dyeing their daily dress. Dyers made most of their income during the Victorian period by dyeing clothes black for mourning.<ref>{{cite book|last=Flanders|first=Judith|title=The Victorian House|year=2003|publisher=Harper Perennial|location=London|isbn=0-00-713189-5|page=341}}</ref> == Technological advancement == The technological changes that affected the manufacture and consumption of clothing in the Victorian age included the following: * the mass production of fabrics — for example, "by the early 1850s there were thousands of steam-powered looms churning out millions of miles of fabric every year"  [62] * the invention of aniline dyes, which were much more vibrantly colored and resistant to fading than the natural dyes that had been used. — . Invented by chemist [[William Henry Perkin]] in 1856, the first aniline dye mauveine (or mauve) "wash[ed] the fashionable landscape in a haze of purple."<ref name=":22">{{Cite book|title=The Dress Diary: Secrets from a Victorian Woman's Wardrobe|last=Strasdin|first=Kate|publisher=Pegasus Books|year=2023|location=New York, New York}}</ref> (247) Other intense and, to the Victorians, intensely exciting colors followed, but the new synthetic additions to fabric sometimes included chemicals harmful to their wearers. For example, a "bright-magenta hue was achieved by adding arsenical-based chemicals to existing aniline dyes, brightening the already luminous shades – but these left residues themselves, along with a toxic labour trail in their wake."<ref name=":22" /> (255) Perhaps the most famous of these is arsenic green, used on fabrics, wallpapers, and trim: "The craze for artificial foliage to adorn the heads and dresses of women of fashion in the mid-nineteenth century had seen the proliferation of flower workshops, where young women in their hundreds laboured to produce the lifelike green leaves and blooms that would make a fetching headdress or would trail becomingly across the bodice of a gown. The lushness of the green was achieved by the application of a powder, a pigment that was created by mixing copper and the highly toxic chemical, arsenic trioxide. The physical effects of working with this poisonous compound were horrific. Contemporary medical drawings depict the green hue of the skin and dreadful open lesions on the hands of the maker, whilst the daily gradual ingestion of the powder by the flower girls was eventually fatal."<ref name=":22" /> (255) * the invention of a sewing machine that could be used in the home. Although sewing machines were already in use in the clothing industry, in 1858 Isaac Merritt Singer began to sell "lightweight domestic machines" for home sewing, radically increasing women's control over their own dress.<ref name=":24" /> (91 [of 298]) * the spread of journalism for women and fashion journalism Perhaps not at the same scale as these but as important in 1850s designs was a technology that turned iron into steel, which could then be drawn into fine wires.<ref name=":3" /> Steel was refined to a malleable state so that thin blades could be curved into concentric circles (called hoops) and connected with wires to form the cage. Technological advancements not only influenced the economy but brought a major change in the fashion styles worn by men and women. As the Victorian era was based on the principles of gender, race and class.<ref>{{cite journal|last1=Graham|first1=P|title=The Victorian Era|url=https://archive.org/details/in.ernet.dli.2015.261548|journal=Digital Library of India}}</ref> Much advancement was in favor of the upper class as they were the ones who could afford the latest technology and change their fashion styles accordingly. In 1830s there was introduction of horse hair crinoline that became a symbol of status and wealth as only the upper-class women could wear it. In 1850s there were more fashion technological advancements hence 1850s could rightly be called a revolution in the Victorian fashion industry such as the innovation of artificial cage crinoline that gave women an artificial hourglass silhouette without layers of petticoats, which was lighter and more hygienic.<ref>{{cite book|last1=Shrimpton|first1=J|title=Victorian Fashion|publisher=Bloomsbury Shire Publications}}</ref> Synthetic dyes, such as [[mauveine]] (aniline purple), were introduced in 1856, adding bright colours to garments. In 1855's ''[[Haute couture]]'' was introduced as tailoring became more mainstream in years to follow.<ref>{{cite book|last1=Aspelund|first1=Karl|title=Fashioning Society|publisher=Fairchild Books}}</ref> Charles Frederick Worth, a prominent English designer, became popular amongst the upper class though its city of destiny always is Paris. Haute couture became popular at the same time that sewing machines were invented.<ref name="Haute Couture">{{cite book|last1=Martin|first1=Richard|last2=Koda|first2=Harold|title=Haute Couture|publisher=The Metropolitan Museum of Art}}</ref> Princess [[Eugénie de Montijo|Eugenie]] of France wore the Englishman dressmaker, Charles Frederick Worth's couture and he instantly became famous in France though he had just arrived in Paris a few years ago. In 1855, Queen Victoria and Prince Albert of Britain welcomed [[Napoleon III]] and Eugenie of France to a full state visit to England. Eugenie was considered a fashion icon in France. Queen Victoria, who had been the fashion icon for European high fashion, was inspired by Eugenie's style and the fashions she wore.{{Citation needed|date=October 2025}} Later, Queen Victoria also appointed Charles Frederick Worth as her dress maker and he became a prominent designer amongst the European upper class. Charles Frederick Worth is known as the father of the haute couture as later the concept of labels were also invented in the late 19th century as custom, made to fit tailoring became mainstream.<ref>{{cite book|last1=Saillard|first1=Olivier|last2=Zazzo|first2=Anne|title=Paris Haute Couture|publisher=Skira Flammarion}}</ref> By the 1860s, when made-to-fit tailoring was popular in Europe, crinolines were considered impractical. In the 1870s, women preferred more slimmer silhouettes, hence bodices grew longer and the polonaise, a skirt and bodice made together, was introduced. In 1870s the Cuirass Bodice, a piece of armour that covers the torso and functions like a corset, was invented. Towards the end of Victoria's reign, dresses were flared naturally as crinolines were rejected by middle-class women. Designers such as Charles Frederick Worth were also against them. All these inventions and changes in fashion led to women's liberation as tailored looks improved posture and were more practical.<ref name="Haute Couture"/> dressmakers, couturiers, modistes == Home decor == {{main|Victorian decorative arts}} Home decor started spare, veered into the elaborately draped and decorated style we today regard as Victorian, then embraced the retro-chic of [[William Morris]] as well as pseudo-[[Japonaiserie]]. == Myths and Oversimplifications == === Modesty === {{main|Victorian morality}} {{Original research|section|date=May 2008}} [[File:1868-skirt-lengths-girl-ages-Harpers-Bazar.gif|thumb|upright|"The proper length for little girls' skirts at various ages", from ''[[Harper's Bazaar]]'', showing a 1900 idea of how the hemline should descend towards the ankle as a girl got older]]Many myths and exaggerations about the period persist to the modern day. Examples include the idea of men's clothing is seen as formal and stiff, women's as elaborate and over-done; clothing covered the entire body, and even the glimpse of an ankle was scandalous. Critics contend that [[corset]]s constricted women's bodies and lives. Homes are described as gloomy, dark, cluttered with massive and over-ornate furniture and proliferating [[bric-a-brac]]. Myth has it that even piano legs were scandalous, and covered with tiny [[pantalette]]s. === Tight Lacing === Tight-lacing, which was not possible until the development of the grommet in 1828, was famously controversial in the Victorian age, generating many column inches of profitable newspaper copy, in part because it was (and still is) fetishistic and subversive in that adolescent girls used it as a means of rebellion and upper-working- or lower-middle-class shop girls saw it as a means of upward mobility.<ref name=":21">{{Cite book|title=Fashion and Fetishism: Corsets, Tight-Lacing and Other Forms of Body-sculpture|last=Kunzle|first=David|publisher=History Press|year=2013|isbn=978 0 7524 9545 3|location=Stroud, Gloucestershire|pages=}}</ref> (71 [of 1182]) No evidence exists that tight lacing was widespread or particularly dangerous.<ref name=":21" /> () In truth, men's formal clothing may have been less colourful than it was in the previous century, but brilliant [[waistcoat]]s and [[cummerbund]]s provided a touch of colour, and [[smoking jacket]]s and [[robe|dressing gown]]s were often of rich Oriental [[brocade]]s. This phenomenon was the result of the growing textile manufacturing sector, developing mass production processes, and increasing attempts to market fashion to men.<ref name="shannon597"/> Corsets stressed a woman's sexuality, exaggerating hips and bust by contrast with a tiny waist. Women's [[evening gown]]s bared the shoulders and the tops of the breasts. The [[jersey dress]]es of the 1880s may have covered the body, but the stretchy novel fabric fit the body like a glove.<ref>{{cite book |last=Gernsheim |first=Alison |title=Victorian & Edwardian Fashion: A Photographic Survey |year=1981 |publisher=Dover Publications |location=New York |page=65|edition=New |isbn=0-486-24205-6}}</ref> Home furnishing was not necessarily ornate or overstuffed. However, those who could afford lavish draperies and expensive ornaments, and wanted to display their wealth, would often do so. Since the Victorian era was one of increased social mobility, there were ever more ''[[nouveaux riches]]'' making a rich show. The items used in decoration may also have been darker and heavier than those used today, simply as a matter of practicality. London was noisy and its air was full of [[soot]] from countless coal fires. Hence those who could afford it draped their windows in heavy, sound-muffling curtains, and chose colours that didn't show soot quickly. When all washing was done by hand, curtains were not washed as frequently as they might be today. There is no actual evidence that piano legs were considered scandalous. Pianos and tables were often draped with [[shawl]]s or cloths—but if the shawls hid anything, it was the cheapness of the furniture. There are references to lower-middle-class families covering up their [[pine]] tables rather than show that they couldn't afford [[mahogany]]. The piano leg story seems to have originated in the 1839 book, ''A Diary in America'' written by Captain [[Frederick Marryat]], as a satirical comment on American prissiness.<ref>{{cite book |last1=Marryat |first1=C.B. |title=A Diary in America: With Remarks on Its Institutions |date=1839 |publisher=Longman, Orme, Brown, Green, and Longmans |location=London, England |volume=2 |pages=246–247 |url=https://books.google.com/books?id=2-VEAAAAIAAJ&pg=PA246}} From pp. 246-247: "I was requested by a lady to escort her to a seminary for young ladies, and on being ushered into the reception-room, conceive my astonishment at beholding a square piano-forte with four ''limbs''. However, that the ladies who visited their daughters, might feel in its full force the extreme delicacy of the mistress of the establishment, and her care to preserve in their utmost purity the ideas of the young ladies under her charge, she had dressed all these four limbs in modest little trousers, with frills at the bottom of them!"</ref> Victorian manners may have been as strict as imagined—on the surface. One simply did not speak publicly about sex, childbirth, and such matters, at least in the respectable middle and upper classes. However, as is well known, discretion covered a multitude of sins. Prostitution flourished. Upper-class men and women indulged in [[adultery|adulterous]] liaisons. == Gallery == {{gallery |2=A mid-Victorian interior: ''Hide and Seek'' by [[James Tissot]], c. 1877 Image:Winterhalter Elisabeth.jpg|3=Dress designed by [[Charles Frederick Worth]] for [[Elisabeth of Bavaria|Elisabeth of Austria]] painted by [[Franz Xaver Winterhalter]].|4=File:Frith A Private View detail.jpg|5=[[William Powell Frith]]'s painting of 1883 contrasts women's [[Aesthetic dress]] (left and right) with fashionable attire (center).|6=File:Tissot lilacs 1875.jpg|7=Day dress, c. 1875 [[James Tissot]] painting.|8=File:James Abbot McNeill Whistler 011.jpg|9=[[James McNeill Whistler|Whistler]]'s [[Portrait of Lady Meux]], 1882 Image:Jeanna_Samary-Renoir.png|10=[[Pierre-Auguste Renoir|Renoir]]'s portrait of [[Jeanne Samary]] in an [[evening gown]], 1878|11=File:Melville_-_Queen_Victoria.jpg|12=Portrait by [[Alexander Melville (artist)|Alexander Melville]] of [[Victoria of the United Kingdom|Queen Victoria]], 1845|13=File:Henry Treffry Dunn Rossetti and Dunton at 16 Cheyne Walk.jpg|14=An artistic interior: [[Dante Gabriel Rossetti]] reading to [[Theodore Watts-Dunton]] in the drawing room at No. 16 [[Cheyne Walk]], 1882|15=File:Punch - Masculine beauty retouched1.png|16=Men's swimwear: Cartoon from ''[[Punch (magazine)|Punch]]'' by [[George du Maurier]]}} == See also == * [[Emily Clapham]] * [[Victorian decorative arts]] * [[Victorian dress reform]] * [[Victorian morality]] * [[Victoriana]] * [[Women in the Victorian Era]] * [[Charles Frederick Worth]] === Time periods === * [[1830s in fashion]] * [[1840s in fashion]] * [[1850s in fashion]] * [[1860s in fashion]] * [[1870s in fashion]] * [[1880s in fashion]] * [[1890s in fashion]] === Women's clothing === * [[Corset]] * [[Corset controversy]] * [[Tightlacing]] * [[Bloomers (clothing)|Bloomers]] * [[Bodice]] === Contemporary interpretations === * [[Steampunk]] * [[Neo-Victorian]] * [[Lolita Fashion|Lolita]] == References == {{Reflist}} == Further reading == *{{cite book |author=Phipps, Elena| title= ''From Queen to Empress: Victorian dress 1837-1877'' | location=New York | publisher=The Metropolitan Museum of Art | year=1988 | isbn=0870995340| url= http://libmma.contentdm.oclc.org/cdm/compoundobject/collection/p15324coll10/id/69547/rec/235 | display-authors=etal}} * Sweet, Matthew – ''Inventing the Victorians'', St. Martin's Press, 2001 {{ISBN|0-312-28326-1}} == External links == * [http://www.victorians.co.uk/victorian-fashion Victorian Fashion] {{Webarchive|url=https://web.archive.org/web/20180407223711/http://www.victorians.co.uk/victorian-fashion |date=7 April 2018 }} * [https://www.victorianvoices.net/topics/fashion/index.shtml VictorianVoices.net] – Fashion articles and illustrations from Victorian periodicals; extensive fashion image gallery * [http://www.cracked.com/article_19575_5-ridiculous-sex-myths-from-history-you-probably-believe.html Victorian myths] * [http://www.victorianstation.com/lifestylemenu.htm Victorian fashion, etiquette, and sports] {{Webarchive|url=https://web.archive.org/web/20180103162620/http://www.victorianstation.com/lifestylemenu.htm |date=3 January 2018 }} * [http://www.thesmartset.com/article/article12180701.aspx Background on "A Diary in America"] * [http://www.mccord-museum.qc.ca/en/keys/webtours/VQ_P2_17_EN.html Form and Fashion] — the evolution of women's dress during the 19th century (many photographs) * [http://www.mccord-museum.qc.ca/en/keys/games/jeu2/ Educational Game: Mix and Match] — build a 19th-century dress using a virtual mannequin * {{cite web |publisher= [[Victoria and Albert Museum]] |url= http://www.vam.ac.uk/content/articles/v/victorian-dress-at-v-and-a/ |title= Victorian Dress |work= Fashion, Jewellery & Accessories |date= 14 January 2011 |access-date= 2011-04-03}} *[http://cv.vic.gov.au/stories/creative-life/fashion-detective-fashion-fiction-and-forensics/ Fashion detective: Fashion, Fiction and Forensics in nineteenth century Australian fashion] on Culture Victoria {{Timeline of clothing and fashion|state=collapsed}}{{Victorian era|state=collapsed}} [[Category:Victorian fashion| ]] [[Category:19th-century fashion|*]] [[Category:1900s fashion]] [[Category:History of Western fashion]] [[Category:19th century in the arts]] =From ''Women in the Victorian era''= ===Victorian women's fashion=== {{Multiple issues|{{tone|date=March 2023}} {{more footnotes needed|date=March 2023}}|section=y}}{{Further|Victorian fashion}} The ideal Victorian woman was pure, chaste, refined, and modest. This ideal was supported by etiquette and manners. The etiquette extended to the pretension of never acknowledging the use of undergarments (sometimes generically referred to as "unmentionables"). The discussion of such a topic, it was feared, would gravitate towards unhealthy attention on anatomical details. As one Victorian lady expressed it: "[those] are not things, my dear, that we speak of; indeed, we try not even to think of them", in contrast to current norms.<ref>{{cite book |last=Cunnington |first=C. Willett |title=English Women's Clothing in the Nineteenth Century: A Comprehensive Guide with 1,117 Illustrations |publisher=Dover Publications |year=1990 |isbn=978-0-486-26323-6 |pages=20}}</ref> The pretence of avoiding acknowledgement of anatomical realities met with embarrassing failure on occasion. In 1859, the Hon. Eleanor Stanley wrote about an incident where the [[Louisa Cavendish, Duchess of Devonshire|Duchess of Manchester]] moved too quickly while manoeuvring over a [[stile]], tripping over her large [[hoop skirt]]: {{blockquote|[the Duchess] caught a hoop of her cage in it and went regularly head over heels lighting on her feet with her cage and whole petticoats above, above her head. They say there was never such a thing seen – and the other ladies hardly knew whether to be thankful or not that a part of her undergarments consisted in a pair of scarlet tartan [[knickerbockers (clothing)|knickerbockers]] (the things Charlie shoots in) which were revealed to the view of all the world in general and the [[Aimable Pélissier|Duc de Malakoff]] in particular".<ref>{{cite book|last=Cunnington|first=C. Willett|title=English Women's Clothing in the Nineteenth Century: A Comprehensive Guide with 1,117 Illustrations|year=1990|publisher=Dover Publications|isbn=978-0-486-26323-6|pages=20–1}}</ref>}} However, despite the fact that Victorians considered the mention of women's undergarments in mixed company unacceptable, men's entertainment made great comedic material out of the topic of ladies' [[bloomers (clothing)|bloomers]], including men's magazines and music hall skits.<ref>{{cite book |last=Cunnington |first=C. Willett |title=English Women's Clothing in the Nineteenth Century: A Comprehensive Guide with 1,117 Illustrations |publisher=Dover Publications |year=1990 |isbn=978-0-486-26323-6 |pages=22}}</ref> Victorian women's clothing followed trends that emphasised elaborate dresses, skirts with wide volume created by the use of layered material such as [[crinoline]]s, hoop skirt frames, and heavy fabrics. Because of the impracticality and health impact of the era's fashions, a [[Victorian dress reform|dress reform movement]] began among women. The ideal silhouette of the time demanded a narrow waist, which was accomplished by constricting the abdomen with a laced [[corset]]. While the silhouette was striking, and the dresses themselves were often exquisitely detailed creations, the fashions were cumbersome. At best, they restricted women's movements and at worst, they had a harmful effect on women's health. Physicians turned their attention to the use of corsets and determined that they caused several medical problems: compression of the thorax, restricted breathing, organ displacement, poor circulation, and prolapsed uterus.<ref name="O'Connor"/> Articles advocating the reform of women's clothing by the British National Health Society, the Ladies' Dress Association, and the [[Rational Dress Society]] were reprinted in ''The Canada Lancet'', Canada's medical journal. In 1884, Dr J. Algernon Temple of Toronto even voiced concern that the fashions were having a negative impact on the health of young women from the working classes. He pointed out that a young working-class woman was likely to spend a large part of her earnings on fine hats and shawls, while "her feet are improperly protected, and she wears no flannel petticoat or woollen stockings".<ref name="O'Connor"/> [[File:Bloomers.jpg|thumb|1850s illustration of a woman wearing [[bloomers]]]] [[Florence Pomeroy]], Lady Haberton, was president of the Rational Dress movement in Britain. At a National Health Society exhibition held in 1882, Viscountess Haliburton presented her invention of a "[[divided skirt]]", which was a long skirt that cleared the ground, with separate halves at the bottom made with material attached to the bottom of the skirt. She hoped that her invention would become popular by supporting women's freedom of physical movement, but the British public was not impressed by the invention, perhaps because of the negative "unwomanly" association of the style with the American [[Bloomers]] movement.<ref>{{cite book|last=Murray|first=Janet Horowitz|title=Strong-Minded Women and Other Lost Voices from 19th Century England|year=1982|publisher=Pantheon Books|location=New York|isbn=0-394-71044-4|pages=[https://archive.org/details/strongmindedwome00jane/page/68 68–70]|url=https://archive.org/details/strongmindedwome00jane/page/68}}</ref> [[Amelia Jenks Bloomer]] had encouraged the wearing of visible bloomers by feminists to assert their right to wear comfortable and practical clothing, but it was no more than a passing fashion itself among radical feminists. The movement to reform women's dress would persist and have long-term success, however; by the 1920s, [[Coco Chanel]] was successful at selling a progressive, far less restrictive silhouette that abandoned the corset and raised hemlines. The new silhouette symbolised modernism for trendy young women and became the 20th century standard. Other Paris designers continued reintroducing pants for women and the trend was gradually adopted over the next century. Fashion trends, in one sense, travelled "full circle" over the course of the Victorian era. The popular women's styles during the [[Georgian era]], and at the very beginning of Victoria's reign, emphasized a simple style influenced by flowing gowns worn by women in [[Ancient Greek clothing|Ancient Greece]] and [[Clothing in ancient Rome|Rome]]. The [[Empire waist]] silhouette was replaced by a trend towards ornate styles and an artificial silhouette, with the restrictiveness of women's clothing reaching its low point during the mid-century passion for narrow corseted waists and hoop skirts. The iconic wide-brimmed women's hats of the later Victorian era also followed the trend towards ostentatious display. Hats began the Victorian era as simple [[Bonnet (headgear)|bonnets]]. By the 1880s, milliners were tested by the competition among women to top their outfits with the most creative (and extravagant) hats, designed with expensive materials such as silk flowers and exotic plumes such as ostrich and peacock. As the Victorian era drew to a close, however, fashions were showing indications of a popular backlash against excessive styles. Model, actress and socialite [[Lillie Langtry]] took London by storm in the 1870s, attracting notice for wearing simple black dresses to social events. Combined with her natural beauty, the style appeared dramatic. Fashions followed her example (as well as Queen Victoria's wearing of mourning black later in her reign). According to [[Harold Koda]], the former Curator-in-chief of the [[Costume Institute at The Met|Metropolitan Museum of Art's Costume Institute]],<ref>{{cite web|url=http://www.metmuseum.org/about-the-museum/press-room/exhibitions/2014/death-becomes-her|title=Death Becomes Her: A Century of Mourning Attire : October 21, 2014-February 1, 2015|website=Metmuseuim.org|access-date=7 November 2021}}</ref> "The predominantly black palette of [[mourning]] dramatizes the evolution of period silhouettes and the increasing absorption of fashion ideals into this most codified of etiquettes," said Koda, "The veiled widow could elicit sympathy as well as predatory male advances. As a woman of sexual experience without marital constraints, she was often imagined as a potential threat to the social order." ====Evolution of Victorian women's fashion==== <gallery> File:Fashion plate December 1844.jpg|Ladies' December Fashions (1844). Hand-coloured steel engraving from a women's magazine. File:Thegalleryofhmscalcutta james tissot 1876.jpg|''[[The Gallery of HMS Calcutta]]'' by [[James Tissot]] (1876). [[Bustle]]s were fashionable in the 1870s and 1880s. File:Mrs lillie langtry george frederic watts 1880.jpg|''Mrs. Lillie Langtry'' by [[George Frederic Watts]] (1880). File:Five-women-on-queenslander-steps-r.jpg|Fashionable women in [[Queensland]], Australia around 1900. </gallery> {{Short description|Irish writer (born 1963)}} {{Use Irish English|date=August 2025}} {{Use dmy dates|date=August 2025}} {{Infobox writer | name = Darach Ó Scolaí | image = Darach Ó Scolaí.JPG | alt = Man holding prize-winning book | caption = Ó Scolaí in 2019 | birth_name = Darach Ó Scolaí | birth_date = {{Birth date and age|1963|df=y}} | birth_place = [[County Galway]], The Republic of Ireland | death_date = | death_place = | occupation = Writer, artist, publisher | alma_mater = [[University of Galway]] | years_active = 1998–present | genre = Novel, retelling, translation, play, screenplay, illustrated book for children and adults | other_names = | spouse = | children = 3 | awards = [[Awards and Honors received by Darach Ó Scolaí|Awards and Honors]] | signature = | website = }}[[File:Darach Ó Scolaí.JPG|thumb|Darach Ó Scolaí, holding ''Oileán an Órchiste'' (his translation of Robert Louis Stevenson's ''Treasure Island'')]] == Darach Ó Scolaí == Darach Ó Scolaí (<small>Irish:</small> [/ˈda.rax/ /oː/ /sˠkˠoː/l̪ˠəi/]; born 1963<ref>{{Cite web|url=https://portraidi.ie/en/darach-o-scolai/|title=Darach Ó Scolaí|date=20 October 2017|website=Portráidí (Portraits of Irish-Language Writers)|access-date=1 August 2025}}</ref>) is an Irish author who works in a number of genres, from novels, plays and screenplays to illustrated books for children and adults. He began his literary career in 1998 writing screenplays, stage plays, retellings and translations; he began to publish novels in 2008. Ó Scolaí is widely recognized as a leading figure in contemporary Irish literature, known as “one of the most important Irish language writers of his generation”<ref>{{Cite journal|last=Poirtéir|first=Cathal|date=2022|title=? Suil an Daill: Constant Tensions and Shifting Allegiances|url=https://booksirelandmagazine.com/suil-an-daill-constant-tensions-and-shifting-allegiances/|journal=Books Ireland}}</ref> and "one of the great Irish language novelists [duine d’úrscéalaithe móra na Gaeilge]."<ref name=":17" /> His writing has been called “the high literature of the Irish language.”<ref>Ó Coimín, Maitiú. ''Nós'' 2 February 2018). Qtd. in "Táin Bó Cuailnge." ''Leabhar Breac''. Retrieved 25 August 2025.</ref> Much of his fiction is based on a knowledge of traditional Irish tales and narrative practices as well as Irish history. He specializes in literary and [[wikipedia:Historical_fiction|historical fiction]], or as novelist Alan Titley says, Ó Scolaí’s “peak (for now), or at least his greatest imaginative interest, is the historical novel [tá an chuma air gurb é a bhuaic (go fóill), nó ar a laghad, a mhórspéis samhlaíochta, an t-úrscéal staire].”<ref name=":11">{{Cite journal|last=Titley|first=Alan|date=Fall 2020|title=An Stíl Go Deo!: Soather Dharach Uí Scolaí (The style would be forever!: Worker Darach Ó Scolaí)|url=https://www.jstor.org/stable/27046090|journal=Comhar|volume=80, No. 10|pages=27|via=JSTOR}}</ref> His retellings of old stories and tales from their original Middle and Early-Modern Irish into Modern Irish ([[wikipedia:Irish_language|Gaeilge]]) are respected for their accessibility to students and language learners as well as for their artistry. Ó Scolaí also regularly reviews books and lectures and writes on literature and culture. Beyond his writing, Ó Scolaí is a publisher and has co-produced a number of film, television shows and stage plays. == Life == Ó Scolaí was born in Dublin and raised in the Galway [[wikipedia:Gaeltacht#Galway Gaeltacht|Gaeltacht]] (Irish-speaking) regions of Cois Fharraige on the north shore of Galway Bay, in the Republic of Ireland, where he lives now with his wife and children in Lochán Beag (Indreabhán).<ref name=":7">{{Cite journal|date=30 October 2024|title=Duais don úrscéal liteartha is fearr buaite ag Darach Ó Scolaí ag Oireachtas na Samhna|url=https://tuairisc.ie/duais-don-ursceal-liteartha-is-fearr-buaite-ag-darach-o-scolai-ag-oireachtas-na-samhna/|journal=Tuairisc}}</ref><ref>{{Cite journal|last=Ní Scolaí|first=Aifric|date=2024|title=Darach Ó Scolaí|url=https://www.taiscecf.ie/ealaiontoiri?category=Scr%C3%ADbhneoir|journal=Taisce Chois Fharraige}}</ref> He graduated the [[wikipedia:University_of_Galway|University of Galway]] (then University College Galway) with a B.A. in 1983.<ref>{{Cite web|url=https://www.linkedin.com/in/darach-ó-scolaí-20026920/|title=Darach Ó Scolaí|last=Ó Scolaí|first=Darach|date=August 2025|website=LinkedIn}}</ref> === Writing and Publishing === Ó Scolaí writes in Irish ([[wikipedia:Irish_language|Gaeilge]]), his native language, and lives in an area defined for the predominant presence of Irish as the vernacular language, the language spoken at home. Irish was the language of his parents' home and is the language of children as well. He is fluent in Irish and English and conversant in French. None of his works has been translated into English. ==== Leabhar Breac ==== In 1995 Darach Ó Scolaí and his brother Caomhán Ó Scolaí — a [[wikipedia:Typography|typographer]] and designer — founded the publishing house Leabhar Breac at Indreabhán (Inverin), County Galway. Their father “Séamas Ó Scolaí was an editor at An Gúm and worked on the Irish-English dictionary team [bhí a n-athair Séamas Ó Scolaí ina eagarthóir sa Ghúm agus d’oibrigh sé ar fhoireann an fhoclóra Gaeilge-Béarla].”<ref name=":0">{{Cite web|url=https://leabharbreac.com/en/about-us/|title=About Us|date=2024|website=Leabhar Breac|access-date=1 July 2025}}</ref> Darach Ó Scolaí has been publisher and literary editor at Leabhar Breac since its founding. Named for [[wikipedia:An_Leabhar_Breac|An Leabhar Breac (The Speckled Book)]], Leabhar Breac publishing house has more than 140 books in print.<ref name=":0" /> Leabhar Breac aims to publish Irish-language books that meet “a high literary and artistic standard.”<ref name=":0" /> Besides the content, Leabhar Breac is known for the typically "superb [thar cionn]" quality of the design and production of the "physical book [leabhar fisiciúil]."<ref name=":8">{{Cite journal|last=Ní Mhuilneoir|first=Gráinne|date=30 July 2024|title=‘Bláthnaid’ – leabhar álainn i sraithín álainn faoi mhná|url=https://tuairisc.ie/blathnaid-leabhar-alainn-i-sraithin-alainn-faoi-mhna/|journal=Tuairisc}}</ref> Its books regularly win awards for literary and artistic quality. Leabhar Breac also publishes translations for children and adults from various early versions of Irish as well as from French and English (and has published translations of books for young readers from Spanish, Catalan, and Italian as well). Leabhar Breac prints its books in Ireland. === Stage and Screen === ==== Rosg ==== In 1998 along with Ciarán Ó Cofaigh,<ref name=":1">{{Cite web|url=http://www.rosg.ie/en/about/History_6/|title=About Us: History|date=July 2025|website=Rosg|access-date=1 August 2025}}</ref> Ó Scolaí co-founded the film and television production company [http://www.rosg.ie/en/ Rosg] and was co-director until 2006. Rosg produced Ó ScolaÍ’s films ''Cosa Nite'' (1999), ''An Leabhar'' (2001) and ''Na Cloigne'' (2010). He left Rosg in 2006 to devote his time to other artistic activities. ==== Ealaín ar Oileán ==== In 2004, along with Val Balance, Ó Scolaí co-founded the annual artists' symposium Ealaín ar Oileán (trans., Art on an Island). The Irish-language symposium was held annually in the Áras Éanna arts and cultural center on Inis Oírr ([[wikipedia:Inisheer|Inisheer]], the smallest of the [[wikipedia:Aran_Islands|Aran Islands]]) from 2004 to 2013. Ó Scolaí was its co-director from its founding<ref>{{Cite web|url=https://ga.wikipedia.org/wiki/Darach_Ó_Scolaí.|title=Darach Ó Scolaí|date=3 February 2024|website=Vicipéid|access-date=1 July 2025}}</ref> until 2013. Besides being its co-director, Ó Scolaí has taken part in this conference as an artist<ref>{{Cite journal|date=16 January 2005|title=Darach Ó Scolaí|url=https://web.archive.org/web/20050116163252/http://bliainiris.com/authors/darach_oscolai.html|journal=Bliainiris}}</ref> and writer<ref name=":2">{{Cite web|url=http://ealainaroilean.ie/ealainaroilean.html|title=The Conference|date=7 September 2013|website=Ealaín ar Oileán|archive-url=https://web.archive.org/web/20130907083744/http://ealainaroilean.ie/ealainaroilean.html|archive-date=7 September 2013|access-date=1 August 2025}}</ref>. ==== Salamandar ==== In 2006 Ó Scolaí founded the stage production company Salamandar and directed his own play ''An Braon Aníos''. His plays ''An tSeanbhróg'' (2009) and ''Craos'' (2008) were also produced by Salamandar.<ref name=":19">{{Cite web|url=https://leabharbreac.com/en/product-category/darach-o-scolai/|title=Darach Ó Scolaí|date=2024|website=Leabhar Breac|access-date=1 July 2025}}</ref> == Works == === Novels === * [[wikipedia:An_Cléireach|''An Cléireach'' (trans., ''The Clerk'')]], Leabhar Breac, 2007. The Oireachtas Prize for Literary Fiction, 2007; The Ó Súilleabháin Award (Book of the Year) in 2008, and "named as ‘the best novel since the turn of the Century’ by Comhar."<ref>{{Cite web|url=https://leabharbreac.com/en/shop/fiction/an-cleireach/|title=An Cléireach - Leabhar Breac - Irish language novel|website=Leabhar Breac|language=en-US|access-date=2025-10-24}}</ref> * ''Na Comharthaí'' (trans., ''The Signs''), Leabhar Breac, 2014. * ''Súil an Daill'' (trans., ''The Eye of the Blind''), Leabhar Breac, 2021. The Oireachtas Prize for Literary Fiction, 2019.<ref name=":4">{{Cite web|url=https://leabharbreac.com/en/shop/fiction/suil-an-daill/|title=Súil an Daill|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> * ''Bódléar'', Leabhar Breac, 2024. The Oireachtas Prize for Literary Fiction, 2024<ref name=":7" />; The Ó Súilleabháin Award (Book of the Year) in 2025; featured in the 2025 Listen-Up Irish Summer Challenge for students of the Irish language.<ref>{{Cite news|url=https://connachttribune.ie/novel-approach-helps-people-learn-irish-in-a-creative-way/|title=Novel approach helps people learn Irish in a creative way|last=Murphy|first=Judy|date=3 October 2025|work=Connaught Tribune|access-date=24 October 2025}}</ref> === Retellings, Translations and Editions === The retellings and translations are into modern Irish. * ''Feis Tigh Chonáin'' (trans., ''The Feast of Conán's House''), Leabhar Breac, 2000; a retelling of a 15^th-century tale from the [[wikipedia:Fenian_Cycle|Fenian Cycle]].<ref>{{Cite web|url=https://leabharbreac.com/en/shop/fiction/feis-tigh-chonain/|title=Feis Tigh Chonáin|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> * ''An Ceithearnach Caolriabhach'' (trans., ''The Narrow-Striped Kern''), Leabhar Breac, 2002; a retelling from c. 1500, also illustrated by Darach Ó ScolaÍ.<ref>{{Cite web|url=https://leabharbreac.com/en/shop/fiction/an-ceithearnach-caolriabhach/|title=An Ceithearnach Caolriabhach|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> * ''Táin Bó Cuailnge'' (trans., ''The Cattle Raid of Cooley''), Leabhar Breac, 2017, both a modern edition of an 11th-century epic and an annotated edition.<ref name=":3">{{Cite web|url=https://leabharbreac.com/en/shop/darach-o-scolai/tain-bo-cuailnge-2-2/|title=Táin Bó Cuailnge|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> "''Táin Bó Cuailnge'' won the Aodán Mac Poilín Memorial Prize 2017."<ref name=":19" /> * ''Deirdre'', Leabhar Breac, 2023, a “picture book for adults” with artist Anastasia Melnykova.<ref>{{Cite web|url=https://leabharbreac.com/en/shop/darach-o-scolai/deirdre/|title=Deirdre|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> Part of the [[wikipedia:Ulster_Cycle|Ulster Cycle]], ''Deirdre'' is a retelling of the story of possibly the most widely known Irish figure from the early tales and sagas.<ref>{{Cite book|title=A Dictionary of Celtic Mythology|last=MacKillop|first=James|publisher=Oxford University Press|year=2004|isbn=9780198609674|pages=181}}</ref> * ''Bláthnaid'', Leabhar Breac, 2024, a “picture book for adults” with artist Anastasia Melnykova; “one of the great stories of the [[wikipedia:Ulster_Cycle|Ulster Cycle]].”<ref name=":4" /> * ''Sadhbh,'' Leabhar Breac, 2025, a picture book for adult readers, illustrated by Alé Mercado; a retelling of the medieval tale ''Ceasacht Inghine Ghuile (''trans., ''The Complaint of Guile's Daughter'').<ref name=":5">{{Cite web|url=https://leabharbreac.com/en/tales-of-wonder/|title=Tales of Wonder|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> * ''Eoghan Béal'', Leabhar Breac, 2025, a picture book for adult readers illustrated by Alé Mercado<ref name=":5" />; a retelling of the medieval tale ''[https://ga.wikipedia.org/wiki/Caithr%C3%A9im_Cellaig Cathréim Ceallaigh]'' from ''The Yellow Book of Leacan.''<ref name=":5" /> === For Young Readers === Ó Scolaí has written illustrated books for young readers (8–10 years old) in two series, the Fionn Series and the Scéalta Staire series, and translated a large number of classics and popular books for children of all ages. The number of these written and translated works suggests a commitment to children and their literacy in Irish. The Fionn Series “is a retelling ... of the great legends of the Fianna for the young Irish readers of today.”<ref name=":6">{{Cite web|url=https://leabharbreac.com/en/shop/oige-en/8-9/doiteoir-na-samhna/|title=Dóiteoir na Samhna|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> [[wikipedia:The_Boyhood_Deeds_of_Fionn|Macgnímartha Finn (The Boyhood Deeds of Fionn)]] is a medieval story in the [[wikipedia:Fenian_Cycle|Fenian Cycle]]. * ''An Bradán Feasa'' (trans., ''The Salmon of Knowledge''), Leabhar Breac, 2010, “shortlisted for the Réics Carlo award 2010.”<ref name=":9">{{Cite web|url=https://leabharbreac.com/en/shop/oige-en/8-9/an-bradan-feasa/|title=An Bradán Feasa|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> * ''Dóiteoir na Samhna'' (trans., ''The Halloween Burner''), 2010.<ref name=":6" /> * ''Bodach an Chóta Lachna'' (trans., ''The Churl in the Dun Coat''), 2011.<ref>{{Cite web|url=https://leabharbreac.com/en/shop/oige-en/7-8/bodach-an-chota-lachna/|title=Bodach an Chóta Lachna|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> The Scéalta Staire (Historical Stories) series<ref name=":9" /> * ''Mánas Ó Dónaill'', 2000. * ''Seán Ó Néill'', Leabhar Breac, 2000. * ''Gráinne Mhaol Ní Mháille'', Leabhar Breac, 2003. * ''Tadhg Dall Ó hUiginn'', Leabhar Breac, 2003. ==== Translations ==== * Robert Louis Stevenson, ''Oileán an Órchiste'' (trans. of ''Treasure Island''), Leabhar Breac, 2014.<ref>{{Cite journal|date=2025-06-19|title=Oireachtas na Gaeilge|url=https://en.wikipedia.org/w/index.php?title=Oireachtas_na_Gaeilge&oldid=1296394643|journal=Wikipedia|language=en}}</ref> * Robert Louis Stevenson, ''An Fuadach'' (trans. of ''Kidnapped''), Leabhar Breac, 2016. * Clement Clarke Moore, ''Cuairt San Nioclás'' (trans. of ''A Visit from St. Nicholas'', or "'Twas the Night Before Christmas"), Leabhar Breac, 2022. '''''The Corto Maltese Graphic Novels''''' Written in Italian by Hugo Pratt and translated by Ó Scolaí, both adults and teenagers read this series of Italian adventure graphic novels.<ref>{{Cite journal|date=2025-07-01|title=Corto Maltese|url=https://en.wikipedia.org/w/index.php?title=Corto_Maltese&oldid=1298285365|journal=Wikipedia|language=en}}</ref> Ó Scolaí's '''translation of ''Corto Maltese''''' was listed in 2017 among "The 30 Irish books that Irish people love."<ref>{{Cite journal|last=Ó Murchú|first=Eoin P.|date=09/06/2017|title=Na 30 leabhar Gaeilge is fearr leis na Gaeil [The 30 Irish books that Irish people love]|url=https://nos.ie/cultur/leabhair/an-30-leabhar-gaeilge-is-fearr-leis-na-gaeil/|journal=Nós}}</ref> * Hugo Pratt, ''Corto: Port na Farraige Goirt'', Leabhar Breac, 2013. * Hugo Pratt, ''Corto: The Golden House in Samarkand'', 2014. * Hugo Pratt, ''Corto: Na Liopard-Fhir ó Rufiji'' (trans. of ''Corto: The Leopard Men of Rufiji''), Leabhar Breac, 2014. * Hugo Pratt, ''Corto: In Ainm Dé Uilthrócairigh'' (trans. of ''Corto: In the Name of God All-Merciful''), Leabhar Breac, 2014. * Hugo Pratt, ''Corto: Tóraíocht Eile'' (trans. of ''Corto: Another Quest''), Leabhar Breac, 2014. * Hugo Pratt, ''Corto: Sa tSibéir'' (trans. of ''Corto: In Siberia''), Leabhar Breac, 2016. '''''Other Translations for Children''''' Ó Scolaí has translated into Irish six books from the ''Le Pavillon Noir'' (trans., ''Jolly Roger'') series by Alain Surget; four books from the ''Catalan First Steps'' series by Enric Lluch Girbés and the ''Caitlín & Cormac'' series by Joan Carles; three books from the ''Louisette le Taupe'' series by Bruno Heitz, and three books from the ''Loup'' series by Orianne Lallemand. === Plays and Screenplays === ==== Stage Plays ==== Ó Scolaí was writer and director of the original productions of two plays in the ''Trí Bhraon'' (trans., ''Three Drops'') trilogy; ''Coinneáil Orainn'' was directed by Darach Mac Con Iomaire and staged by An Taibhdhearc. All three plays have been published in book form by Leabhar Breac. * ''Coinneáil Orainn'' (trans., ''We'll Keep Going''), 2005.<ref>{{Cite web|url=https://irishplayography.com/play?playid=32553|title=Coinneáil Orainn|date=2025|website=PlayographyIreland: A Comprehensive Database of New Irish Plays Produced Professionally Since 1904.|access-date=25 August 2025}}</ref> The first play in the ''Trí Bhraon'' (''Three Drops'') trilogy. [[wikipedia:Taibhdhearc_na_Gaillimhe|An Taibhdhearc]], the national Irish-language theatre of Ireland, toured the country in 2005 with ''Coinneáil Orainn''.<ref>{{Cite web|url=https://leabharbreac.com/en/shop/darach-o-scolai/coinneail-orainn/|title=Coinneáil Orainn|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> Walter Macken Prize, 2005; BBC Stewart Parker Award, 2006.<ref>{{Cite web|url=https://irishplayography.com/person/darach-scola|title=Darach Ó Scolaí|date=2025|website=PlayographyIreland: A Comprehensive Database of New Irish Plays Produced Professionally Since 1904.|access-date=25 August 2025}}</ref> * ''Branwen'', 2006, by Darach Ó Scolaí and Ifor ap Glyn, in Irish, Welsh and English, co-produced by Project Arts Centre and Llwyfan Gogledd Cymru, toured the Republic of Ireland and Wales.<ref>{{Cite web|url=https://irishplayography.com/play?playid=32418|title=Branwen|date=2025|website=PlayographyIreland: A Comprehensive Database of New Irish Plays Produced Professionally Since 1904|access-date=25 August 2025}}</ref> * ''An Braon'' Aníos (trans., ''Rising Damp''), 2006, directed by Ó Scolaí.<ref>{{Cite web|url=https://irishplayography.com/play?playid=32461|title=An Braon Aníos|date=2025|website=PlayographyIreland: A Comprehensive Database of New Irish Plays Produced Professionally Since 1904|access-date=25 August 2025}}</ref> The second play in the ''Trí Bhraon'' (''Three Drops'') trilogy. “The Salamandar company toured the country in 2006-07 with this play, and Salamandar also produced a radio version of the play for RTÉ Raidió na Gaeltachta in 2009.”<ref>{{Cite web|url=https://leabharbreac.com/en/shop/darach-o-scolai/an-braon-anios/|title=An Braon Aníos|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> * ''Craos'' (trans., ''Gluttony''), 2008, directed by Ó Scolaí.<ref name=":13">{{Cite web|url=https://irishplayography.com/play?playid=32867|title=Craos|date=2025|website=PlayographyIreland: A Comprehensive Database of New Irish Plays Produced Professionally Since 1904|access-date=25 August 2025}}</ref> The third play in the ''Trí Bhraon'' (''Three Drops'') trilogy, it toured to Cork and Belfast.<ref name=":13" /> A review of the 2008 Salamander performance in the ''Irish Times'' says, “a humorous play which offers plenty to think about, fine acting, and sparklingly witty dialogue.”<ref>{{Cite web|url=https://leabharbreac.com/en/shop/darach-o-scolai/craos-2/|title=Craos|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> * ''A+E'', 2008, by Ríonach Ní Néill and Darach Ó Scolaí, "dance and music drama," co-produced by Ciotóg and Salamandar.<ref>{{Cite web|url=https://irishplayography.com/play?playid=32962|title=A+E|date=2025|website=PlayographyIreland: A Comprehensive Database of New Irish Plays Produced Professionally Since 1904|access-date=25 August 2025}}</ref> * ''An tSeanbhróg'' (trans., ''The Old Shoe''), 2009, produced by Salamander<ref>{{Cite web|url=https://irishplayography.com/play?playid=33042|title=An tSeanbhróg|date=2025|website=PlayographyIreland: A Comprehensive Database of New Irish Plays Produced Professionally Since 1904|access-date=25 August 2025}}</ref> and staged in the Axis Arts Centre, Dublin, and the Letterkenny Arts Centre. * '''In ''Mhuir Fhíondorcha/The Wine-Dark Sea: The Homer Project'', Ó Scolaí's translation of Homer's Cyclops story, performed at the 2019 IMRAM festival'''.<ref>{{Cite news|url=https://www.irishtimes.com/culture/books/imram-a-festival-celebrating-the-irish-language-1.4047610|title=Imram: a festival celebrating the Irish language. Liam Carson reveals the myths and legends appearing in this year’s programme|last=Carson|first=Liam|date=11 October 2019|work=The Irish Times|access-date=15 October 2025}}</ref> ==== Screenplays ==== * ''Cosa Nite'' (trans., ''Washed Feet''), short film, 1998 (dir. Dearbhla Walsh, prod. Ciarán Ó Cofaigh, Rosg); "a prose version of ''Cosa Nite'' was published (Rosg 2000)."<ref name=":9" /> Nominated for an Irish Film and Television Award.<ref>{{Citation|title=Cosa Nite (Short 1998) - Awards - IMDb|url=https://www.imdb.com/title/tt0191917/awards/|accessdate=2025-08-25|language=en-US}}</ref> * ''Na Glúnta'' (trans., ''The Generations''), 2001<ref>{{Cite web|url=https://www.iftn.ie/production/production_companies/production_sub/feature/?act1=record&aid=70&rid=3917&tpl=filmography_dets&only=1&force=1|title=Na Glúnta {{!}} The Irish Film & Television Network|website=www.iftn.ie|access-date=2025-08-25}}</ref>, co-directors Ciarán Ó Cofaigh & Darach Ó Scolaí, prod. Ciarán Ó Cofaigh, Rosg. * ''An Leabhar'' (trans., ''The Book''), short film, 2000, (dir. Robert Quinn, prod. Ciarán Ó Cofaigh, Rosg) Rosg, 2000.<ref>{{Citation|title=An Leabhar|url=https://www.imdb.com/title/tt0963767/|publisher=Bord Scannán na hÉireann / The Irish Film Board, ROSG|accessdate=2025-08-25|first=Robert|last=Quinn|others=Colm O&apos;Maonlai, Peadar O&apos;Treasaigh, Diarmuid Mac an Adhastair}}</ref> * ''Na Cloigne'' [trans., The Heads], 3-episide series, 2010 (dir. Robert Quinn, prod. Ciarán Ó Cofaigh, Rosg), TG4.<ref>{{Cite web|url=https://www.imdb.com/title/tt1607924/|title=Na cloigne|date=2010|website=IMDb|access-date=25 August 2025}}</ref> === Nonfiction === Ó Scolaí's essays and lectures are published and his interviews are broadcast regularly, making for a large body of nonfiction critical and analytical work. Here are a few, almost all published in [https://comhar.ie/iris/scribhneoiri/darach-o-scolai/ Comhar]: * “Ceol Ciúin na nÉagmaise” (trans., “The Silent Music of Absence ['''the Fall?''']”), an essay on the 2014 Nobel Prize winner for literature, [[wikipedia:Patrick_Modiano|Patrick Modiano]], ''Comhar'', December 2014. * The Ó Cadhain Lecture: [https://leachtaiuichadhain.clo.ie/leachtai/2014 “Cuimhne agus Díchuimhne (trans., “Memory & Forgetfulness"]), 2014. * “Rithim agus Réim” ("Rhythm and Register"), a public lecture in the University College Dublin lecture series “Ó Thrácht go Twitter” (trans., "From Talk to Twitter"), 2014. * Review of Pádraig Ó Cíobháin’s ''Dréachta Chrích Fodla'', '''Comhar?, ??'''. * “Na Geilt i mBun an Tí” (trans., "The Madmen in Charge"), a talk at the Merriman Winter School, Comhar April 2012.<ref name=":18">{{Cite web|url=http://darachoscolai.ie/beathaisneis.html|title=Darach Ó Scolaí: Beathaisnéis|website=darachoscolai.ie|access-date=2025-09-26}}</ref> * The EFACIS podcast: Síle Ní Choincheannain talks to Darach Ó Scolaí about the historical novel. == Critical Reception == Ó Scolaí’s style has been called “crisp and elegant, and rich in language while being highly readable,”<ref>{{Cite journal|last=Heussaf|first=Anna|date=Summer 2025|title=Bláthnaid—A tale of love, violence and sorcery retold for readers today|url=https://booksirelandmagazine.com/blathnaid-a-tale-of-love-violence-and-sorcery/|journal=Books Ireland}}</ref> with “an unsurpassed richness and precision of language.”<ref name=":12">{{Cite journal|last=Ó Cróinín|first=Breandán|date=Summer 2025|title=unknown|journal=The Limerick Leader}}</ref> “Whimsical, hilarious, and subtly learned” is how Éilis Ní Dhuibhne described his writing.<ref name=":20" /> === Original Works === Ó Scolaí’s first novel, the 2007 ''An Cléireach'' (''The Clerk'') won two prizes and was described as “one of the great historical novels in the Irish language and among the best books written in the language since the beginning of this century.”<ref name=":12" /> Novelist Alan Titley says, “In ''An Cléireach'' Ó Scolaí creates the Ireland of war in the 17th century more fully than any other Irish writer on the subject of war since ''L’Attaque'' Eoghain Ó Thuairisc around 1798 [In ''An Cléireach'' cruthaíonn Ó Scolaí Éire an chogaidh san 17ú haois níos iomláine ná mar a dhein aon scríbhneoir Gaeilge eile ar ábhar cogaidh ó ''L’Attaque'' Eoghain Uí Thuairisc timpeall ar 1798].”<ref name=":11" />{{rp|25, Col. 1a}} Not all the reviews of this first novel were so positive, however; Proinsias O' Drisceoil says for the Irish Times says,<blockquote>This then is a novel in search of a plot, a story that attempts to attain a significance that eludes it.<ref>{{Cite news|url=https://www.irishtimes.com/news/a-disaffected-clerk-in-the-confederates-1.943070|title=A disaffected clerk in the confederates|last=O' Drisceoil|first=Proinsias|date=5 July 2008|work=The Irish Times|access-date=16 October 2025}}</ref></blockquote> In the ''Oxford Handbook of Modern Irish Fiction'' Pádraig Ó Siadhail analyzes rather than reviews ''An Cléireach'': <blockquote>In ''An Cléireach'', Ó Scolaí revisits the trauma of Cromwellian Ireland. The primary narrative device is once again the first-hand account, in this case by Tadhg Ó Dúbháin, a clerk and quartermaster in the Confederate Army in 1650. We sample the hardships, the friendships, the tensions, the rivalries, and the petty jealousies amongst comrades in arms, including remnants of the Gaelic literary class, as the Confederate soldiers, increasingly a rabble more than a cohesive unit, retreat in advance of Cromwell’s forces. ''An Cléireach'' concludes with the narrator and his family in exile in continental Europe. But along the retreat route, and central to the novel, members of the Confederate army camp, rest up, and tell versions of a story about the keeper of the treasured manuscript "Saltair an Easpaig" (The Bishop’s Psalter). Their versions raise issues about memory construction, the limitations of individual perspectives, personal agendas, and how minor changes in the telling of a story can alter our understanding of history, Thus, ''An Cléireach'' complements ''Fontenoy'' in moving beyond more realistic recreation of a historical event or period to interrogate the notion of history as construct.<ref>{{Cite book|title=The Oxford Handbook of Modern Irish Fiction|last=Ó Siadhail|first=Pádraig|publisher=Oxford University Press|year=2020|isbn=9780198754893|editor-last=Harte|editor-first=Liam|pages=598–99|chapter=Contemporary Irish Fiction}}</ref> </blockquote> Of ''Súil an Daill,'' in ''Nós'', Cathal Seoighe says, "The book deserves a significant place among the collection of high-quality books published in recent years that would make you feel sorry for someone who does not speak Irish [Tá áit shuntasach ag dul don leabhar i measc an chnuasaigh leabhair ar ardchaighdeán a foilsíodh le roinnt blianta anuas a d’fhágfadh trua agat don té atá gan Ghaeilge]."<ref>{{Cite journal|last=Seoighe|first=Cathal|date=09/26/2022|title=‘Dar leathmhagairle an diabhail, is leabhar den scoth é seo!’ ['According to the devil’s half-wit, this is a great book!’]|url=https://nos.ie/cultur/leabhair/dar-leathmhagairle-an-diabhail-is-leabhar-den-scoth-e-seo/|journal=Nós}}</ref> ''Bódléar'', Ó Scolaí's most recent book, is a “beautiful novel. There is magic and craftsmanship in it. A small miracle of a book and it is highly recommended.”<ref>{{Cite web|url=https://leabharbreac.com/bodlear-mioruilt-bheag-de-leabhar/|title=Bódléar: Míorúilt bheag de leabhar (Bódléar: A Small Miracle of a Book)|last=Ní Ghairbhí|first=Róisín|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> Éilis Ní Dhuibhne in the ''Irish Times'' says,<blockquote>what a gem! An affectionately gentle satire of the Irish poetic scene during one creatively fluid 19th-century year, the story focuses on a Maigue poet and schoolteacher who goes on a trip to France and returns with camembert, a cafetiere, ‘Fleurs du Mal’, and a mission to convert the local traditionalists to la modernité. Whimsical, hilarious, and subtly learned, it’s absolutely delightful!<ref name=":20">{{Cite journal|last=Ní Dhuibhne|first=Éilis|date=30 June 2025|title=Éilís Ní Dhuibhne on the best Irish language books of 2025 so far: Including a history of the Gaeltacht Civil Rights Movements, a gem of a novel by Darach Ó Scolaí and Joe McHugh’s entertaining account of learning Irish|url=https://www.irishtimes.com/culture/books/review/2025/06/30/eilis-ni-dhuibhne-on-the-best-irish-language-books-of-2025-so-far/|journal=The Irish Times|pages=22}}</ref></blockquote> === Retellings and Translations === ==== ''Táin Bó Cuailnge'' ==== ''Táin Bó Cuailnge'' [''The Cattle Raid of Cooley''] is a modern edition of an 11th-century epic into modern Irish.<ref name=":3" /> Gearóid Denvir reviewed ''Táin Bó Cuailnge'' for ''Comhar'':<blockquote>Darach Ó Scolaí has ​​achieved a feat in this challenging reworking. He has found a high level of the Irish language to tell his story – as he has done before in his groundbreaking novel An Cléireach (2007, Leabhar Breac) and in his other prose works. This book is a decoration of the language, literature and culture of the Irish language, following the path of the old storytellers and writers and presenting material from the tradition to his own generation according to the understandings of his own time. The book will be a classic that will be of great interest to all readers of the Irish language, both ordinary readers, students, scholars and writers, and there should be a copy in every home in the country. [Tá éacht déanta ag Darach Ó Scolaí san athleagan dúshlánach seo. Tá réim ard den teanga Ghaeilge aimsithe aige lena scéal a inseacht – mar a rinne sé cheana ina úrscéal ceannródaíoch An Cléireach (2007, Leabhar Breac) agus i saothair eile phróis dá chuid. Is maisiú ar an teanga agus ar litríocht agus cultúr na Gaeilge an leabhar seo a leanas conair na seanscéalaithe agus na seanscríobhaithe agus ábhar de chuid an traidisiúin á chur i láthair a ghlúine féin aige de réir thuiscintí a linne féin. Clasaic a bheas sa leabhar a gcuirfidh léitheoirí uilig na Gaeilge, idir ghnáthléitheoirí, mhic léinn, scoláirí agus scríbhneoirí spéis thar na bearta ann, agus ba cheart cóip a bheith i chuile theach sa tír.]<ref name=":15">{{Cite journal|last=Denvir|first=Gearóid|date=April 2018|title=Táin Bó Cuailgne|url=https://comhar.ie/iris/78/4/leirmheas/|journal=Comhar|via=JSTOR}}</ref> </blockquote>Cathal Poirtéir says, "The freshness and richness of Ó Scolaí’s version are a joy …. The author delights us with the linguistic and stylistic richness of the ancient epic in a modern-Irish version that reflects the original’s spirit and language."<ref>{{Cite journal|last=Poirtéir|first=Cathal|date=May/June 2018|title=Leabhair Idir Lámha|url=https://www.jstor.org/stable/26564180|journal=Books Ireland|pages=46–47|via=JSTOR}}</ref>{{rp|47}} Novelist and academic Alan Titley calls Ó Scolaí's "a wonderful gutsy telling" of ''Táin Bó Cuailnge''.<ref>{{Cite news|url=https://www.irishtimes.com/culture/2023/03/11/the-tain-retold-maeve-and-ailills-spat-could-be-out-of-a-soap-opera/|title=The Táin retold: ‘Maeve and Ailill’s spat could be out of a soap opera’|last=Titley|first=Alan|date=11 March 2023|work=The Irish Times|access-date=16 October 2025}}</ref> ==== ''Deirdre'' ==== Marie Whelton, in "Léann Teanga" ("Language Studies"), in the 2024 ''An Reiviú'' says,<blockquote>this version [of ''Deirdre''] by Darach Ó Scolaí succeeds in skillfully capturing and portraying the complexity of gender and power issues in the ‘Deirdre’ tradition [éiríonn leis an leagan seo le Darach Ó Scolaí castacht cheisteanna na hinscne agus na cumhachta i dtraidisiún scéal Dheirdre a ghabháil agus a léiriú go sciliúil]. … There is no doubt that this new version greatly contributes to the legacy of the story and that it revives that legacy thoughtfully and artistically [Níl amhras faoi ach go gcuireann an leagan úr seo go mór le hoidhreacht an scéil agus go ndéanann sé an oidhreacht sin a athbheochan go tuisceanach agus go healaíonta.].<ref name=":16">{{Cite web|url=https://www.tara.tcd.ie/tara8/server/api/core/bitstreams/3c20175a-7631-44b2-8b0f-f454edd712b4/content|title=An Artistic Retelling of Deirdre's Tale and the Defeat of Conor Review of Deirdre or the Ship of Mac Uisnigh by Darach Ó Scolaí [Athinsint Ealaíonta ar Oidhe Dheirdre agus ar Ansmacht Chonchúir Léirmheas ar Deirdre nó Loingeas Mhac Uisnigh le Darach Ó Scolaí]|last=Whelton|first=Marie|date=2024|website=The Review [An Reiviú], Language Studies [Léann Teanga]|access-date=25 September 2025}}</ref></blockquote> === Works for Young Readers === Meadhbh Ní Eadhra said of ''Bodach an Chóta Lachna'' that it was "Beautiful Irish, but easy to understand for young readers."<ref>Ní Eadhra, Meadhbh. In ''Gaelscéal'', qtd. in "Bodach an Chóta Lachna" https://leabharbreac.com/en/shop/oige-en/7-8/bodach-an-chota-lachna/.</ref> == Awards and Honors == Ó Scolaí's works are regularly nominated and make the short list for prizes, an honor in itself, but they are generally not listed here unless they are named as the first-place winner in their category. === Oireachtas Prize === The Oireachtas Prize is the literary prize awarded by [[wikipedia:Oireachtas_na_Gaeilge|Oireachtas na Gaeilge]], the annual arts festival dedicated to Irish language, arts and culture. Darach Ó Scolaí has won the Oireachtas Prize for Literary Fiction three times, once for ''An Cléireach'' (''The Clerk'') in 2007, for ''Súil an Daill'' (''The Eye of the Blind'') in 2021 and for ''Bódléar'' in 2024. * 2007, for ''An Cléireach'' (trans., ''The Clerk'') — “(a special prize commemorating the 400th anniversary of the foundation of Coláiste na nGael in Louvain, awarded under the auspices of the Franciscan Province of Ireland). The prize of €10,000 was the largest prize ever awarded to an Irish language novel [(duais speisialta chomórtha 400 bliain bhunú Choláiste na nGael i Lobháin a bronnadh faoi urraíocht Phroibhinse Phroinsiasach na hÉireann). Ba é an duais €10,000 sin an duais ba mhó a bronnadh riamh ar úrscéal Gaeilge].”<ref name=":18" /> * 2021, for ''Súil an Daill'' (''The Eye of the Blind'') * 2024, for ''Bódléar'' === Ó Shúilleabháin Award, Irish language “Book of the Year” === The first prize of this award includes €5,000 to the publisher and €2,500 to the author of the winning work.<ref name=":10">{{Cite journal|date=15 August 2023|title=20 saothar san iomaíocht do ‘Leabhair Ghaeilge na Bliana 2023’|url=https://tuairisc.ie/20-saothar-san-iomaiocht-do-leabhair-ghaeilge-na-bliana-2023/|journal=Tuairisc}}</ref> * ''An Cléireach'' (''The Clerk'').<ref>{{Cite web|url=http:/www.gaelport.com/uploads/documents/edition19.html|title=Eagrán / Edition 19 - 04 11 2008|date=4/11/2008|website=Internet Archive|archive-url=https://web.archive.org/web/20130525011340/http:/www.gaelport.com/uploads/documents/edition19.html|archive-date=25 May 2013|access-date=25 August 2025}}</ref> * ''Táin Bó Cuailnge'', 2018. * ''Bódléar'', 2025. ==== De Bhaldraithe Award ==== The Gradam de Bhaldraithe is awarded to the best work in translation.<ref name=":10" /> * ''Cuairt San Nioclás,'' a translation of Clement Clarke Moore's ''A Visit from St. Nicholas'', or "'Twas the Night Before Christmas."<ref name=":10" /> ==== Other ==== * Walter Macken Prize, for ''Coinneáil Orainn'' (trans., ''We'll Keep Going''), 2005 * Bháiteir Uí Mhaicín Memorial Award, for ''Coinneáil Orainn'' (trans., ''We'll Keep Going''), 2005<ref>{{Cite news|url=https://www.irishtimes.com/gaeilge/tuarascail/duais-oireachtais-1.501571|title=Oireachtas Prize: Over €50,000 was awarded to writers in the Oireachtas Literary Competitions at an event in Dublin last night. Winners… [Duais Oireachtais: Bronnadh breis agus €50,000 ar scríbhneoirí i gComórtais Liteartha an Oireachtais ar ócáid i mBaile Átha Cliath aréir. Bhuaigh…]|work=5 October 2005|access-date=15 October 2025}}</ref> * BBC Stewart Parker Award, for ''Coinneáil Orainn'' (trans., ''We'll Keep Going''), 2006 * The Aodán Mac Póilín Commemorative Prize, for ''Táin Bó Cuailnge'' (trans., ''The Cattle Raid of Cooley''), 2017 == External Links == * Leabhar Breac website: https://leabharbreac.com/en/ * Leabhar Breac Facebook pages: * Rosg website: [http://www.rosg.ie/en/ <nowiki>http://ww</nowiki>w.rosg.ie/en/] * Art on the Island (Ealaín ar Oileán) website, archived at the Wayback Machine: https://web.archive.org/web/20130601000520/http://ealainaroilean.ie/ 31 March 2012, 1 June 2013 and 8 January 2014 * Darach Ó Scolaí's website Archived 25 September 2015 at the Wayback Machine: https://web.archive.org/web/20150925103456/http://darachoscolai.ie/ * Youtube video of [https://www.youtube.com/watch?v=OlP2AmSBzXc Breandán Ó Cróinin introducing Deirdre at the book launch] in the pub Tigh Mholly (Molly’s House). == Primordial Ooze == * Known for his sensitivity to language and voices. * Finish scanning through JSTOR * Scan through Irish Times, 56 hits * Check Goodreads * Check YouTube (In the spring of 2013, the arts programme Imeall interviewed the author on TG4.) * Check both Wikipedias for pages on the origins of the retold tales (like Deirdre) and link to this article * Propose link from University of Galway page once Darach’s is up * Write Irish National Biography (<nowiki>https://www.dib.ie</nowiki>) to propose an article about Darach once the Wikip article is done? See what they say. * Link to Ó Scolaí from the Wikipedia * Make sure links '''to''' Wikipedia in the actual encyclopedia work right === Not Placed Yet === * "So here are the books that Irish people love the most! [Mar sin seo iad na leabhair is gile leis na Gaeil!]" — "32. An Cléireach – Darach Ó Scolaí (2)" [18 books got 2 votes, and then they're alphabetized by author's last name, so the 32 of 34 doesn't signify the specificity it seems to]<ref name=":14">{{Cite journal|last=Ó Murchú|first=Eoin P.|date=9 June 2017|title=Na 30 leabhar Gaeilge is fearr leis na Gaeil. [The 30 best Irish books for Irish people]|url=https://nos.ie/cultur/leabhair/an-30-leabhar-gaeilge-is-fearr-leis-na-gaeil/|journal=Nós}}</ref> * "Below is a list of those 111 works – a list that shows a great deal of diversity in the reading habits of Irish speakers.Here is a list of those 111 works – a list that shows a great deal of diversity in the reading habits of Irish speakers [Anseo thíos tá liosta den 111 saothar sin – liosta a léiríonn éagsúlacht an-mhór i nósanna léitheoireachta Gaeilgeoirí.Anseo thíos tá liosta den 111 saothar sin – liosta a léiríonn éagsúlacht an-mhór i nósanna léitheoireachta Gaeilgeoirí]." "Corto Maltese – Hugo Pratt (aistrithe ag Darach Ó Scolaí)"<ref name=":14" /> * "Ceann eile de bhuaicphointí na hÉigse a bheidh sa seisiún le Darach Ó Scolaí, duine d’úrscéalaithe móra na Gaeilge, agus duine de chomhbhunaitheoirí teach foilsitheoireachta Leabhar Breac. [Another highlight of the Éigse will be the session with Darach Ó Scolaí, one of the great Irish language novelists, and one of the co-founders of the publishing house Leabhar Breac.]"<ref name=":17">{{Cite journal|last=Nós|date=4 May 2023|title=Éigse na Bruiséile le filleadh i mí na Bealtaine. [Éigse na Bruséile to return in May]|url=https://nos.ie/cultur/eigse-na-bruiseile-le-filleadh-i-mi-na-bealtaine/|journal=Nós}}</ref> === Things Taken Out for Now === “’The play is a comedy about language, lies, bureaucracy and Gaeltacht grants, in the tradition of Myles na Gcopaleen,’ according to Norma-Jean Kenny in the ''Galway Advertizer'', ‘in which the author comments and criticizes the institutions of the Irish language in Ireland without ceasing.’" Supposedly a quotation by Gearóid Denvir reviewing ''Táin Bó Cuailnge'' for ''Comhar'' (but I don't find it in the article): This book has long been needed by Irish language readers and there is no doubt that it will become a classic in time and surpass Thomas Kinsella’s English version. This version remains faithful to the language of the original while at the same time finding an appropriate language in today’s Irish. Ó Scolaí masterfully overcomes the difficulties of the original’s rhetorical difficulties and the versions of the original poetic texts are extremely effective.[supposedly <ref name=":15" />] “The biggest prize ever awarded for a novel in Irish was presented at a special ceremony in the National Concert Hall in Dublin, today (Thursday, 4 October 2007). Darach Ó Scolaí, writer, artist & playwright from Casla, Co. Galway, was awarded €10,000 for his literary novel, ‘An Ardscoil’. This work, under the new title ‘An Cléireach’, will be launched at Oireachtas na Samhna in Westport in November. This is the first novel from his pen, a story set in the late seventeenth century. This competition was sponsored by the Franciscan Province of Ireland.” (archive, Oireachtas na Gaeilge site, 04 October, 2007) ''Súil an Daill'' (trans., ''The Eye of the Blind''), Leabhar Breac, 2021. number 2 in ''Comhar'' literary magazine’s list of best books of 2021. '''{6}.''' *William Shakespeare, ''Romeo agus Juliet'' (trans. of ''Romeo and Juliet''), Leabhar Breac, 2016. *Jonathan Swift, ''Camchuairt Ghuilivéir'' (trans. of ''Gulliver's Travels''), Leabhar Breac, 2016. *Hugo Pratt, ''Corto Maltese'' '''''Flag of Bones (Bratach na gCnámh) Series''''' Leabhar Breac published the Bratach na gCnámh series of books for young readers. Written in French by Alain Surget, illustrated by Annette Marnat and translated by Darach Ó Scolaí, this series uses the history of Caribbean Sea pirates<ref>{{Cite web|url=https://leabharbreac.com/en/product-category/alain-surget/|title=Alain Surget Archives|website=Leabhar Breac|language=en-US|access-date=2025-09-30}}</ref>: *Alain Surget, ''Éalú as Páras'' (''Escape from Paris''), Annette Marnat (Illustr.), Leabhar Breac, 2011. * Alain Surget, ''Oilean na Siorcanna'' (''Shark Island''), Annette Marnat (Illustr.), Leabhar Breac, 2011. * Alain Surget, ''Long na dTaibhsi'' (''Ship of the Ghosts''), Annette Marnat (Illustr.), Leabhar Breac, 2011. * Alain Surget, ''San Ochtapas Dubh'' (''In the Black Octopus''), Annette Marnat (Illustr.), Leabhar Breac, 2013. * Alain Surget, ''San Ionsai ar Veracruz'' (''The Attack on Veracruz''), Annette Marnat (Illustr.), Leabhar Breac, 2013. '''''For "First Readers" (children to 6 years old or so)''''' These books were written originally in Catalan by Spanish author Enric Lluch Girbés and translated into Irish by Ó ScolaÍ: *Enric Lluch, ''Ag Péinteáil an Tí'' (''Painting the House''), Anna Clariana (Illustr.), Leabhar Breac, 2017. *Enric Lluch, ''An Colúr Bacach'' (''The Lazy Dove''), Anna Clariana (Illustr.), Leabhar Breac, 2017. *Enric Lluch, ''An Phluais'' (''The Cave''), Anna Clariana (Illustr.), Leabhar Breac, 2017. *Enric Lluch, ''Madra Dhaideo'' (''Grandpa's Dog''), Anna Clariana (Illustr.), Leabhar Breac, 2017. *Enric Lluch, ''Fiacail Mháire'' (''Mary's Tooth''), Anna Clariana (Illustr.), Leabhar Breac, 2017. '''''Bruno Heitz''''' Leabhar Breac published a series of 3 Heitz books for small children. Published originally in French, this series of three comic books is about a blind mole named Cáitín Chaoch in Irish (and ''Louisette la taupe'' in French).<ref>{{Cite web|url=https://leabharbreac.com/en/product-category/bruno-heitz-en/|title=Bruno Heitz Archives|website=Leabhar Breac|language=en-US|access-date=2025-10-02}}</ref> Ó Scolaí translated these: *Bruno Heitz (author and illustr.), ''Práinneach'' (''Urgent''), Leabhar Breac, 2020 *Bruno Heitz (author and illustr.), ''Preab san Aer'' (''Bounce in the Air''), Leabhar Breac, 2020. '''''Books for Toddlers''''' Leabhar Breac has published 14 books written by French author Orianne Lallemand's and illustrated by Eleonore Thuillier, about Lallemmand's popular character Loup, Wolf. These are translated by Ó Scolaí: *Orianne Lallemand, ''An Mac Tire a Raibh Faitios an Domhain Air'' (trans. of ''The Son Who Saw the World in His Eyes''), Eleonore Thuillier  Illustr.), Leabhar Breac, 2018. *Orianne Lallemand, ''Macan agus an Goban'' (trans. of ''Macan and the Goblin''), Eleonore Thuillier (Illustr.), Leabhar Breac, 2018. * Orianne Lallemand, ''A Mac Tíre a Chuaigh go Tóin na Farraige'' (trans. of ''The Wolf Who Went to the Bottom of the Sea''), Éléanore Thuillier  (Illustr.), Leabhar Breac, 2019. '''''Board Books (for babies)''''' J. C. (Joan Carles) Girbés Aparisi is a Catalan author and editor. These books were written in Catalan and translated by Ó Scolai. *J. C. Girbés, ''An Phicnic'' (''The Picnic''), Silvia Ortega (Illustr.), Leabhar Breac, 2013. * J. C. Girbés, ''An Chóisir'' (''The Party''), Silvia Ortega (Illustr.), Leabhar Breac, 2013. *J. C. Girbés, ''Lá Mór Fada'' (''A Long Day''), Silvia Ortega (Illustr.), Leabhar Breac, 2014. *J. C. Girbés, ''Tabhair Leat do Leabhar'' (''Bring Your Book''), Silvia Ortega (Illustr.), Leabhar Breac, 2014. ==== Gradam Réics Carló ==== The Réics Carló prize is awarded for the best book in the Irish language for young readers. It is named for one of the characters of 20th-century writer [[wikipedia:Cathal_Ó_Sándair|Cathal Ó Sándair (Charles Saunders)]]. * ''An Bradán Feasa'' was “shortlisted for the Réics Carlo award 2010.”<ref name=":9" /> == References == {{reflist}} 55f2jzw5952pljrcs3md5lp5jbm6kvh 2823747 2823684 2026-08-20T21:47:07Z Scogdill 1331941 2823747 wikitext text/x-wiki {{Short description|Dress worn by Queen Victoria at her wedding to Prince Albert in 1840}} = Sandbox = Page to draft revisions for Wikipedia articles. For Gwladys Robinson, see Gwladys Lowther Robinson, [[Social Victorians/People/Ripon|Marchioness of Ripon]] and, earlier, [[Social Victorians/People/Lowther|Countess of Lonsdale]] ==References== {{reflist|2}} [[Category:1840 works]] [[Category:Royal wedding dresses|Victoria Queen]] [[Category:1840s fashion]] [[Category:British royal attire]] [[Category:Dresses in the Royal Collection of the United Kingdom|Victoria, Wedding]] [[Category:Diamond Jubilee of Queen Victoria]] = Victorian fashion = '''Victorian fashion''' consists of the various fashions and trends in [[Culture of the United Kingdom|British culture]] that emerged and developed in the [[United Kingdom of Great Britain and Ireland|United Kingdom]] and the [[British Empire]] throughout the [[Victorian era]], roughly from the 1830s through the 1890s. The period saw many changes in fashion, including changes in styles, fashion technology and the methods of distribution. Various movements in architecture, literature, and the [[decorative arts|decorative]] and [[visual arts]] as well as a changing perception of [[gender roles]] also influenced fashion. Under [[Queen Victoria]]'s reign, England enjoyed a period of growth along with technological advancement. [[Mass production]] of sewing machines in the 1850s as well as the advent of synthetic dyes introduced major changes in fashion.<ref name=":3">{{Cite book|title=The Culture of Fashion|last=Breward|first=Christopher|publisher=Manchester University Press|year=1995|pages=145–180}}</ref> Clothing could be made more quickly and cheaply. Fashion made more extreme and more rapid changes than it had in prior centuries. Advancement in printing and proliferation of fashion magazines allowed the masses to participate in the evolving trends of high fashion, opening the market of mass consumption and advertising. By 1905, clothing was increasingly factory made and often sold in large, fixed-price department stores, spurring an age of consumerism with the rising middle classes, who benefited from the [[Industrial Revolution|industrial revolution]].<ref name=":3" /> ==Women's fashions== [[File:Fashions.jpg|thumb|upright|Illustration depicting fashions throughout the 19th century]]During the [[Victorian era|Victorian Era]], women generally inhabited the private, domestic sphere.<ref>{{Cite web|url=https://www.bl.uk/romantics-and-victorians/articles/gender-roles-in-the-19th-century|title=Gender roles in the 19th century|website=The British Library|access-date=2016-10-21|archive-date=8 July 2022|archive-url=https://web.archive.org/web/20220708075142/https://www.bl.uk/romantics-and-victorians/articles/gender-roles-in-the-19th-century|url-status=dead}}</ref> Unlike in earlier centuries when women labored with their husbands and brothers or worked in family businesses, during the nineteenth century, gender roles became more rigidly defined. Farm labourers was no longer in such a high demand after the [[Industrial Revolution]], and women were more likely to perform domestic work or, if married, give up paid work entirely. Dress reflected these new lifestyles, and was, for the middle and upper classes, less utilitarian.<p> Clothes were seen as an expression of women's place in society<ref>{{Cite book|title=Victorian and Edwardian Fashion - A Photographic Survey|last=Gernsheim|first=Alison|publisher=Dover Publications Inc.|year=1963|location=New York|pages=26}}</ref> and were differentiated by [[social class]]. Most women wore a [[corset]] over a [[chemise]], followed by a gown or [[skirt]] paired with a [[bodice]], [[blouse]], or [[chemisette]]. The shape of the skirt would be supported by layers of petticoats or, later in the period, structured support such as cage crinolines or bustles. The clothing of [[Upper class|upper-class women]], who generally did not do paid labor, was often elaborately decorated with more layers and [[Trim (sewing)|trims]]. [[Middle class|Middle-class women]] wore less complex dress styles with less expensive trim. [[Working class|Working-class]] clothing was simpler still, with less expensive fabric, fewer layers still and little trim. Including the undergarments, the amount of fabric in women's clothing made it much heavier and the construction made it much more restrictive than ours, especially in the waist (due to the boning in the corset) and the shoulders (due to the popularity of dropped shoulder seams). The amount, quality and type of fabric were displays of wealth and status.<p> Throughout the 19th century, journalism targeting women increased enormously and addressed an increasingly more class-diverse audience. According to the ''Dictionary of Nineteenth-Century Journalism'',<blockquote><p> The closely allied fashion and women's journals can be divided into three phases: titles such as the ''Lady's Magazine'' continued eighteenth-century models, addressing readers as "ladies" and catering to a leisured, fashionable elite; a more domesticated format by the 1840s, targeting middle-class women with instructive and entertaining content including dressmaking and etiquette articles ...; finally, from the 1870s, a livelier, more engaging style of fashion reporting influenced by the New Journalism was integrated with an increased amount of imagery, including better quality fashion plates ....<ref>{{Cite book|title=Dictionary of Nineteenth-Century Journalism In Great Britain and Ireland|last=Beetham|first=Margaret Rachel|last2=A|first2=R|publisher=Academia Press and the British Library|year=2009|editor-last=Brake|editor-first=Laurel, and Marysa Demoor|location=Gent|pages=215a–c|chapter=Fashion Journals}}</ref></blockquote>By the end of the century, women's periodicals were including patterns for dressmaking in their pages, reflecting the presence of middle- and working-class readers as well as technological change like sewing machines for home use and mass-produced fabrics and trim.[[File:1837 Dress.jpg|alt=This dress features a low waistline, and the bodice is worn over the hips to further emphasise the silhouette|thumb|upright|An undressed woman In 1837, featuring a fashionable hairstyle, busked corset, and layers of petticoats.]]It is important not to oversimplify the fashion of the Victorian age. The rate of change in fashion accelerated in the 19th century to the point that styles were distinctly different from one decade to the next (see "When Was That Dress in Fashion?", above right). The styles of Elizabethan England, in contrast, changed much less extremely over the course of a century. The most important characteristics for the analysis of 19th-century fashion include silhouette or line, corsets or stays, the neckline and the sleeves. The silhouette in particular but also the color, the variety of available fabrics and the distribution of information and opinion about fashion were the result of [[Social Victorians/People/Gwladys Robinson#Technological advancement|technological changes]] made throughout the century, but centering in the 1850s.[[File:The Engageants sleeves.jpg|thumb|Engageants, worn to fill open sleeves, were made of light fabrics like lace, linen, lawn or cambric.]] * '''Silhouette''': Silhouette changed over time supported by the evolution of the foundation garments. In fact the line or silhouette of garments changed about every ten years. Just as outer clothing changed, foundation garments were also modified to give the wearer a different silhouette. Over the course of the century most Europeans and some in their colonies wore the same kinds of undergarments and similar outer garments. For example, wide skirts were supported by layers of petticoats that used woven horsehair to stiffen them.<ref>{{Cite web |title=Corsets, crinolines and bustles: fashionable Victorian underwear · V&A |url=https://www.vam.ac.uk/articles/corsets-crinolines-and-bustles-fashionable-victorian-underwear |access-date=2025-10-27 |website=Victoria and Albert Museum |language=en}}</ref> By 1856 the [[Crinoline|cage crinoline]] (a domed structure using steel bands and wires) replaced the petticoats, making the skirts lighter in weight and easier to walk in. The line of the outer garments was influenced by how full the skirt was, how small the waist was and its location relative to the natural waistline, how the sleeves were shaped, and how deep the neckline went. * '''Corsets''': [[Corset]]s or stays were ubiquitous, providing adjustable bust and posture support, helping to shape the body into the fashionable silhouette and preventing horizontal creasing in the bodice. Foundation garments were constantly evolving throughout the century. Over the course of the century, almost all women and some men wore corsets. After the late 1850s, an individual could lace a corset without help.<ref name=":24">{{Cite book|title=Victorian Fashions for Women|last=Kay|first=Fiona|last2=Storey|first2=Neil R.|publisher=Pen & Sword History|year=2022|isbn=978 1 39900 416 9|location=Yorkshire and Philadelphia|pages=30-31}}</ref> Most corsets were constructed with a busk, "(a flat length of whalebone, wood or steel) inserted in a channel down the centre to smooth out the front of the dress."<ref>{{Cite book|title=Victorian Fashions for Women|last=Kay|first=Fiona|publisher=Storey|year=Neil R.|isbn=978 1 39900 416 9|location=Yorkshire and Philadelphia|pages=13}}</ref> The drawing of an undressed woman (above right) shows a self-laced corset with what may be a split busk. * '''Neckline''': Necklines changed over the course of the century as bodices and sleeves evolved. The less formal daywear had a higher neckline, regardless of class and decade. For formal wear, which varied widely by class and kind of event, the neckline was often lower and off the shoulder and finished with a [[Collar (clothing)|bertha]] (lace collar or flounce) or multiple bands of fabric pleats. This [[décolletage|décolleté evening style]] popularized shawls or [[cape]]lets and required a [[Corsets|corset]] without shoulder straps. The fashion was for dressmakers to produce two bodices with each skirt, one closed décolletage for day and one décolleté for evening. * '''Sleeves''': Over the course of the century, styles in sleeves changed radically and more than one sleeve style was fashionable at the same time. Some of the most popular styles included gigot, pagoda, ''engageants'' (see right), bishop and leg-of-mutton sleeves. The changes were in the [[armscye]], the wrist treatment, and the fullness at the shoulder, elbow and wrist. For example, as [[crinoline]]s began to appear in the 1850s, sleeves were shaped like large bells known as pagoda sleeves. [[Engageante]]s, or false sleeves, were stitched inside full or open sleeves like pagoda sleeves. They were easy to remove, launder and restitch into position. Even though the changes in fashion over the century were sometimes rapid and extreme, they were also evolutionary.[[File:Dress - MET 1971.47.3a–e.jpg|thumb|English day dress, c. 1836, with bow details and puffed sleeves]] === 1830s dress style === [[File:Princess Victoria and Dash by George Hayter.jpg|alt=Old portrait of a teenage girl in a white formal dress, with a dog|thumb|Princess Victoria and her dog Dash, 1833|left]]During the beginning of Queen Victoria's reign in 1837, the fashionable silhouette was an hourglass shape with wide shoulders, emphasized by puffed [[gigot sleeves]], a full skirt, and a slim waist. Corsets were extended over the abdomen and down towards the hips, and worn with a busk.<ref name=":0">{{Cite book|title=From Queen to Empress - Victorian Dress 1837-1877|last=Goldthorpe|first=Caroline|publisher=The Metropolitan Museum of Art|year=1988|location=New York|pages=23–24}}</ref> A chemise was worn under the corset and cut relatively low in the neck so that it could not be seen. Over the corset was a tight-fitting bodice featuring a high, straight waistline. Under the ankle-length skirt were layers of petticoats<ref name=":0" /> stiffened with horsehair. (Skirts would not be extremely full for another two decades.) To contrast with the narrow waist, necklines were low and wide. Queen Victoria's 1833 white dress (left) shows an off-the-shoulder neckline, a higher waist and an ankle-length skirt held out by horsehair. The c. 1836 yellow day dress (right) shows gigot sleeves, a higher neckline and a skirt held out by petticoats. Always a mark of wealth and status, Princess Victoria's white dress shows that she is formally dressed, perhaps for court, although the pose itself suggests some informality as well. === 1840s dress style === The 1840s saw an increase in domestic magazines targeting women, along with new varieties in the weave of ready-made fabrics as well as new and much more vibrant colors because of the invention of aniline dyes. And the industrial revolution supplied women with more varieties of color and weave in ready-made fabrics. Cotton replaced silk as a basic fabric, especially among middle-class women because silk was expensive, limiting who could afford it. The elements of fashion changed rapidly during this transitional decade.[[File:Magasin för konst, nyheter och moder 1844, illustration nr 8.jpg|thumb|1844 [[fashion plate]] depicting fashionable clothing for men and women, including illustrations of a [[glove]], a fanchon, and [[Bonnet (headgear)|bonnets]]]]At the beginning of the 1840s, skirts began to widen and become dome shaped (because the skirt pieces changed from rectangles to gores, which are wider at the bottom). The waistline lowered with a point formed at the bottom of both the bodice and corset, which gave a rather rigid look to the silhouette. During this decade, the amount of trim decreased in general, although trim was still plentiful. In addition to the flowers, feathers, and ribbons many of the decorations on the dress were made of the fabric of the dress (tucks and pleats, flounces, ruffles). At the end of the decades waists rose to the natural waistline.[[File:Woman's_Dress_LACMA_M.2007.211.744_(1_of_7).jpg|left|thumb|English silk day dress of the second half of the 1840s, with dropped shoulder seams, tight sleeves, and a pointed waist.]]Although corsets narrowed the bodices and gave them a point in the early 1840s, by the end of the decade, they returned to the natural waistline. Corsets lost their straps by the end of the decade.  Busks in the front of the corset were split by Jean Julien Joselin in 1829,<ref name=":24" /> (75 [of 298]) but the corset wouldn’t stay closed until 1848 when Joseph Cooper patented the "slot and stud" which is still in use today.<ref name=":24" /> (75 [of 298]) Necklines remained wide with further use of lace berthas to frame the upper body. At the end of the decade, necklines were raised and remained high. Dresses were stiffer due to boning in the bodice as well as the corset. Skirts lengthened, while in 1847 widths increased with the introduction of the [http://3.bp.blogspot.com/-bOuPyjWzwT8/TuKx-x1R12I/AAAAAAAAAF0/oRs6AyGH0gw/s1600/CI53.51.15_B1870Amer.Horsehair.jpg horsehair crinoline], which was stiffened with horsehair and starch. The petticoats were numerous and became bulky and heavy and sometimes entangled the feet. Petticoats had another disadvantage: the number of waistbands increased with each additional petticoat. Skirts often had one or two flounces at the bottom that increased the look of fullness (see, for example, the 1844 fashion plate, right). To achieve the narrow waist, skirts were attached to bodices using very tight organ [[pleat]]s secured at each fold.<ref name=":1">{{Cite book |last=Goldthorpe |first=Caroline |title=From Queen to Empress - Victorian Dress 1837-1877 |publisher=The Metropolitan Museum of Art |year=1988 |location=New York |pages=32}}</ref> . Sleeves narrowed with smaller decorative additions (see, for example, the English silk day dress, left). They eventually widened at the wrists into open pagoda-type sleeves requiring engageants to cover the forearms. Shawls were used to convert a simple dress into a more formal outfit. The popularity of shawls grew because of the very soft and beautifully dyed and woven cashmere shawls from India with a paisley design (after the Scottish town that manufactured shawls).<ref name=":24" /> (48 [of 298]) Head coverings were ''de regeur'', dominated by poke bonnets.<ref name=":24" /> (51 [of 298]) (The mannequin in the English silk day dress, above left, is wearing a poke bonnet.) Cosmetics became more popular, with instructions The Handbook of the Toilette (anonymous, many editions beginning in 1839. Unfortunately many contained toxic elements like calcium oxide (or quicklime) found hair dye that was recommended to stay in the hair for 3 to 8 hours.<ref name=":24" /> (47 [of 298]) By the end of the 1840s skirts were more dome shaped, necklines were higher and wider and sleeves broadened at the bottom. === 1850s dress style === The 1850s saw revolutionary [[Social Victorians/People/Gwladys Robinson#Technological advancement|changes in technologies]] affecting the manufacture and consumption of clothing, especially * the mass production of fabrics * the invention of synthetic dyes * the manufacture of inexpensive, flexible and lightweight steel * the invention of a sewing machine that could be used in the home * the spread of fashion journalism and journalism for women According to the ''Dictionary of Nineteenth-Century Journalism'', "The 1850s and 1860s saw the eclipse of the older ladies' journals [that began in the 18th century and targeted upper-class women] and the emergence of the magazine for middle-class ... women."<ref>{{Cite book|title=Dictionary of Nineteenth-Century Journalism In Great Britain and Ireland.|last=Beetham|first=Margaret Rachel|publisher=Academia Press and the British Library|year=2009|editor-last=Brake|editor-first=Laurel, and Marysa Demoor|location=Gent|pages=683–684|chapter=Women's Periodicals}}</ref> (684) Nine fashion magazines were being published in London by 1850 and fourteen by 1859 as part of the burgeoning collection of magazines for women, both domestic magazines aimed at middle-class women and journalism focused mostly on fashion.<ref name=":24" /> (63 [of 298]) The journalism aimed at middle-class women introduced haute couture, making the styles, names of couturiers and fashion houses familiar to them for the first time. These technological changes were revolutionary because of the impact they had on fashion over the course of the rest of the century. Their impact on fashion arises largely because most women were taught a wide range of seamstress skills and, due to reforms in education over the century, more women could read.[[File:Ensemble_MET_DT6845.jpg|thumb|A day ensemble c. 1855, featuring tiers of ruffles and pagoda style sleeves.]] ==== Silhouette ==== The 1850s are considered a transitional decade in 19th-century fashion because little changed in the silhouette and appearance of clothing, but technological changes would make increasingly important structural differences in what was available for people to wear. Skirts widened with the disappearance of the many layers of petticoats but did not change their basic shape. Beyond the silhouette, the design elements of the dress (like sleeves, neckline, or skirt) were barely changed as they evolved from the 1840s to the 1860s. While the silhouette and elements of design did not change significantly, the effect of the technological changes related to the manufacture and consumption of clothing was to give individual (and especially middle-class women) more agency over how their dresses got made and who made them, what fabrics their dresses were made of, how broad a range of options they could choose from and how easy it was to move in their dresses. The number of flounces and ruffles on the skirt increased, making the skirt look wider (see the c. 1855 day ensemble, right). ==== Neckline ==== [[File:1850's Evening Dress.jpg|thumb|1850s evening dress with a bertha|left]] With trim and a front closure in the corset and the bodice, the bodice emphasized a distinct V-shape. Necklines of day dresses were sometimes cut into a V-shape, causing a need to cover the bust area with a chemisette. For evening, a wide, low neckline was popular, often with a [[Collar (clothing)|bertha]] (see the 1850s even dress with a bertha, left).<ref name="h608">{{cite book |last=Arnold |first=Janet |title=Patterns of fashion. 2: Englishwomen's dresses and their construction: 1860 - 1940 |date=1993 |publisher=MacMillan |isbn=978-0-89676-027-1 |publication-place=London |page=}}</ref> ==== Sleeves ==== Pagoda sleeves and under sleeves (''engageants'') continued to be popular for most of the decade. ==== Foundations ==== [[File:1856 Cage Crinoline.jpg|alt=1st patented cage crinoline.Fullness of the skirt is even further emphasised.|thumb|1850s fashionable silhouette and the cage crinoline needed to support it.]] In 1856, the invention of the first [[Crinoline|cage crinoline]] allowed for even wider skirts. The cage crinoline was constructed by joining thin metal strips together with wires to form a circular cage-like structure that could support a very wide skirt (see 1950s silhouette and cage crinoline, right). Although often ridiculed by journalists and cartoonists of the time as the crinoline swelled in size, this innovation freed women from the heavy weight of petticoats.<ref name=":4">{{Cite book |last=Steele |first=Valerie |url=https://archive.org/details/fashioneroticism0000stee |title=Victorian Fashion. Fashion and Eroticism: Ideals of Feminine Beauty from the Victorian Era to the Jazz Age |publisher=Oxford University Press |year=1985 |isbn=978-0-19-503530-8 |pages=[https://archive.org/details/fashioneroticism0000stee/page/51 51]–84 |url-access=registration}}</ref> For a description of the [[Social Victorians/People/Gwladys Robinson#Technological advancement|technological advancement]] that made cage crinolines possible, see below.) Not visible on the outside garment, the cage crinoline was the foundation for the huge dome-shaped skirts that dominated the decade. It was safer and easier to walk in a cage because the hoops held the skirt away from the feet and legs of the wearer. Without the innumerable petticoats more women began to wear drawers or "pantalettes" for modesty and warmth. The dome shape made possibly by the cage foundation changed the way skirts were cut. Instead of rectangles, gores were cut with one end of the skirt piece wider than the other end,<ref name="w586">{{cite book |last=Arnold |first=Janet |title=Patterns of fashion. 2: Englishwomen's dresses and their construction: 1860 - 1940 |date=1993 |publisher=MacMillan |isbn=0-333-13607-1 |publication-place=London |page=}}</ref> preventing bulkiness at the waist from gathered fabric and created a skirt bottom much wider than the top. Bloomers, designed by American Amelia Jenks Bloomer,  introduced bifurcated garments for women, essentially trousers or pants with a seam between the legs. Even pantalettes had no seam between the legs; it was simply left open. This experiment failed and women didn’t wear pants until the 20th century. The 1850s saw two other developments that permanently changed the clothing available to Victorian women (and men). Created in 1856, the first synthetic dyes were much more vivid and vibrant than natural dyes and resisted fading.<ref name=":24" /> (92 [of 298]) Because Victorian photography was black and white, we do not typically see the gaudy and saturated colours that many Victorians loved.<ref name=":3" /> Also, although sewing machines had already been invented, changing the accessibility and value of individual articles of clothing, it was the invention of and widespread sale of "lightweight domestic machines" for home sewing that affected large numbers of women.<ref name=":24" /> (91 [of 298]) Cage crinolines remained popular for perhaps 5 years among the fashion forward and perhaps 10 years for the less adventurous.[[File:Woman's_silk_taffeta_dress_c._1865.jpg|thumb|An 1865 English silk morning dress.]] [[File:Mrs_Ellinor_Guthrie_by_Frederic_Leighton.jpg|thumb|English dress, 1864, with simple trim.]] === 1860s dress style === ==== Foundations ==== The cage crenoline reached their greatest width during the 1860s. Photographs show that the fashion-forward Empress Eugénie of France, Empress Elisabeth of Austria and Countess Pauline von Metternich had stopped wearing the very large crinoline cages as early as 1862, but most middle- and upper-class women (including Queen Victoria) wore them for much of the rest of the decade. During the first half of the 1860s, crinolines began decreasing in size at the top, while retaining their volume at the bottom, creating a more pyramidal shape.<ref name=":2">{{Cite book|title=From Queen to Empress - Victorian Dress 1837-1877|last=Goldthorpe|first=Caroline|publisher=The Metropolitan Museum of Art|year=1988|location=New York|pages=}}</ref> (26) Then the fullness began to move to the back while the front became flat and close to the body. As the back fullness increased, skirts sometimes lengthened into trains. (The 1865 English silk dress, above right, shows the flattening of the front at the waist and the development of the train.) In order to emphasize the back, the train was gathered together to form soft folds and [[Drapery|draperies]].<ref>{{Cite book|title=Making Victorian Costumes for Women|last=Audin|first=Heather|publisher=Crowood|year=2015|pages=45}}</ref> This line or silhouette would eventually evolve into a bustle in the next decade. Decoration or trim often appeared only at the bottom of the skirt (see English dress, 1864, below right). Flounces and ruffles diminished as geometric designs in trim gained popularity.<ref name=":24" /> (102 [of 298]) Skirts were also decorated with overskirts of the same fabric or a different shade of the same color. Waistlines were pointed in front below the natural waistline. By mid-century the waist was seated at the natural waistline often with a wide belt and large decorative buckle.   ==== Bodices and Sleeves ==== Bodices often had buttons down the front because both the corset and the bodice opened in the front. Necklines were generally high and rounded. Some dresses were cut without separating the bodice and skirt so it could be buttoned from the neck to the bottom of the skirt. It became popular for dresses to be made as one skirt and two bodices, one for day wear and one for formal wear.<ref name=":0" /> (43) Sleeves narrowed but remained loose on the arms and were wrist length. Sometimes the sleeves were full at the shoulder, but they were not very puffed. ==== General Trends ==== A greater and richer variety of fabrics was available to the always upwardly-aspirational middle class, with silk essential in the dress of wealthy middle- and upper-class women. Dresses were cut and pieced together to accommodate the more active life women had in sports, walking and even riding bicycles. The trends that began in the 1860s continued through the 1870s and into the 1880s; the changes were evolutionary. === 1870s dress style === ==== Silhouette ==== [[File:Black_net_ball_dress_1874.png|thumb|A black net ball dress, 1874]]In 1877, dresses moulded to fit the figure, as increasingly slimmer and more restrictive silhouettes were favored. Although dress styles took on a more natural form, corsetry was still required and the now ''de regueur'' train was often supported with a bustle cage.<ref name=":2" /> (50) The armscye, for the first time in the Victorian period, moved from a dropped position up to the shoulders and would remain there for the rest of the era. The most famous designer of this conservative, very fitted and restrictive style was British-born Frederick Worth, who designed the “princess” construction for dresses, which we still use today, and who popularized and then “killed,” according to his obituary in ''The Lady’s Treasury'',<ref>“‘Death of the Chief Ruler of the Fashionable World’, The Ladies’ Treasury (1 April 1895), p. 274.” In ''Fashioning the Victorians: A Critical Sourcebook''. Ed., Rebecca N. Mitchell. Dress, Body, Culture Series, gen. ed., Joanne B. Eicher. Bloomsbury Visual Arts, 2018. Pp. 487–491 of 565.</ref> the crinoline cage. The princess construction was named for Alexandra, Princess of Wales, who preferred a lean, tailored style. By 1879 corsets were being built using "princess" seams to support the tailoring of the smooth, straight dresses like the ones designed by Maison Worth. Because Queen Victoria had been in mourning since 1861, the Princess Alexandra was expected to lead in the haute couture of the day. She set a trend for tailored dresses that was quickly picked up by all classes. Unlike the tailored designs, what Maison Worth created was ornate with many decorative elements, including fringe, which was widely used (along with ribbon, braid, ball fringe, ruching, epaulettes, pieces of the same fabric in a lighter or darker shade, pieces of a different-textured fabric like velvet or velveteen, etc.). No single silhouette dominated the 1870s, however, because of the different lines created by the bustle, the overskirt and the layers of the polonaise, or a combination of these three skirt treatments. Foundation garments changed very little, although perhaps the greatest change came in corsets. In 1870 women were wearing corsets that came to just below the waist with a pointed center front. ==== Skirts ==== [[File:Woman's_Polonaise_Dress_LACMA_M.2007.211.777a-f_(1_of_4).jpg|left|thumb|An c. 1875 English polonaise]]The trend for wide skirts slowly disappeared during the 1870s, as women started to prefer a slimmer silhouette. Skirts went from their most extreme width to their most narrow, waists went to a natural level and the backside took the point of interest in the ensemble. The back of the dress became the focal point of the design. The relationship between the various skirt treatments was very complex, in part because skirts became architectural. (The bustle on the 1874 black net ball dress, above right, has been gathered and bunched and would require padding to keep the draping in place. It also has an overskirt.) The skirt began the decade rather flat in front with most of the fabric pulled to the back and pleated. As the skirt evolved, the gathered fabric draped gracefully at the back. In the next fashion the extra fabric was bunched into large poufs below the waist in back. Then a pad supported the extra fabric, and then by the end of the decade a [[tournure]] or bustle kept the elaborate draping of the back of the skirt and train in place. In general, trains were present on every dress, including day dresses, but they were narrower and longer with tiers and drapes. Petticoats, which could be washed separately, kept the longer trains off the ground. [[overskirt|Overskirts]] became extremely popular, often tied up into an apron effect at the front with a [[Polonaise (clothing)|polonaise]] or puffed draperies at the back.<ref name="g4223">{{cite book |last=Cunnington |first=Cecil Willett |title=English Women's Clothing in the Nineteenth Century |date=1990-05-01 |publisher=Courier Corporation |isbn=0-486-26323-1 |publication-place=New York |page=}}</ref> A revival of an 18th-century romanticization of what a milkmaid might have worn, the 1870s polonaise is a garment featuring both an overskirt and bodice often of the same fabric (see c. 1875 English polonaise, left). Over time, the overskirt shortened into a detached [[Basque (clothing)|basque]], resulting in an elongation of the bodice over the hips. (The early 1870s fashion plate, below right, shows an assortment of ways overskirts were worn, including one for a girl.)[[File:1870's Dress.jpg|alt=Dresses featuring the Bustle & Polonaise|thumb|An early 1870s fashion plate]] ==== Neckline ==== Necklines were high, and lines were sleek and fitted. ==== Sleeves ==== Pagoda sleeves began to lose their three-decade-long popularity in 1875,<ref name=":24" /> (102 [of 298]) but most sleeve treatments were narrow the sleeves and came to the wrist. ==== General Trends ==== An unusual trend occurred during the 1870s in hairstyles, which grew very large with added braids, buns, coils, poufs and strands. The elaborate hairstyles required multiple hair pieces and featured tiny, over-decorated hats fastened almost vertically on the head. Although women had already been supplementing their own hair, these extremely large styles caused enormous demand in the human hair market. () The practice of constructing a dress with one skirt and two bodices (one for day and one for evening wear) continued from the 1860s. === 1880s dress style === [[File:1885 Bustle.jpg|alt=Horizontal protrusion at the back.|thumb|The lobster tail bustle of around 1885.]] The saw the growing popularity of austere, menswear inspired tailoring.<ref name=":4" /> Some credited the change in silhouette to the [[Victorian dress reform]], which consisted of a few movements including the [[Artistic Dress movement|Aesthetic Costume]] Movement and the [[Victorian dress reform|Rational Dress Movement]] in the mid-to-late Victorian Era advocating for a natural silhouette and lightweight underwear, and rejecting [[tightlacing]]. However, these movements did not gain widespread support. Others noted the growth in cycling and tennis as acceptable feminine pursuits that demanded a greater ease of movement in women's clothing.<ref name=":3" /> Still others argued that the growing popularity of tailored semi-masculine suits was simply a fashionable style, and indicated neither advanced views nor the need for practical clothes.<ref name=":4" /> [[File:Edward_Hughes_-_Juliette_Gordon_Low_-_Google_Art_Project.jpg|left|thumb|An 1887 portrait of English evening dress with higher shoulder placement, simple trims, and a V-shaped neckline.]] After a period of slim, train-less skirts with heavy decoration, the bustle made a re-appearance in 1883, and it featured a further exaggerated horizontal protrusion at the back. Due to the additional fullness, drapery moved towards the sides or front panel of the skirt instead. Bodices shortened, now ending above the hips. Skirts were much less full than the last time the bustle was in fashion in the 1870s and instead focused on a slim front with a shelf-like back protrusion. Sleeves of bodices were thinner and tighter, while necklines became higher again, with a high collar being ubiquitous for daytime, a trend that would continue into the 1890s. For the evening, the bertha fell out of favor, replaced by V-shaped necklines or draped styles due to the new higher shoulder.<ref name="g4223"/> Sleeves tightened again during the [[1880s in Western fashion|1880s]] and the armscye moved back up the shoulders.<ref name="y040">{{cite book |last=Severa |first=Joan L. |title=Dressed for the Photographer |date=1995 |publisher=Kent State University Press |isbn=0-87338-512-8 |publication-place=Kent, Ohio |page=}}</ref> === 1890s dress style === [[File:Lady_Beatrice_Pole-Carew.jpg|thumb|English socialite Lady Beatrice Pole-Carew in the mid-1890s, with puffed sleeves.]] By 1890, the crinoline and bustle were fully abandoned, and skirts flared in an A-line. Necklines were high, while sleeves of bodices initially peaked at the shoulders, but increased in size in the middle of the decade to a puffed [[Sleeve|leg-of-mutton]] style.The sleeves grew to a volume rivaling the 1830s and even sometimes required a cushion to retain their fullness. This sleeve style narrowed down towards the end of the decade. Women also adopted the style of the tailored jacket during this period, with menswear influences such as necktie inspired neckwear continuing from the previous decade. == Hats and headwear == [[File:Ford.madox.brown.last.emma.study.jpg|thumb|''Emma Hill'' by [[Ford Madox Brown]] (1853), a woman wearing a later version of the [[poke bonnet]]]] [[File:Hoed,_objectnr_KA_1237.tif|left|thumb|Perched bonnet style of the early 1870s.]] Hats were crucial to a respectable appearance for both men and women. To go bareheaded was simply not proper. The top hat, for example, was standard formal wear for upper- and middle-class men.<ref name=":4" /> For women, the styles of hats changed over time and were designed to match their outfits. During the early Victorian decades, hats were modest in size and design, straw and fabric bonnets being the popular choice. [[Poke bonnet]]s, which had been worn during the late [[Regency period]], had high, small crowns and brims that grew larger until the 1830s, when the face of a woman wearing a poke bonnet could only be seen directly from the front. They had rounded brims, echoing the rounded form of the bell-shaped hoop skirts. Bonnets shrunk at the end of the 1860s and moved to a perched position in the early 1870s as hairstyles grew in scale and intricacy. This led to the popularization of hats, which became the headwear of choice for the remainder of the Victorian era.<ref name="g4223"/> [[File:The_London_and_Paris_ladies'_magazine_(Apr_1885)_03.png|thumb|Flower pot style hat of 1885.]] The 1880s saw a hat inspired by the top hat for women known as the flowerpot hat, and the 1890s saw the popularity of the boater. The hats of the late Victorian era were covered with elaborate creations of silk flowers, ribbons, and above all, exotic plumes; hats sometimes included entire exotic birds that had been stuffed. Many of these plumes came from birds in the Florida everglades, which were nearly made entirely extinct by overhunting. By 1899, early environmentalists like [[Adeline Knapp]] were engaged in efforts to curtail the hunting for plumes. By 1900, more than five million birds a year were being slaughtered, and nearly 95 per cent of Florida's shore birds had been killed by [[Plume hunting|plume hunter]]s.<ref>{{cite web|title=Everglades National Park|url=https://www.pbs.org/nationalparks/parks/everglades/|archive-url=https://web.archive.org/web/20090927085907/http://www.pbs.org/nationalparks/parks/everglades/|url-status=dead|archive-date=27 September 2009|publisher=PBS|access-date=7 November 2011}}</ref> == Shoes == The women's shoes of the early Victorian period were narrow and heelless, in black or white satin. By 1850s and 1860s, they were slightly broader with a low heel and made of leather or cloth. Ankle-length laced or buttoned boots were also popular. From the 1870s to the twentieth century, heels grew higher and toes more pointed. Low-cut pumps were worn for the evening.<ref name=":4" /> == Cosmetics == [[Victorian-era cosmetics]] were typically minimal, as makeup was associated by the middle classes with promiscuity. However, small amounts of pale face powder or powdered blush were more widely used.<ref>{{Cite book |last=Goodman |first=Ruth |title=How to be a Victorian |date=2014 |publisher=Penguin Books |isbn=978-0-670-92136-2 |location=London}}</ref> Some cosmetics contained toxic or caustic ingredients like lead, mercury, ammonia, and arsenic {{Citation needed|date=October 2025}}. Hair color == Men's fashion == [[File:Mens Coats 1872 Fashion Plate.jpg|thumb|upright|Drawing of Victorian men 1870s]] During the [[1840s in fashion|1840s]], men wore tight-fitting, calf length [[frock coat]]s and a [[waistcoat]] or vest. Sleeves were full at the top and waists were tight, creating an hourglass form. Waistcoats were single- or double-breasted, with shawl or notched collars, and might be finished in double points at the lowered waist. For more formal occasions, a cutaway morning coat was worn with light trousers during the daytime, and a dark tail coat and trousers was worn in the evening. Shirts were made of linen or cotton with low collars, occasionally turned down, and were worn with wide [[Cravat (early)|cravat]]s or neck ties. Trousers had fly fronts, and [[breeches]] were used for formal functions and when horseback riding. Men wore [[top hat]]s, with wide brims in sunny weather. During the [[1850s in fashion|1850s]], men started wearing shirts with high upstanding or turnover [[collar (clothing)|collars]] and [[necktie#Four-in-hand|four-in-hand necktie]]s tied in a bow, or tied in a knot with the pointed ends sticking out like "wings". The upper-class continued to wear top hats, and [[bowler hat]]s were worn by the working class. In the [[1860s in fashion|1860s]], men started wearing wider neckties that were tied in a bow or looped into a loose knot and fastened with a stickpin. Frock coats were shortened to knee-length and were worn for business, while the mid-thigh length [[sack coat]] slowly displaced the frock coat for less-formal occasions, with the overall effect of a looser silhouette. Top hats briefly became the very tall "stovepipe" shape, but a variety of other hat shapes were popular. During the [[1870s in fashion|1870s]], three-piece suits grew in popularity along with patterned fabrics for shirts. Neckties were the four-in-hand and, later, the [[Ascot tie]]s. A narrow ribbon tie was an alternative for tropical climates, especially in the Americas. Both frock coats and sack coats became shorter and more form fitting. Flat straw boaters were worn when boating. During the [[1880s in fashion|1880s]], formal evening dress remained a dark tail coat and trousers with a dark waistcoat, a white bow tie, and a shirt with a winged collar. In mid-decade, the dinner jacket or [[tuxedo]], was used in more relaxed formal occasions. The [[Norfolk jacket]] and tweed or woolen breeches were used for rugged outdoor pursuits such as shooting. Knee-length topcoats, often with contrasting velvet or fur collars, and calf-length overcoats were worn in winter. Men's shoes had higher heels and a narrow toe. Starting from the [[1890s in fashion|1890s]], the [[blazer]] was introduced, and was worn for sports, sailing, and other casual activities.<ref>{{cite web|last=Landow|first=George|url=http://www.victorianweb.org/art/costume/90s/2.html|title=Men's informal sporting dress, late 1880s and '90s}}</ref> Throughout much of the Victorian era most men wore fairly short hair. This was often accompanied by various forms of facial hair including moustaches, side-burns, and full beards. A clean-shaven face did not come back into fashion until the end of the 1880s and early 1890s.<ref>{{cite web|url=http://www.victorianweb.org/art/costume/nunn21.html|title=Victorian Men's Fashions, 1850–1900: Hair}}</ref> Distinguishing what men really wore from what was marketed to them in periodicals and advertisements is difficult, as reliable records do not exist.<ref name="shannon597">{{cite journal|last=Shannon|first=Brent|title=Refashioning Men: Fashion, Masculinity, and the Cultivation of the Male Consumer in Britain, 1860–1914|journal=Victorian Studies|year=2004|volume=46|issue=4|pages=597–630|doi=10.1353/vic.2005.0022}}</ref> Influence of Bertie, Albert Edward, Prince of Wales ==Mourning black== {{See also |Mourning stationery}} [[File:The royal children in mourning Mar 1862.jpg|thumb|Victoria's five daughters (Alice, Helena, Beatrice, Victoria and Louise), photographed wearing mourning black beneath a bust of their late father, Prince Albert (1862)]] [[File:Mourning dress MET 50.40.3a-b front CP4.jpg|alt=Black Victorian mourning dress|thumb|Mourning Dress, 1894–95]] In Britain, black is the colour traditionally associated with mourning for the dead. The customs and etiquette expected of men, and especially women, were rigid during much of the Victorian era. The expectations depended on a complex hierarchy of close or distant relationship with the deceased. The closer the relationship, the longer the mourning period and the wearing of black. The wearing of full black was known as First Mourning, which had its own expected attire, including fabrics, and an expected duration of 4 to 18 months. Following the initial period of First Mourning, the mourner would progress to Second Mourning, a transition period of wearing less black, which was followed by Ordinary Mourning, and then Half-mourning. Some of these stages of mourning were shortened or skipped completely if the mourner's relationship to the deceased was more distant. Half-mourning was a transition period when black was replaced by acceptable colours such as lavender and mauve, possibly considered acceptable transition colours because of the tradition of [[Church of England]] (and [[Catholic Church|Catholic]]) clergy wearing lavender or mauve [[Stole (vestment)|stoles]] for funeral services, to represent the [[Passion (Christianity)|Passion of Christ]].<ref>{{cite web|title=The Colors of the Church Year|url=http://fullhomelydivinity.org/articles/colors.htm|publisher=Consortium of Country Churches|access-date=6 November 2011|archive-date=13 November 2011|archive-url=https://web.archive.org/web/20111113075214/http://fullhomelydivinity.org/articles/colors.htm|url-status=dead}}</ref> The mourning dress on the right was worn by Queen Victoria, "it shows the traditional touches of mourning attire, which she wore from the death of her husband, Prince Albert (1819–1861), until her own death."<ref>{{Cite web|url=https://www.metmuseum.org/art/collection/search/155839?&searchField=All&sortBy=Relevance&deptids=8&ft=queen+victoria&offset=0&rpp=20&amp;pos=2|title=Mourning Dress, 1894–95|last=The Metropolitan Museum of Art|date=7 September 2019|website=The Metropolitan Museum of Art|access-date=7 September 2019}}</ref> === Norms for mourning=== ''Manners and Rules of Good Society, or, Solecisms to be Avoided'' (London, Frederick Warne & Co., 1887) gives clear instructions, such as the following:<ref>{{cite book|last=Flanders|first=Judith|title=The Victorian House|year=2003|publisher=Harper Perennial|location=London|isbn=0-00-713189-5|pages=378–83}}</ref> {| class="wikitable" |- ! Relationship to deceased !! First mourning !! Second mourning !! Ordinary mourning !! Half-mourning |- | Wife for husband || 1-year, 1-month; [[bombazine]] fabric covered with [[Crape|crepe]]; [[widow's cap]], [[lawn cuff]]s, collars || 6 months: less crepe || 6 months: no crepe, silk or wool replaces bombazine; in last 3 months jet jewellery and ribbons can be added || 6 months: colours permitted are grey, lavender, mauve, and black-and-grey |- | Daughter for parent || 6 months: black with black or white crepe (for young girls); no linen cuffs and collars; no jewellery for first 2 months || 4 months: less crepe || – || 2 months as above |- | Wife for husband's parents || 18 months in black bombazine with crepe || – || 3 months in black || 3 months as above |- | Parent for son- or daughter-in-law's parent || – Black armband in representation of someone lost || – || 1-month black || – |- | Second wife for parent of a first wife || – || – || 3 months black || – |} The complexity of these etiquette rules extends to specific mourning periods and attire for siblings, step-parents, aunts and uncles distinguished by blood and by marriage, nieces, nephews, first and second cousins, children, infants, and "connections" (who were entitled to ordinary mourning for a period of "1–3 weeks, depending on level of intimacy"). Men were expected to wear mourning black to a lesser extent than women, and for a shorter mourning period. After the mid-19th century, men would wear a black hatband and black suit, but for only half the prescribed period of mourning expected of women. Widowers were expected to mourn for a mere three months, whereas the proper mourning period expected for widows was up to four years.<ref>{{cite book|last=Flanders|first=Judith|title=The Victorian House|year=2003|publisher=Harper Perennial|location=London|isbn=0-00-713189-5|pages=378–9}}</ref> Women who mourned in black for longer periods were accorded great respect in public for their devotion to the departed, the most prominent example being Queen Victoria herself. Women with lesser financial means tried to keep up with the example being set by the middle and upper classes by dyeing their daily dress. Dyers made most of their income during the Victorian period by dyeing clothes black for mourning.<ref>{{cite book|last=Flanders|first=Judith|title=The Victorian House|year=2003|publisher=Harper Perennial|location=London|isbn=0-00-713189-5|page=341}}</ref> == Technological advancement == The technological changes that affected the manufacture and consumption of clothing in the Victorian age included the following: * the mass production of fabrics — for example, "by the early 1850s there were thousands of steam-powered looms churning out millions of miles of fabric every year"  [62] * the invention of aniline dyes, which were much more vibrantly colored and resistant to fading than the natural dyes that had been used. — . Invented by chemist [[William Henry Perkin]] in 1856, the first aniline dye mauveine (or mauve) "wash[ed] the fashionable landscape in a haze of purple."<ref name=":22">{{Cite book|title=The Dress Diary: Secrets from a Victorian Woman's Wardrobe|last=Strasdin|first=Kate|publisher=Pegasus Books|year=2023|location=New York, New York}}</ref> (247) Other intense and, to the Victorians, intensely exciting colors followed, but the new synthetic additions to fabric sometimes included chemicals harmful to their wearers. For example, a "bright-magenta hue was achieved by adding arsenical-based chemicals to existing aniline dyes, brightening the already luminous shades – but these left residues themselves, along with a toxic labour trail in their wake."<ref name=":22" /> (255) Perhaps the most famous of these is arsenic green, used on fabrics, wallpapers, and trim: "The craze for artificial foliage to adorn the heads and dresses of women of fashion in the mid-nineteenth century had seen the proliferation of flower workshops, where young women in their hundreds laboured to produce the lifelike green leaves and blooms that would make a fetching headdress or would trail becomingly across the bodice of a gown. The lushness of the green was achieved by the application of a powder, a pigment that was created by mixing copper and the highly toxic chemical, arsenic trioxide. The physical effects of working with this poisonous compound were horrific. Contemporary medical drawings depict the green hue of the skin and dreadful open lesions on the hands of the maker, whilst the daily gradual ingestion of the powder by the flower girls was eventually fatal."<ref name=":22" /> (255) * the invention of a sewing machine that could be used in the home. Although sewing machines were already in use in the clothing industry, in 1858 Isaac Merritt Singer began to sell "lightweight domestic machines" for home sewing, radically increasing women's control over their own dress.<ref name=":24" /> (91 [of 298]) * the spread of journalism for women and fashion journalism Perhaps not at the same scale as these but as important in 1850s designs was a technology that turned iron into steel, which could then be drawn into fine wires.<ref name=":3" /> Steel was refined to a malleable state so that thin blades could be curved into concentric circles (called hoops) and connected with wires to form the cage. Technological advancements not only influenced the economy but brought a major change in the fashion styles worn by men and women. As the Victorian era was based on the principles of gender, race and class.<ref>{{cite journal|last1=Graham|first1=P|title=The Victorian Era|url=https://archive.org/details/in.ernet.dli.2015.261548|journal=Digital Library of India}}</ref> Much advancement was in favor of the upper class as they were the ones who could afford the latest technology and change their fashion styles accordingly. In 1830s there was introduction of horse hair crinoline that became a symbol of status and wealth as only the upper-class women could wear it. In 1850s there were more fashion technological advancements hence 1850s could rightly be called a revolution in the Victorian fashion industry such as the innovation of artificial cage crinoline that gave women an artificial hourglass silhouette without layers of petticoats, which was lighter and more hygienic.<ref>{{cite book|last1=Shrimpton|first1=J|title=Victorian Fashion|publisher=Bloomsbury Shire Publications}}</ref> Synthetic dyes, such as [[mauveine]] (aniline purple), were introduced in 1856, adding bright colours to garments. In 1855's ''[[Haute couture]]'' was introduced as tailoring became more mainstream in years to follow.<ref>{{cite book|last1=Aspelund|first1=Karl|title=Fashioning Society|publisher=Fairchild Books}}</ref> Charles Frederick Worth, a prominent English designer, became popular amongst the upper class though its city of destiny always is Paris. Haute couture became popular at the same time that sewing machines were invented.<ref name="Haute Couture">{{cite book|last1=Martin|first1=Richard|last2=Koda|first2=Harold|title=Haute Couture|publisher=The Metropolitan Museum of Art}}</ref> Princess [[Eugénie de Montijo|Eugenie]] of France wore the Englishman dressmaker, Charles Frederick Worth's couture and he instantly became famous in France though he had just arrived in Paris a few years ago. In 1855, Queen Victoria and Prince Albert of Britain welcomed [[Napoleon III]] and Eugenie of France to a full state visit to England. Eugenie was considered a fashion icon in France. Queen Victoria, who had been the fashion icon for European high fashion, was inspired by Eugenie's style and the fashions she wore.{{Citation needed|date=October 2025}} Later, Queen Victoria also appointed Charles Frederick Worth as her dress maker and he became a prominent designer amongst the European upper class. Charles Frederick Worth is known as the father of the haute couture as later the concept of labels were also invented in the late 19th century as custom, made to fit tailoring became mainstream.<ref>{{cite book|last1=Saillard|first1=Olivier|last2=Zazzo|first2=Anne|title=Paris Haute Couture|publisher=Skira Flammarion}}</ref> By the 1860s, when made-to-fit tailoring was popular in Europe, crinolines were considered impractical. In the 1870s, women preferred more slimmer silhouettes, hence bodices grew longer and the polonaise, a skirt and bodice made together, was introduced. In 1870s the Cuirass Bodice, a piece of armour that covers the torso and functions like a corset, was invented. Towards the end of Victoria's reign, dresses were flared naturally as crinolines were rejected by middle-class women. Designers such as Charles Frederick Worth were also against them. All these inventions and changes in fashion led to women's liberation as tailored looks improved posture and were more practical.<ref name="Haute Couture"/> dressmakers, couturiers, modistes == Home decor == {{main|Victorian decorative arts}} Home decor started spare, veered into the elaborately draped and decorated style we today regard as Victorian, then embraced the retro-chic of [[William Morris]] as well as pseudo-[[Japonaiserie]]. == Myths and Oversimplifications == === Modesty === {{main|Victorian morality}} {{Original research|section|date=May 2008}} [[File:1868-skirt-lengths-girl-ages-Harpers-Bazar.gif|thumb|upright|"The proper length for little girls' skirts at various ages", from ''[[Harper's Bazaar]]'', showing a 1900 idea of how the hemline should descend towards the ankle as a girl got older]]Many myths and exaggerations about the period persist to the modern day. Examples include the idea of men's clothing is seen as formal and stiff, women's as elaborate and over-done; clothing covered the entire body, and even the glimpse of an ankle was scandalous. Critics contend that [[corset]]s constricted women's bodies and lives. Homes are described as gloomy, dark, cluttered with massive and over-ornate furniture and proliferating [[bric-a-brac]]. Myth has it that even piano legs were scandalous, and covered with tiny [[pantalette]]s. === Tight Lacing === Tight-lacing, which was not possible until the development of the grommet in 1828, was famously controversial in the Victorian age, generating many column inches of profitable newspaper copy, in part because it was (and still is) fetishistic and subversive in that adolescent girls used it as a means of rebellion and upper-working- or lower-middle-class shop girls saw it as a means of upward mobility.<ref name=":21">{{Cite book|title=Fashion and Fetishism: Corsets, Tight-Lacing and Other Forms of Body-sculpture|last=Kunzle|first=David|publisher=History Press|year=2013|isbn=978 0 7524 9545 3|location=Stroud, Gloucestershire|pages=}}</ref> (71 [of 1182]) No evidence exists that tight lacing was widespread or particularly dangerous.<ref name=":21" /> () In truth, men's formal clothing may have been less colourful than it was in the previous century, but brilliant [[waistcoat]]s and [[cummerbund]]s provided a touch of colour, and [[smoking jacket]]s and [[robe|dressing gown]]s were often of rich Oriental [[brocade]]s. This phenomenon was the result of the growing textile manufacturing sector, developing mass production processes, and increasing attempts to market fashion to men.<ref name="shannon597"/> Corsets stressed a woman's sexuality, exaggerating hips and bust by contrast with a tiny waist. Women's [[evening gown]]s bared the shoulders and the tops of the breasts. The [[jersey dress]]es of the 1880s may have covered the body, but the stretchy novel fabric fit the body like a glove.<ref>{{cite book |last=Gernsheim |first=Alison |title=Victorian & Edwardian Fashion: A Photographic Survey |year=1981 |publisher=Dover Publications |location=New York |page=65|edition=New |isbn=0-486-24205-6}}</ref> Home furnishing was not necessarily ornate or overstuffed. However, those who could afford lavish draperies and expensive ornaments, and wanted to display their wealth, would often do so. Since the Victorian era was one of increased social mobility, there were ever more ''[[nouveaux riches]]'' making a rich show. The items used in decoration may also have been darker and heavier than those used today, simply as a matter of practicality. London was noisy and its air was full of [[soot]] from countless coal fires. Hence those who could afford it draped their windows in heavy, sound-muffling curtains, and chose colours that didn't show soot quickly. When all washing was done by hand, curtains were not washed as frequently as they might be today. There is no actual evidence that piano legs were considered scandalous. Pianos and tables were often draped with [[shawl]]s or cloths—but if the shawls hid anything, it was the cheapness of the furniture. There are references to lower-middle-class families covering up their [[pine]] tables rather than show that they couldn't afford [[mahogany]]. The piano leg story seems to have originated in the 1839 book, ''A Diary in America'' written by Captain [[Frederick Marryat]], as a satirical comment on American prissiness.<ref>{{cite book |last1=Marryat |first1=C.B. |title=A Diary in America: With Remarks on Its Institutions |date=1839 |publisher=Longman, Orme, Brown, Green, and Longmans |location=London, England |volume=2 |pages=246–247 |url=https://books.google.com/books?id=2-VEAAAAIAAJ&pg=PA246}} From pp. 246-247: "I was requested by a lady to escort her to a seminary for young ladies, and on being ushered into the reception-room, conceive my astonishment at beholding a square piano-forte with four ''limbs''. However, that the ladies who visited their daughters, might feel in its full force the extreme delicacy of the mistress of the establishment, and her care to preserve in their utmost purity the ideas of the young ladies under her charge, she had dressed all these four limbs in modest little trousers, with frills at the bottom of them!"</ref> Victorian manners may have been as strict as imagined—on the surface. One simply did not speak publicly about sex, childbirth, and such matters, at least in the respectable middle and upper classes. However, as is well known, discretion covered a multitude of sins. Prostitution flourished. Upper-class men and women indulged in [[adultery|adulterous]] liaisons. == Gallery == {{gallery |2=A mid-Victorian interior: ''Hide and Seek'' by [[James Tissot]], c. 1877 Image:Winterhalter Elisabeth.jpg|3=Dress designed by [[Charles Frederick Worth]] for [[Elisabeth of Bavaria|Elisabeth of Austria]] painted by [[Franz Xaver Winterhalter]].|4=File:Frith A Private View detail.jpg|5=[[William Powell Frith]]'s painting of 1883 contrasts women's [[Aesthetic dress]] (left and right) with fashionable attire (center).|6=File:Tissot lilacs 1875.jpg|7=Day dress, c. 1875 [[James Tissot]] painting.|8=File:James Abbot McNeill Whistler 011.jpg|9=[[James McNeill Whistler|Whistler]]'s [[Portrait of Lady Meux]], 1882 Image:Jeanna_Samary-Renoir.png|10=[[Pierre-Auguste Renoir|Renoir]]'s portrait of [[Jeanne Samary]] in an [[evening gown]], 1878|11=File:Melville_-_Queen_Victoria.jpg|12=Portrait by [[Alexander Melville (artist)|Alexander Melville]] of [[Victoria of the United Kingdom|Queen Victoria]], 1845|13=File:Henry Treffry Dunn Rossetti and Dunton at 16 Cheyne Walk.jpg|14=An artistic interior: [[Dante Gabriel Rossetti]] reading to [[Theodore Watts-Dunton]] in the drawing room at No. 16 [[Cheyne Walk]], 1882|15=File:Punch - Masculine beauty retouched1.png|16=Men's swimwear: Cartoon from ''[[Punch (magazine)|Punch]]'' by [[George du Maurier]]}} == See also == * [[Emily Clapham]] * [[Victorian decorative arts]] * [[Victorian dress reform]] * [[Victorian morality]] * [[Victoriana]] * [[Women in the Victorian Era]] * [[Charles Frederick Worth]] === Time periods === * [[1830s in fashion]] * [[1840s in fashion]] * [[1850s in fashion]] * [[1860s in fashion]] * [[1870s in fashion]] * [[1880s in fashion]] * [[1890s in fashion]] === Women's clothing === * [[Corset]] * [[Corset controversy]] * [[Tightlacing]] * [[Bloomers (clothing)|Bloomers]] * [[Bodice]] === Contemporary interpretations === * [[Steampunk]] * [[Neo-Victorian]] * [[Lolita Fashion|Lolita]] == References == {{Reflist}} == Further reading == *{{cite book |author=Phipps, Elena| title= ''From Queen to Empress: Victorian dress 1837-1877'' | location=New York | publisher=The Metropolitan Museum of Art | year=1988 | isbn=0870995340| url= http://libmma.contentdm.oclc.org/cdm/compoundobject/collection/p15324coll10/id/69547/rec/235 | display-authors=etal}} * Sweet, Matthew – ''Inventing the Victorians'', St. Martin's Press, 2001 {{ISBN|0-312-28326-1}} == External links == * [http://www.victorians.co.uk/victorian-fashion Victorian Fashion] {{Webarchive|url=https://web.archive.org/web/20180407223711/http://www.victorians.co.uk/victorian-fashion |date=7 April 2018 }} * [https://www.victorianvoices.net/topics/fashion/index.shtml VictorianVoices.net] – Fashion articles and illustrations from Victorian periodicals; extensive fashion image gallery * [http://www.cracked.com/article_19575_5-ridiculous-sex-myths-from-history-you-probably-believe.html Victorian myths] * [http://www.victorianstation.com/lifestylemenu.htm Victorian fashion, etiquette, and sports] {{Webarchive|url=https://web.archive.org/web/20180103162620/http://www.victorianstation.com/lifestylemenu.htm |date=3 January 2018 }} * [http://www.thesmartset.com/article/article12180701.aspx Background on "A Diary in America"] * [http://www.mccord-museum.qc.ca/en/keys/webtours/VQ_P2_17_EN.html Form and Fashion] — the evolution of women's dress during the 19th century (many photographs) * [http://www.mccord-museum.qc.ca/en/keys/games/jeu2/ Educational Game: Mix and Match] — build a 19th-century dress using a virtual mannequin * {{cite web |publisher= [[Victoria and Albert Museum]] |url= http://www.vam.ac.uk/content/articles/v/victorian-dress-at-v-and-a/ |title= Victorian Dress |work= Fashion, Jewellery & Accessories |date= 14 January 2011 |access-date= 2011-04-03}} *[http://cv.vic.gov.au/stories/creative-life/fashion-detective-fashion-fiction-and-forensics/ Fashion detective: Fashion, Fiction and Forensics in nineteenth century Australian fashion] on Culture Victoria {{Timeline of clothing and fashion|state=collapsed}}{{Victorian era|state=collapsed}} [[Category:Victorian fashion| ]] [[Category:19th-century fashion|*]] [[Category:1900s fashion]] [[Category:History of Western fashion]] [[Category:19th century in the arts]] =From ''Women in the Victorian era''= ===Victorian women's fashion=== {{Multiple issues|{{tone|date=March 2023}} {{more footnotes needed|date=March 2023}}|section=y}}{{Further|Victorian fashion}} The ideal Victorian woman was pure, chaste, refined, and modest. This ideal was supported by etiquette and manners. The etiquette extended to the pretension of never acknowledging the use of undergarments (sometimes generically referred to as "unmentionables"). The discussion of such a topic, it was feared, would gravitate towards unhealthy attention on anatomical details. As one Victorian lady expressed it: "[those] are not things, my dear, that we speak of; indeed, we try not even to think of them", in contrast to current norms.<ref>{{cite book |last=Cunnington |first=C. Willett |title=English Women's Clothing in the Nineteenth Century: A Comprehensive Guide with 1,117 Illustrations |publisher=Dover Publications |year=1990 |isbn=978-0-486-26323-6 |pages=20}}</ref> The pretence of avoiding acknowledgement of anatomical realities met with embarrassing failure on occasion. In 1859, the Hon. Eleanor Stanley wrote about an incident where the [[Louisa Cavendish, Duchess of Devonshire|Duchess of Manchester]] moved too quickly while manoeuvring over a [[stile]], tripping over her large [[hoop skirt]]: {{blockquote|[the Duchess] caught a hoop of her cage in it and went regularly head over heels lighting on her feet with her cage and whole petticoats above, above her head. They say there was never such a thing seen – and the other ladies hardly knew whether to be thankful or not that a part of her undergarments consisted in a pair of scarlet tartan [[knickerbockers (clothing)|knickerbockers]] (the things Charlie shoots in) which were revealed to the view of all the world in general and the [[Aimable Pélissier|Duc de Malakoff]] in particular".<ref>{{cite book|last=Cunnington|first=C. Willett|title=English Women's Clothing in the Nineteenth Century: A Comprehensive Guide with 1,117 Illustrations|year=1990|publisher=Dover Publications|isbn=978-0-486-26323-6|pages=20–1}}</ref>}} However, despite the fact that Victorians considered the mention of women's undergarments in mixed company unacceptable, men's entertainment made great comedic material out of the topic of ladies' [[bloomers (clothing)|bloomers]], including men's magazines and music hall skits.<ref>{{cite book |last=Cunnington |first=C. Willett |title=English Women's Clothing in the Nineteenth Century: A Comprehensive Guide with 1,117 Illustrations |publisher=Dover Publications |year=1990 |isbn=978-0-486-26323-6 |pages=22}}</ref> Victorian women's clothing followed trends that emphasised elaborate dresses, skirts with wide volume created by the use of layered material such as [[crinoline]]s, hoop skirt frames, and heavy fabrics. Because of the impracticality and health impact of the era's fashions, a [[Victorian dress reform|dress reform movement]] began among women. The ideal silhouette of the time demanded a narrow waist, which was accomplished by constricting the abdomen with a laced [[corset]]. While the silhouette was striking, and the dresses themselves were often exquisitely detailed creations, the fashions were cumbersome. At best, they restricted women's movements and at worst, they had a harmful effect on women's health. Physicians turned their attention to the use of corsets and determined that they caused several medical problems: compression of the thorax, restricted breathing, organ displacement, poor circulation, and prolapsed uterus.<ref name="O'Connor"/> Articles advocating the reform of women's clothing by the British National Health Society, the Ladies' Dress Association, and the [[Rational Dress Society]] were reprinted in ''The Canada Lancet'', Canada's medical journal. In 1884, Dr J. Algernon Temple of Toronto even voiced concern that the fashions were having a negative impact on the health of young women from the working classes. He pointed out that a young working-class woman was likely to spend a large part of her earnings on fine hats and shawls, while "her feet are improperly protected, and she wears no flannel petticoat or woollen stockings".<ref name="O'Connor"/> [[File:Bloomers.jpg|thumb|1850s illustration of a woman wearing [[bloomers]]]] [[Florence Pomeroy]], Lady Haberton, was president of the Rational Dress movement in Britain. At a National Health Society exhibition held in 1882, Viscountess Haliburton presented her invention of a "[[divided skirt]]", which was a long skirt that cleared the ground, with separate halves at the bottom made with material attached to the bottom of the skirt. She hoped that her invention would become popular by supporting women's freedom of physical movement, but the British public was not impressed by the invention, perhaps because of the negative "unwomanly" association of the style with the American [[Bloomers]] movement.<ref>{{cite book|last=Murray|first=Janet Horowitz|title=Strong-Minded Women and Other Lost Voices from 19th Century England|year=1982|publisher=Pantheon Books|location=New York|isbn=0-394-71044-4|pages=[https://archive.org/details/strongmindedwome00jane/page/68 68–70]|url=https://archive.org/details/strongmindedwome00jane/page/68}}</ref> [[Amelia Jenks Bloomer]] had encouraged the wearing of visible bloomers by feminists to assert their right to wear comfortable and practical clothing, but it was no more than a passing fashion itself among radical feminists. The movement to reform women's dress would persist and have long-term success, however; by the 1920s, [[Coco Chanel]] was successful at selling a progressive, far less restrictive silhouette that abandoned the corset and raised hemlines. The new silhouette symbolised modernism for trendy young women and became the 20th century standard. Other Paris designers continued reintroducing pants for women and the trend was gradually adopted over the next century. Fashion trends, in one sense, travelled "full circle" over the course of the Victorian era. The popular women's styles during the [[Georgian era]], and at the very beginning of Victoria's reign, emphasized a simple style influenced by flowing gowns worn by women in [[Ancient Greek clothing|Ancient Greece]] and [[Clothing in ancient Rome|Rome]]. The [[Empire waist]] silhouette was replaced by a trend towards ornate styles and an artificial silhouette, with the restrictiveness of women's clothing reaching its low point during the mid-century passion for narrow corseted waists and hoop skirts. The iconic wide-brimmed women's hats of the later Victorian era also followed the trend towards ostentatious display. Hats began the Victorian era as simple [[Bonnet (headgear)|bonnets]]. By the 1880s, milliners were tested by the competition among women to top their outfits with the most creative (and extravagant) hats, designed with expensive materials such as silk flowers and exotic plumes such as ostrich and peacock. As the Victorian era drew to a close, however, fashions were showing indications of a popular backlash against excessive styles. Model, actress and socialite [[Lillie Langtry]] took London by storm in the 1870s, attracting notice for wearing simple black dresses to social events. Combined with her natural beauty, the style appeared dramatic. Fashions followed her example (as well as Queen Victoria's wearing of mourning black later in her reign). According to [[Harold Koda]], the former Curator-in-chief of the [[Costume Institute at The Met|Metropolitan Museum of Art's Costume Institute]],<ref>{{cite web|url=http://www.metmuseum.org/about-the-museum/press-room/exhibitions/2014/death-becomes-her|title=Death Becomes Her: A Century of Mourning Attire : October 21, 2014-February 1, 2015|website=Metmuseuim.org|access-date=7 November 2021}}</ref> "The predominantly black palette of [[mourning]] dramatizes the evolution of period silhouettes and the increasing absorption of fashion ideals into this most codified of etiquettes," said Koda, "The veiled widow could elicit sympathy as well as predatory male advances. As a woman of sexual experience without marital constraints, she was often imagined as a potential threat to the social order." ====Evolution of Victorian women's fashion==== <gallery> File:Fashion plate December 1844.jpg|Ladies' December Fashions (1844). Hand-coloured steel engraving from a women's magazine. File:Thegalleryofhmscalcutta james tissot 1876.jpg|''[[The Gallery of HMS Calcutta]]'' by [[James Tissot]] (1876). [[Bustle]]s were fashionable in the 1870s and 1880s. File:Mrs lillie langtry george frederic watts 1880.jpg|''Mrs. Lillie Langtry'' by [[George Frederic Watts]] (1880). File:Five-women-on-queenslander-steps-r.jpg|Fashionable women in [[Queensland]], Australia around 1900. </gallery> {{Short description|Irish writer (born 1963)}} {{Use Irish English|date=August 2025}} {{Use dmy dates|date=August 2025}} {{Infobox writer | name = Darach Ó Scolaí | image = Darach Ó Scolaí.JPG | alt = Man holding prize-winning book | caption = Ó Scolaí in 2019 | birth_name = Darach Ó Scolaí | birth_date = {{Birth date and age|1963|df=y}} | birth_place = [[County Galway]], The Republic of Ireland | death_date = | death_place = | occupation = Writer, artist, publisher | alma_mater = [[University of Galway]] | years_active = 1998–present | genre = Novel, retelling, translation, play, screenplay, illustrated book for children and adults | other_names = | spouse = | children = 3 | awards = [[Awards and Honors received by Darach Ó Scolaí|Awards and Honors]] | signature = | website = }}[[File:Darach Ó Scolaí.JPG|thumb|Darach Ó Scolaí, holding ''Oileán an Órchiste'' (his translation of Robert Louis Stevenson's ''Treasure Island'')]] == Darach Ó Scolaí == Darach Ó Scolaí (<small>Irish:</small> [/ˈda.rax/ /oː/ /sˠkˠoː/l̪ˠəi/]; born 1963<ref>{{Cite web|url=https://portraidi.ie/en/darach-o-scolai/|title=Darach Ó Scolaí|date=20 October 2017|website=Portráidí (Portraits of Irish-Language Writers)|access-date=1 August 2025}}</ref>) is an Irish author who works in a number of genres, from novels, plays and screenplays to illustrated books for children and adults. He began his literary career in 1998 writing screenplays, stage plays, retellings and translations; he began to publish novels in 2008. Ó Scolaí is widely recognized as a leading figure in contemporary Irish literature, known as “one of the most important Irish language writers of his generation”<ref>{{Cite journal|last=Poirtéir|first=Cathal|date=2022|title=? Suil an Daill: Constant Tensions and Shifting Allegiances|url=https://booksirelandmagazine.com/suil-an-daill-constant-tensions-and-shifting-allegiances/|journal=Books Ireland}}</ref> and "one of the great Irish language novelists [duine d’úrscéalaithe móra na Gaeilge]."<ref name=":17" /> His writing has been called “the high literature of the Irish language.”<ref>Ó Coimín, Maitiú. ''Nós'' 2 February 2018). Qtd. in "Táin Bó Cuailnge." ''Leabhar Breac''. Retrieved 25 August 2025.</ref> Much of his fiction is based on a knowledge of traditional Irish tales and narrative practices as well as Irish history. He specializes in literary and [[wikipedia:Historical_fiction|historical fiction]], or as novelist Alan Titley says, Ó Scolaí’s “peak (for now), or at least his greatest imaginative interest, is the historical novel [tá an chuma air gurb é a bhuaic (go fóill), nó ar a laghad, a mhórspéis samhlaíochta, an t-úrscéal staire].”<ref name=":11">{{Cite journal|last=Titley|first=Alan|date=Fall 2020|title=An Stíl Go Deo!: Soather Dharach Uí Scolaí (The style would be forever!: Worker Darach Ó Scolaí)|url=https://www.jstor.org/stable/27046090|journal=Comhar|volume=80, No. 10|pages=27|via=JSTOR}}</ref> His retellings of old stories and tales from their original Middle and Early-Modern Irish into Modern Irish ([[wikipedia:Irish_language|Gaeilge]]) are respected for their accessibility to students and language learners as well as for their artistry. Ó Scolaí also regularly reviews books and lectures and writes on literature and culture. Beyond his writing, Ó Scolaí is a publisher and has co-produced a number of film, television shows and stage plays. == Life == Ó Scolaí was born in Dublin and raised in the Galway [[wikipedia:Gaeltacht#Galway Gaeltacht|Gaeltacht]] (Irish-speaking) regions of Cois Fharraige on the north shore of Galway Bay, in the Republic of Ireland, where he lives now with his wife and children in Lochán Beag (Indreabhán).<ref name=":7">{{Cite journal|date=30 October 2024|title=Duais don úrscéal liteartha is fearr buaite ag Darach Ó Scolaí ag Oireachtas na Samhna|url=https://tuairisc.ie/duais-don-ursceal-liteartha-is-fearr-buaite-ag-darach-o-scolai-ag-oireachtas-na-samhna/|journal=Tuairisc}}</ref><ref>{{Cite journal|last=Ní Scolaí|first=Aifric|date=2024|title=Darach Ó Scolaí|url=https://www.taiscecf.ie/ealaiontoiri?category=Scr%C3%ADbhneoir|journal=Taisce Chois Fharraige}}</ref> He graduated the [[wikipedia:University_of_Galway|University of Galway]] (then University College Galway) with a B.A. in 1983.<ref>{{Cite web|url=https://www.linkedin.com/in/darach-ó-scolaí-20026920/|title=Darach Ó Scolaí|last=Ó Scolaí|first=Darach|date=August 2025|website=LinkedIn}}</ref> === Writing and Publishing === Ó Scolaí writes in Irish ([[wikipedia:Irish_language|Gaeilge]]), his native language, and lives in an area defined for the predominant presence of Irish as the vernacular language, the language spoken at home. Irish was the language of his parents' home and is the language of children as well. He is fluent in Irish and English and conversant in French. None of his works has been translated into English. ==== Leabhar Breac ==== In 1995 Darach Ó Scolaí and his brother Caomhán Ó Scolaí — a [[wikipedia:Typography|typographer]] and designer — founded the publishing house Leabhar Breac at Indreabhán (Inverin), County Galway. Their father “Séamas Ó Scolaí was an editor at An Gúm and worked on the Irish-English dictionary team [bhí a n-athair Séamas Ó Scolaí ina eagarthóir sa Ghúm agus d’oibrigh sé ar fhoireann an fhoclóra Gaeilge-Béarla].”<ref name=":0">{{Cite web|url=https://leabharbreac.com/en/about-us/|title=About Us|date=2024|website=Leabhar Breac|access-date=1 July 2025}}</ref> Darach Ó Scolaí has been publisher and literary editor at Leabhar Breac since its founding. Named for [[wikipedia:An_Leabhar_Breac|An Leabhar Breac (The Speckled Book)]], Leabhar Breac publishing house has more than 140 books in print.<ref name=":0" /> Leabhar Breac aims to publish Irish-language books that meet “a high literary and artistic standard.”<ref name=":0" /> Besides the content, Leabhar Breac is known for the typically "superb [thar cionn]" quality of the design and production of the "physical book [leabhar fisiciúil]."<ref name=":8">{{Cite journal|last=Ní Mhuilneoir|first=Gráinne|date=30 July 2024|title=‘Bláthnaid’ – leabhar álainn i sraithín álainn faoi mhná|url=https://tuairisc.ie/blathnaid-leabhar-alainn-i-sraithin-alainn-faoi-mhna/|journal=Tuairisc}}</ref> Its books regularly win awards for literary and artistic quality. Leabhar Breac also publishes translations for children and adults from various early versions of Irish as well as from French and English (and has published translations of books for young readers from Spanish, Catalan, and Italian as well). Leabhar Breac prints its books in Ireland. === Stage and Screen === ==== Rosg ==== In 1998 along with Ciarán Ó Cofaigh,<ref name=":1">{{Cite web|url=http://www.rosg.ie/en/about/History_6/|title=About Us: History|date=July 2025|website=Rosg|access-date=1 August 2025}}</ref> Ó Scolaí co-founded the film and television production company [http://www.rosg.ie/en/ Rosg] and was co-director until 2006. Rosg produced Ó ScolaÍ’s films ''Cosa Nite'' (1999), ''An Leabhar'' (2001) and ''Na Cloigne'' (2010). He left Rosg in 2006 to devote his time to other artistic activities. ==== Ealaín ar Oileán ==== In 2004, along with Val Balance, Ó Scolaí co-founded the annual artists' symposium Ealaín ar Oileán (trans., Art on an Island). The Irish-language symposium was held annually in the Áras Éanna arts and cultural center on Inis Oírr ([[wikipedia:Inisheer|Inisheer]], the smallest of the [[wikipedia:Aran_Islands|Aran Islands]]) from 2004 to 2013. Ó Scolaí was its co-director from its founding<ref>{{Cite web|url=https://ga.wikipedia.org/wiki/Darach_Ó_Scolaí.|title=Darach Ó Scolaí|date=3 February 2024|website=Vicipéid|access-date=1 July 2025}}</ref> until 2013. Besides being its co-director, Ó Scolaí has taken part in this conference as an artist<ref>{{Cite journal|date=16 January 2005|title=Darach Ó Scolaí|url=https://web.archive.org/web/20050116163252/http://bliainiris.com/authors/darach_oscolai.html|journal=Bliainiris}}</ref> and writer<ref name=":2">{{Cite web|url=http://ealainaroilean.ie/ealainaroilean.html|title=The Conference|date=7 September 2013|website=Ealaín ar Oileán|archive-url=https://web.archive.org/web/20130907083744/http://ealainaroilean.ie/ealainaroilean.html|archive-date=7 September 2013|access-date=1 August 2025}}</ref>. ==== Salamandar ==== In 2006 Ó Scolaí founded the stage production company Salamandar and directed his own play ''An Braon Aníos''. His plays ''An tSeanbhróg'' (2009) and ''Craos'' (2008) were also produced by Salamandar.<ref name=":19">{{Cite web|url=https://leabharbreac.com/en/product-category/darach-o-scolai/|title=Darach Ó Scolaí|date=2024|website=Leabhar Breac|access-date=1 July 2025}}</ref> == Works == === Novels === * [[wikipedia:An_Cléireach|''An Cléireach'' (trans., ''The Clerk'')]], Leabhar Breac, 2007. The Oireachtas Prize for Literary Fiction, 2007; The Ó Súilleabháin Award (Book of the Year) in 2008, and "named as ‘the best novel since the turn of the Century’ by Comhar."<ref>{{Cite web|url=https://leabharbreac.com/en/shop/fiction/an-cleireach/|title=An Cléireach - Leabhar Breac - Irish language novel|website=Leabhar Breac|language=en-US|access-date=2025-10-24}}</ref> * ''Na Comharthaí'' (trans., ''The Signs''), Leabhar Breac, 2014. * ''Súil an Daill'' (trans., ''The Eye of the Blind''), Leabhar Breac, 2021. The Oireachtas Prize for Literary Fiction, 2019.<ref name=":4">{{Cite web|url=https://leabharbreac.com/en/shop/fiction/suil-an-daill/|title=Súil an Daill|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> * ''Bódléar'', Leabhar Breac, 2024. The Oireachtas Prize for Literary Fiction, 2024<ref name=":7" />; The Ó Súilleabháin Award (Book of the Year) in 2025; featured in the 2025 Listen-Up Irish Summer Challenge for students of the Irish language.<ref>{{Cite news|url=https://connachttribune.ie/novel-approach-helps-people-learn-irish-in-a-creative-way/|title=Novel approach helps people learn Irish in a creative way|last=Murphy|first=Judy|date=3 October 2025|work=Connaught Tribune|access-date=24 October 2025}}</ref> === Retellings, Translations and Editions === The retellings and translations are into modern Irish. * ''Feis Tigh Chonáin'' (trans., ''The Feast of Conán's House''), Leabhar Breac, 2000; a retelling of a 15^th-century tale from the [[wikipedia:Fenian_Cycle|Fenian Cycle]].<ref>{{Cite web|url=https://leabharbreac.com/en/shop/fiction/feis-tigh-chonain/|title=Feis Tigh Chonáin|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> * ''An Ceithearnach Caolriabhach'' (trans., ''The Narrow-Striped Kern''), Leabhar Breac, 2002; a retelling from c. 1500, also illustrated by Darach Ó ScolaÍ.<ref>{{Cite web|url=https://leabharbreac.com/en/shop/fiction/an-ceithearnach-caolriabhach/|title=An Ceithearnach Caolriabhach|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> * ''Táin Bó Cuailnge'' (trans., ''The Cattle Raid of Cooley''), Leabhar Breac, 2017, both a modern edition of an 11th-century epic and an annotated edition.<ref name=":3">{{Cite web|url=https://leabharbreac.com/en/shop/darach-o-scolai/tain-bo-cuailnge-2-2/|title=Táin Bó Cuailnge|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> "''Táin Bó Cuailnge'' won the Aodán Mac Poilín Memorial Prize 2017."<ref name=":19" /> * ''Deirdre'', Leabhar Breac, 2023, a “picture book for adults” with artist Anastasia Melnykova.<ref>{{Cite web|url=https://leabharbreac.com/en/shop/darach-o-scolai/deirdre/|title=Deirdre|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> Part of the [[wikipedia:Ulster_Cycle|Ulster Cycle]], ''Deirdre'' is a retelling of the story of possibly the most widely known Irish figure from the early tales and sagas.<ref>{{Cite book|title=A Dictionary of Celtic Mythology|last=MacKillop|first=James|publisher=Oxford University Press|year=2004|isbn=9780198609674|pages=181}}</ref> * ''Bláthnaid'', Leabhar Breac, 2024, a “picture book for adults” with artist Anastasia Melnykova; “one of the great stories of the [[wikipedia:Ulster_Cycle|Ulster Cycle]].”<ref name=":4" /> * ''Sadhbh,'' Leabhar Breac, 2025, a picture book for adult readers, illustrated by Alé Mercado; a retelling of the medieval tale ''Ceasacht Inghine Ghuile (''trans., ''The Complaint of Guile's Daughter'').<ref name=":5">{{Cite web|url=https://leabharbreac.com/en/tales-of-wonder/|title=Tales of Wonder|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> * ''Eoghan Béal'', Leabhar Breac, 2025, a picture book for adult readers illustrated by Alé Mercado<ref name=":5" />; a retelling of the medieval tale ''[https://ga.wikipedia.org/wiki/Caithr%C3%A9im_Cellaig Cathréim Ceallaigh]'' from ''The Yellow Book of Leacan.''<ref name=":5" /> === For Young Readers === Ó Scolaí has written illustrated books for young readers (8–10 years old) in two series, the Fionn Series and the Scéalta Staire series, and translated a large number of classics and popular books for children of all ages. The number of these written and translated works suggests a commitment to children and their literacy in Irish. The Fionn Series “is a retelling ... of the great legends of the Fianna for the young Irish readers of today.”<ref name=":6">{{Cite web|url=https://leabharbreac.com/en/shop/oige-en/8-9/doiteoir-na-samhna/|title=Dóiteoir na Samhna|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> [[wikipedia:The_Boyhood_Deeds_of_Fionn|Macgnímartha Finn (The Boyhood Deeds of Fionn)]] is a medieval story in the [[wikipedia:Fenian_Cycle|Fenian Cycle]]. * ''An Bradán Feasa'' (trans., ''The Salmon of Knowledge''), Leabhar Breac, 2010, “shortlisted for the Réics Carlo award 2010.”<ref name=":9">{{Cite web|url=https://leabharbreac.com/en/shop/oige-en/8-9/an-bradan-feasa/|title=An Bradán Feasa|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> * ''Dóiteoir na Samhna'' (trans., ''The Halloween Burner''), 2010.<ref name=":6" /> * ''Bodach an Chóta Lachna'' (trans., ''The Churl in the Dun Coat''), 2011.<ref>{{Cite web|url=https://leabharbreac.com/en/shop/oige-en/7-8/bodach-an-chota-lachna/|title=Bodach an Chóta Lachna|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> The Scéalta Staire (Historical Stories) series<ref name=":9" /> * ''Mánas Ó Dónaill'', 2000. * ''Seán Ó Néill'', Leabhar Breac, 2000. * ''Gráinne Mhaol Ní Mháille'', Leabhar Breac, 2003. * ''Tadhg Dall Ó hUiginn'', Leabhar Breac, 2003. ==== Translations ==== * Robert Louis Stevenson, ''Oileán an Órchiste'' (trans. of ''Treasure Island''), Leabhar Breac, 2014.<ref>{{Cite journal|date=2025-06-19|title=Oireachtas na Gaeilge|url=https://en.wikipedia.org/w/index.php?title=Oireachtas_na_Gaeilge&oldid=1296394643|journal=Wikipedia|language=en}}</ref> * Robert Louis Stevenson, ''An Fuadach'' (trans. of ''Kidnapped''), Leabhar Breac, 2016. * Clement Clarke Moore, ''Cuairt San Nioclás'' (trans. of ''A Visit from St. Nicholas'', or "'Twas the Night Before Christmas"), Leabhar Breac, 2022. '''''The Corto Maltese Graphic Novels''''' Written in Italian by Hugo Pratt and translated by Ó Scolaí, both adults and teenagers read this series of Italian adventure graphic novels.<ref>{{Cite journal|date=2025-07-01|title=Corto Maltese|url=https://en.wikipedia.org/w/index.php?title=Corto_Maltese&oldid=1298285365|journal=Wikipedia|language=en}}</ref> Ó Scolaí's '''translation of ''Corto Maltese''''' was listed in 2017 among "The 30 Irish books that Irish people love."<ref>{{Cite journal|last=Ó Murchú|first=Eoin P.|date=09/06/2017|title=Na 30 leabhar Gaeilge is fearr leis na Gaeil [The 30 Irish books that Irish people love]|url=https://nos.ie/cultur/leabhair/an-30-leabhar-gaeilge-is-fearr-leis-na-gaeil/|journal=Nós}}</ref> * Hugo Pratt, ''Corto: Port na Farraige Goirt'', Leabhar Breac, 2013. * Hugo Pratt, ''Corto: The Golden House in Samarkand'', 2014. * Hugo Pratt, ''Corto: Na Liopard-Fhir ó Rufiji'' (trans. of ''Corto: The Leopard Men of Rufiji''), Leabhar Breac, 2014. * Hugo Pratt, ''Corto: In Ainm Dé Uilthrócairigh'' (trans. of ''Corto: In the Name of God All-Merciful''), Leabhar Breac, 2014. * Hugo Pratt, ''Corto: Tóraíocht Eile'' (trans. of ''Corto: Another Quest''), Leabhar Breac, 2014. * Hugo Pratt, ''Corto: Sa tSibéir'' (trans. of ''Corto: In Siberia''), Leabhar Breac, 2016. '''''Other Translations for Children''''' Ó Scolaí has translated into Irish six books from the ''Le Pavillon Noir'' (trans., ''Jolly Roger'') series by Alain Surget; four books from the ''Catalan First Steps'' series by Enric Lluch Girbés and the ''Caitlín & Cormac'' series by Joan Carles; three books from the ''Louisette le Taupe'' series by Bruno Heitz, and three books from the ''Loup'' series by Orianne Lallemand. === Plays and Screenplays === ==== Stage Plays ==== Ó Scolaí was writer and director of the original productions of two plays in the ''Trí Bhraon'' (trans., ''Three Drops'') trilogy; ''Coinneáil Orainn'' was directed by Darach Mac Con Iomaire and staged by An Taibhdhearc. All three plays have been published in book form by Leabhar Breac. * ''Coinneáil Orainn'' (trans., ''We'll Keep Going''), 2005.<ref>{{Cite web|url=https://irishplayography.com/play?playid=32553|title=Coinneáil Orainn|date=2025|website=PlayographyIreland: A Comprehensive Database of New Irish Plays Produced Professionally Since 1904.|access-date=25 August 2025}}</ref> The first play in the ''Trí Bhraon'' (''Three Drops'') trilogy. [[wikipedia:Taibhdhearc_na_Gaillimhe|An Taibhdhearc]], the national Irish-language theatre of Ireland, toured the country in 2005 with ''Coinneáil Orainn''.<ref>{{Cite web|url=https://leabharbreac.com/en/shop/darach-o-scolai/coinneail-orainn/|title=Coinneáil Orainn|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> Walter Macken Prize, 2005; BBC Stewart Parker Award, 2006.<ref>{{Cite web|url=https://irishplayography.com/person/darach-scola|title=Darach Ó Scolaí|date=2025|website=PlayographyIreland: A Comprehensive Database of New Irish Plays Produced Professionally Since 1904.|access-date=25 August 2025}}</ref> * ''Branwen'', 2006, by Darach Ó Scolaí and Ifor ap Glyn, in Irish, Welsh and English, co-produced by Project Arts Centre and Llwyfan Gogledd Cymru, toured the Republic of Ireland and Wales.<ref>{{Cite web|url=https://irishplayography.com/play?playid=32418|title=Branwen|date=2025|website=PlayographyIreland: A Comprehensive Database of New Irish Plays Produced Professionally Since 1904|access-date=25 August 2025}}</ref> * ''An Braon'' Aníos (trans., ''Rising Damp''), 2006, directed by Ó Scolaí.<ref>{{Cite web|url=https://irishplayography.com/play?playid=32461|title=An Braon Aníos|date=2025|website=PlayographyIreland: A Comprehensive Database of New Irish Plays Produced Professionally Since 1904|access-date=25 August 2025}}</ref> The second play in the ''Trí Bhraon'' (''Three Drops'') trilogy. “The Salamandar company toured the country in 2006-07 with this play, and Salamandar also produced a radio version of the play for RTÉ Raidió na Gaeltachta in 2009.”<ref>{{Cite web|url=https://leabharbreac.com/en/shop/darach-o-scolai/an-braon-anios/|title=An Braon Aníos|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> * ''Craos'' (trans., ''Gluttony''), 2008, directed by Ó Scolaí.<ref name=":13">{{Cite web|url=https://irishplayography.com/play?playid=32867|title=Craos|date=2025|website=PlayographyIreland: A Comprehensive Database of New Irish Plays Produced Professionally Since 1904|access-date=25 August 2025}}</ref> The third play in the ''Trí Bhraon'' (''Three Drops'') trilogy, it toured to Cork and Belfast.<ref name=":13" /> A review of the 2008 Salamander performance in the ''Irish Times'' says, “a humorous play which offers plenty to think about, fine acting, and sparklingly witty dialogue.”<ref>{{Cite web|url=https://leabharbreac.com/en/shop/darach-o-scolai/craos-2/|title=Craos|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> * ''A+E'', 2008, by Ríonach Ní Néill and Darach Ó Scolaí, "dance and music drama," co-produced by Ciotóg and Salamandar.<ref>{{Cite web|url=https://irishplayography.com/play?playid=32962|title=A+E|date=2025|website=PlayographyIreland: A Comprehensive Database of New Irish Plays Produced Professionally Since 1904|access-date=25 August 2025}}</ref> * ''An tSeanbhróg'' (trans., ''The Old Shoe''), 2009, produced by Salamander<ref>{{Cite web|url=https://irishplayography.com/play?playid=33042|title=An tSeanbhróg|date=2025|website=PlayographyIreland: A Comprehensive Database of New Irish Plays Produced Professionally Since 1904|access-date=25 August 2025}}</ref> and staged in the Axis Arts Centre, Dublin, and the Letterkenny Arts Centre. * '''In ''Mhuir Fhíondorcha/The Wine-Dark Sea: The Homer Project'', Ó Scolaí's translation of Homer's Cyclops story, performed at the 2019 IMRAM festival'''.<ref>{{Cite news|url=https://www.irishtimes.com/culture/books/imram-a-festival-celebrating-the-irish-language-1.4047610|title=Imram: a festival celebrating the Irish language. Liam Carson reveals the myths and legends appearing in this year’s programme|last=Carson|first=Liam|date=11 October 2019|work=The Irish Times|access-date=15 October 2025}}</ref> ==== Screenplays ==== * ''Cosa Nite'' (trans., ''Washed Feet''), short film, 1998 (dir. Dearbhla Walsh, prod. Ciarán Ó Cofaigh, Rosg); "a prose version of ''Cosa Nite'' was published (Rosg 2000)."<ref name=":9" /> Nominated for an Irish Film and Television Award.<ref>{{Citation|title=Cosa Nite (Short 1998) - Awards - IMDb|url=https://www.imdb.com/title/tt0191917/awards/|accessdate=2025-08-25|language=en-US}}</ref> * ''Na Glúnta'' (trans., ''The Generations''), 2001<ref>{{Cite web|url=https://www.iftn.ie/production/production_companies/production_sub/feature/?act1=record&aid=70&rid=3917&tpl=filmography_dets&only=1&force=1|title=Na Glúnta {{!}} The Irish Film & Television Network|website=www.iftn.ie|access-date=2025-08-25}}</ref>, co-directors Ciarán Ó Cofaigh & Darach Ó Scolaí, prod. Ciarán Ó Cofaigh, Rosg. * ''An Leabhar'' (trans., ''The Book''), short film, 2000, (dir. Robert Quinn, prod. Ciarán Ó Cofaigh, Rosg) Rosg, 2000.<ref>{{Citation|title=An Leabhar|url=https://www.imdb.com/title/tt0963767/|publisher=Bord Scannán na hÉireann / The Irish Film Board, ROSG|accessdate=2025-08-25|first=Robert|last=Quinn|others=Colm O&apos;Maonlai, Peadar O&apos;Treasaigh, Diarmuid Mac an Adhastair}}</ref> * ''Na Cloigne'' [trans., The Heads], 3-episide series, 2010 (dir. Robert Quinn, prod. Ciarán Ó Cofaigh, Rosg), TG4.<ref>{{Cite web|url=https://www.imdb.com/title/tt1607924/|title=Na cloigne|date=2010|website=IMDb|access-date=25 August 2025}}</ref> === Nonfiction === Ó Scolaí's essays and lectures are published and his interviews are broadcast regularly, making for a large body of nonfiction critical and analytical work. Here are a few, almost all published in [https://comhar.ie/iris/scribhneoiri/darach-o-scolai/ Comhar]: * “Ceol Ciúin na nÉagmaise” (trans., “The Silent Music of Absence ['''the Fall?''']”), an essay on the 2014 Nobel Prize winner for literature, [[wikipedia:Patrick_Modiano|Patrick Modiano]], ''Comhar'', December 2014. * The Ó Cadhain Lecture: [https://leachtaiuichadhain.clo.ie/leachtai/2014 “Cuimhne agus Díchuimhne (trans., “Memory & Forgetfulness"]), 2014. * “Rithim agus Réim” ("Rhythm and Register"), a public lecture in the University College Dublin lecture series “Ó Thrácht go Twitter” (trans., "From Talk to Twitter"), 2014. * Review of Pádraig Ó Cíobháin’s ''Dréachta Chrích Fodla'', '''Comhar?, ??'''. * “Na Geilt i mBun an Tí” (trans., "The Madmen in Charge"), a talk at the Merriman Winter School, Comhar April 2012.<ref name=":18">{{Cite web|url=http://darachoscolai.ie/beathaisneis.html|title=Darach Ó Scolaí: Beathaisnéis|website=darachoscolai.ie|access-date=2025-09-26}}</ref> * The EFACIS podcast: Síle Ní Choincheannain talks to Darach Ó Scolaí about the historical novel. == Critical Reception == Ó Scolaí’s style has been called “crisp and elegant, and rich in language while being highly readable,”<ref>{{Cite journal|last=Heussaf|first=Anna|date=Summer 2025|title=Bláthnaid—A tale of love, violence and sorcery retold for readers today|url=https://booksirelandmagazine.com/blathnaid-a-tale-of-love-violence-and-sorcery/|journal=Books Ireland}}</ref> with “an unsurpassed richness and precision of language.”<ref name=":12">{{Cite journal|last=Ó Cróinín|first=Breandán|date=Summer 2025|title=unknown|journal=The Limerick Leader}}</ref> “Whimsical, hilarious, and subtly learned” is how Éilis Ní Dhuibhne described his writing.<ref name=":20" /> === Original Works === Ó Scolaí’s first novel, the 2007 ''An Cléireach'' (''The Clerk'') won two prizes and was described as “one of the great historical novels in the Irish language and among the best books written in the language since the beginning of this century.”<ref name=":12" /> Novelist Alan Titley says, “In ''An Cléireach'' Ó Scolaí creates the Ireland of war in the 17th century more fully than any other Irish writer on the subject of war since ''L’Attaque'' Eoghain Ó Thuairisc around 1798 [In ''An Cléireach'' cruthaíonn Ó Scolaí Éire an chogaidh san 17ú haois níos iomláine ná mar a dhein aon scríbhneoir Gaeilge eile ar ábhar cogaidh ó ''L’Attaque'' Eoghain Uí Thuairisc timpeall ar 1798].”<ref name=":11" />{{rp|25, Col. 1a}} Not all the reviews of this first novel were so positive, however; Proinsias O' Drisceoil says for the Irish Times says,<blockquote>This then is a novel in search of a plot, a story that attempts to attain a significance that eludes it.<ref>{{Cite news|url=https://www.irishtimes.com/news/a-disaffected-clerk-in-the-confederates-1.943070|title=A disaffected clerk in the confederates|last=O' Drisceoil|first=Proinsias|date=5 July 2008|work=The Irish Times|access-date=16 October 2025}}</ref></blockquote> In the ''Oxford Handbook of Modern Irish Fiction'' Pádraig Ó Siadhail analyzes rather than reviews ''An Cléireach'': <blockquote>In ''An Cléireach'', Ó Scolaí revisits the trauma of Cromwellian Ireland. The primary narrative device is once again the first-hand account, in this case by Tadhg Ó Dúbháin, a clerk and quartermaster in the Confederate Army in 1650. We sample the hardships, the friendships, the tensions, the rivalries, and the petty jealousies amongst comrades in arms, including remnants of the Gaelic literary class, as the Confederate soldiers, increasingly a rabble more than a cohesive unit, retreat in advance of Cromwell’s forces. ''An Cléireach'' concludes with the narrator and his family in exile in continental Europe. But along the retreat route, and central to the novel, members of the Confederate army camp, rest up, and tell versions of a story about the keeper of the treasured manuscript "Saltair an Easpaig" (The Bishop’s Psalter). Their versions raise issues about memory construction, the limitations of individual perspectives, personal agendas, and how minor changes in the telling of a story can alter our understanding of history, Thus, ''An Cléireach'' complements ''Fontenoy'' in moving beyond more realistic recreation of a historical event or period to interrogate the notion of history as construct.<ref>{{Cite book|title=The Oxford Handbook of Modern Irish Fiction|last=Ó Siadhail|first=Pádraig|publisher=Oxford University Press|year=2020|isbn=9780198754893|editor-last=Harte|editor-first=Liam|pages=598–99|chapter=Contemporary Irish Fiction}}</ref> </blockquote> Of ''Súil an Daill,'' in ''Nós'', Cathal Seoighe says, "The book deserves a significant place among the collection of high-quality books published in recent years that would make you feel sorry for someone who does not speak Irish [Tá áit shuntasach ag dul don leabhar i measc an chnuasaigh leabhair ar ardchaighdeán a foilsíodh le roinnt blianta anuas a d’fhágfadh trua agat don té atá gan Ghaeilge]."<ref>{{Cite journal|last=Seoighe|first=Cathal|date=09/26/2022|title=‘Dar leathmhagairle an diabhail, is leabhar den scoth é seo!’ ['According to the devil’s half-wit, this is a great book!’]|url=https://nos.ie/cultur/leabhair/dar-leathmhagairle-an-diabhail-is-leabhar-den-scoth-e-seo/|journal=Nós}}</ref> ''Bódléar'', Ó Scolaí's most recent book, is a “beautiful novel. There is magic and craftsmanship in it. A small miracle of a book and it is highly recommended.”<ref>{{Cite web|url=https://leabharbreac.com/bodlear-mioruilt-bheag-de-leabhar/|title=Bódléar: Míorúilt bheag de leabhar (Bódléar: A Small Miracle of a Book)|last=Ní Ghairbhí|first=Róisín|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> Éilis Ní Dhuibhne in the ''Irish Times'' says,<blockquote>what a gem! An affectionately gentle satire of the Irish poetic scene during one creatively fluid 19th-century year, the story focuses on a Maigue poet and schoolteacher who goes on a trip to France and returns with camembert, a cafetiere, ‘Fleurs du Mal’, and a mission to convert the local traditionalists to la modernité. Whimsical, hilarious, and subtly learned, it’s absolutely delightful!<ref name=":20">{{Cite journal|last=Ní Dhuibhne|first=Éilis|date=30 June 2025|title=Éilís Ní Dhuibhne on the best Irish language books of 2025 so far: Including a history of the Gaeltacht Civil Rights Movements, a gem of a novel by Darach Ó Scolaí and Joe McHugh’s entertaining account of learning Irish|url=https://www.irishtimes.com/culture/books/review/2025/06/30/eilis-ni-dhuibhne-on-the-best-irish-language-books-of-2025-so-far/|journal=The Irish Times|pages=22}}</ref></blockquote> === Retellings and Translations === ==== ''Táin Bó Cuailnge'' ==== ''Táin Bó Cuailnge'' [''The Cattle Raid of Cooley''] is a modern edition of an 11th-century epic into modern Irish.<ref name=":3" /> Gearóid Denvir reviewed ''Táin Bó Cuailnge'' for ''Comhar'':<blockquote>Darach Ó Scolaí has ​​achieved a feat in this challenging reworking. He has found a high level of the Irish language to tell his story – as he has done before in his groundbreaking novel An Cléireach (2007, Leabhar Breac) and in his other prose works. This book is a decoration of the language, literature and culture of the Irish language, following the path of the old storytellers and writers and presenting material from the tradition to his own generation according to the understandings of his own time. The book will be a classic that will be of great interest to all readers of the Irish language, both ordinary readers, students, scholars and writers, and there should be a copy in every home in the country. [Tá éacht déanta ag Darach Ó Scolaí san athleagan dúshlánach seo. Tá réim ard den teanga Ghaeilge aimsithe aige lena scéal a inseacht – mar a rinne sé cheana ina úrscéal ceannródaíoch An Cléireach (2007, Leabhar Breac) agus i saothair eile phróis dá chuid. Is maisiú ar an teanga agus ar litríocht agus cultúr na Gaeilge an leabhar seo a leanas conair na seanscéalaithe agus na seanscríobhaithe agus ábhar de chuid an traidisiúin á chur i láthair a ghlúine féin aige de réir thuiscintí a linne féin. Clasaic a bheas sa leabhar a gcuirfidh léitheoirí uilig na Gaeilge, idir ghnáthléitheoirí, mhic léinn, scoláirí agus scríbhneoirí spéis thar na bearta ann, agus ba cheart cóip a bheith i chuile theach sa tír.]<ref name=":15">{{Cite journal|last=Denvir|first=Gearóid|date=April 2018|title=Táin Bó Cuailgne|url=https://comhar.ie/iris/78/4/leirmheas/|journal=Comhar|via=JSTOR}}</ref> </blockquote>Cathal Poirtéir says, "The freshness and richness of Ó Scolaí’s version are a joy …. The author delights us with the linguistic and stylistic richness of the ancient epic in a modern-Irish version that reflects the original’s spirit and language."<ref>{{Cite journal|last=Poirtéir|first=Cathal|date=May/June 2018|title=Leabhair Idir Lámha|url=https://www.jstor.org/stable/26564180|journal=Books Ireland|pages=46–47|via=JSTOR}}</ref>{{rp|47}} Novelist and academic Alan Titley calls Ó Scolaí's "a wonderful gutsy telling" of ''Táin Bó Cuailnge''.<ref>{{Cite news|url=https://www.irishtimes.com/culture/2023/03/11/the-tain-retold-maeve-and-ailills-spat-could-be-out-of-a-soap-opera/|title=The Táin retold: ‘Maeve and Ailill’s spat could be out of a soap opera’|last=Titley|first=Alan|date=11 March 2023|work=The Irish Times|access-date=16 October 2025}}</ref> ==== ''Deirdre'' ==== Marie Whelton, in "Léann Teanga" ("Language Studies"), in the 2024 ''An Reiviú'' says,<blockquote>this version [of ''Deirdre''] by Darach Ó Scolaí succeeds in skillfully capturing and portraying the complexity of gender and power issues in the ‘Deirdre’ tradition [éiríonn leis an leagan seo le Darach Ó Scolaí castacht cheisteanna na hinscne agus na cumhachta i dtraidisiún scéal Dheirdre a ghabháil agus a léiriú go sciliúil]. … There is no doubt that this new version greatly contributes to the legacy of the story and that it revives that legacy thoughtfully and artistically [Níl amhras faoi ach go gcuireann an leagan úr seo go mór le hoidhreacht an scéil agus go ndéanann sé an oidhreacht sin a athbheochan go tuisceanach agus go healaíonta.].<ref name=":16">{{Cite web|url=https://www.tara.tcd.ie/tara8/server/api/core/bitstreams/3c20175a-7631-44b2-8b0f-f454edd712b4/content|title=An Artistic Retelling of Deirdre's Tale and the Defeat of Conor Review of Deirdre or the Ship of Mac Uisnigh by Darach Ó Scolaí [Athinsint Ealaíonta ar Oidhe Dheirdre agus ar Ansmacht Chonchúir Léirmheas ar Deirdre nó Loingeas Mhac Uisnigh le Darach Ó Scolaí]|last=Whelton|first=Marie|date=2024|website=The Review [An Reiviú], Language Studies [Léann Teanga]|access-date=25 September 2025}}</ref></blockquote> === Works for Young Readers === Meadhbh Ní Eadhra said of ''Bodach an Chóta Lachna'' that it was "Beautiful Irish, but easy to understand for young readers."<ref>Ní Eadhra, Meadhbh. In ''Gaelscéal'', qtd. in "Bodach an Chóta Lachna" https://leabharbreac.com/en/shop/oige-en/7-8/bodach-an-chota-lachna/.</ref> == Awards and Honors == Ó Scolaí's works are regularly nominated and make the short list for prizes, an honor in itself, but they are generally not listed here unless they are named as the first-place winner in their category. === Oireachtas Prize === The Oireachtas Prize is the literary prize awarded by [[wikipedia:Oireachtas_na_Gaeilge|Oireachtas na Gaeilge]], the annual arts festival dedicated to Irish language, arts and culture. Darach Ó Scolaí has won the Oireachtas Prize for Literary Fiction three times, once for ''An Cléireach'' (''The Clerk'') in 2007, for ''Súil an Daill'' (''The Eye of the Blind'') in 2021 and for ''Bódléar'' in 2024. * 2007, for ''An Cléireach'' (trans., ''The Clerk'') — “(a special prize commemorating the 400th anniversary of the foundation of Coláiste na nGael in Louvain, awarded under the auspices of the Franciscan Province of Ireland). The prize of €10,000 was the largest prize ever awarded to an Irish language novel [(duais speisialta chomórtha 400 bliain bhunú Choláiste na nGael i Lobháin a bronnadh faoi urraíocht Phroibhinse Phroinsiasach na hÉireann). Ba é an duais €10,000 sin an duais ba mhó a bronnadh riamh ar úrscéal Gaeilge].”<ref name=":18" /> * 2021, for ''Súil an Daill'' (''The Eye of the Blind'') * 2024, for ''Bódléar'' === Ó Shúilleabháin Award, Irish language “Book of the Year” === The first prize of this award includes €5,000 to the publisher and €2,500 to the author of the winning work.<ref name=":10">{{Cite journal|date=15 August 2023|title=20 saothar san iomaíocht do ‘Leabhair Ghaeilge na Bliana 2023’|url=https://tuairisc.ie/20-saothar-san-iomaiocht-do-leabhair-ghaeilge-na-bliana-2023/|journal=Tuairisc}}</ref> * ''An Cléireach'' (''The Clerk'').<ref>{{Cite web|url=http:/www.gaelport.com/uploads/documents/edition19.html|title=Eagrán / Edition 19 - 04 11 2008|date=4/11/2008|website=Internet Archive|archive-url=https://web.archive.org/web/20130525011340/http:/www.gaelport.com/uploads/documents/edition19.html|archive-date=25 May 2013|access-date=25 August 2025}}</ref> * ''Táin Bó Cuailnge'', 2018. * ''Bódléar'', 2025. ==== De Bhaldraithe Award ==== The Gradam de Bhaldraithe is awarded to the best work in translation.<ref name=":10" /> * ''Cuairt San Nioclás,'' a translation of Clement Clarke Moore's ''A Visit from St. Nicholas'', or "'Twas the Night Before Christmas."<ref name=":10" /> ==== Other ==== * Walter Macken Prize, for ''Coinneáil Orainn'' (trans., ''We'll Keep Going''), 2005 * Bháiteir Uí Mhaicín Memorial Award, for ''Coinneáil Orainn'' (trans., ''We'll Keep Going''), 2005<ref>{{Cite news|url=https://www.irishtimes.com/gaeilge/tuarascail/duais-oireachtais-1.501571|title=Oireachtas Prize: Over €50,000 was awarded to writers in the Oireachtas Literary Competitions at an event in Dublin last night. Winners… [Duais Oireachtais: Bronnadh breis agus €50,000 ar scríbhneoirí i gComórtais Liteartha an Oireachtais ar ócáid i mBaile Átha Cliath aréir. Bhuaigh…]|work=5 October 2005|access-date=15 October 2025}}</ref> * BBC Stewart Parker Award, for ''Coinneáil Orainn'' (trans., ''We'll Keep Going''), 2006 * The Aodán Mac Póilín Commemorative Prize, for ''Táin Bó Cuailnge'' (trans., ''The Cattle Raid of Cooley''), 2017 == External Links == * Leabhar Breac website: https://leabharbreac.com/en/ * Leabhar Breac Facebook pages: * Rosg website: [http://www.rosg.ie/en/ <nowiki>http://ww</nowiki>w.rosg.ie/en/] * Art on the Island (Ealaín ar Oileán) website, archived at the Wayback Machine: https://web.archive.org/web/20130601000520/http://ealainaroilean.ie/ 31 March 2012, 1 June 2013 and 8 January 2014 * Darach Ó Scolaí's website Archived 25 September 2015 at the Wayback Machine: https://web.archive.org/web/20150925103456/http://darachoscolai.ie/ * Youtube video of [https://www.youtube.com/watch?v=OlP2AmSBzXc Breandán Ó Cróinin introducing Deirdre at the book launch] in the pub Tigh Mholly (Molly’s House). == Primordial Ooze == * Known for his sensitivity to language and voices. * Finish scanning through JSTOR * Scan through Irish Times, 56 hits * Check Goodreads * Check YouTube (In the spring of 2013, the arts programme Imeall interviewed the author on TG4.) * Check both Wikipedias for pages on the origins of the retold tales (like Deirdre) and link to this article * Propose link from University of Galway page once Darach’s is up * Write Irish National Biography (<nowiki>https://www.dib.ie</nowiki>) to propose an article about Darach once the Wikip article is done? See what they say. * Link to Ó Scolaí from the Wikipedia * Make sure links '''to''' Wikipedia in the actual encyclopedia work right === Not Placed Yet === * "So here are the books that Irish people love the most! [Mar sin seo iad na leabhair is gile leis na Gaeil!]" — "32. An Cléireach – Darach Ó Scolaí (2)" [18 books got 2 votes, and then they're alphabetized by author's last name, so the 32 of 34 doesn't signify the specificity it seems to]<ref name=":14">{{Cite journal|last=Ó Murchú|first=Eoin P.|date=9 June 2017|title=Na 30 leabhar Gaeilge is fearr leis na Gaeil. [The 30 best Irish books for Irish people]|url=https://nos.ie/cultur/leabhair/an-30-leabhar-gaeilge-is-fearr-leis-na-gaeil/|journal=Nós}}</ref> * "Below is a list of those 111 works – a list that shows a great deal of diversity in the reading habits of Irish speakers.Here is a list of those 111 works – a list that shows a great deal of diversity in the reading habits of Irish speakers [Anseo thíos tá liosta den 111 saothar sin – liosta a léiríonn éagsúlacht an-mhór i nósanna léitheoireachta Gaeilgeoirí.Anseo thíos tá liosta den 111 saothar sin – liosta a léiríonn éagsúlacht an-mhór i nósanna léitheoireachta Gaeilgeoirí]." "Corto Maltese – Hugo Pratt (aistrithe ag Darach Ó Scolaí)"<ref name=":14" /> * "Ceann eile de bhuaicphointí na hÉigse a bheidh sa seisiún le Darach Ó Scolaí, duine d’úrscéalaithe móra na Gaeilge, agus duine de chomhbhunaitheoirí teach foilsitheoireachta Leabhar Breac. [Another highlight of the Éigse will be the session with Darach Ó Scolaí, one of the great Irish language novelists, and one of the co-founders of the publishing house Leabhar Breac.]"<ref name=":17">{{Cite journal|last=Nós|date=4 May 2023|title=Éigse na Bruiséile le filleadh i mí na Bealtaine. [Éigse na Bruséile to return in May]|url=https://nos.ie/cultur/eigse-na-bruiseile-le-filleadh-i-mi-na-bealtaine/|journal=Nós}}</ref> === Things Taken Out for Now === “’The play is a comedy about language, lies, bureaucracy and Gaeltacht grants, in the tradition of Myles na Gcopaleen,’ according to Norma-Jean Kenny in the ''Galway Advertizer'', ‘in which the author comments and criticizes the institutions of the Irish language in Ireland without ceasing.’" Supposedly a quotation by Gearóid Denvir reviewing ''Táin Bó Cuailnge'' for ''Comhar'' (but I don't find it in the article): This book has long been needed by Irish language readers and there is no doubt that it will become a classic in time and surpass Thomas Kinsella’s English version. This version remains faithful to the language of the original while at the same time finding an appropriate language in today’s Irish. Ó Scolaí masterfully overcomes the difficulties of the original’s rhetorical difficulties and the versions of the original poetic texts are extremely effective.[supposedly <ref name=":15" />] “The biggest prize ever awarded for a novel in Irish was presented at a special ceremony in the National Concert Hall in Dublin, today (Thursday, 4 October 2007). Darach Ó Scolaí, writer, artist & playwright from Casla, Co. Galway, was awarded €10,000 for his literary novel, ‘An Ardscoil’. This work, under the new title ‘An Cléireach’, will be launched at Oireachtas na Samhna in Westport in November. This is the first novel from his pen, a story set in the late seventeenth century. This competition was sponsored by the Franciscan Province of Ireland.” (archive, Oireachtas na Gaeilge site, 04 October, 2007) ''Súil an Daill'' (trans., ''The Eye of the Blind''), Leabhar Breac, 2021. number 2 in ''Comhar'' literary magazine’s list of best books of 2021. '''{6}.''' *William Shakespeare, ''Romeo agus Juliet'' (trans. of ''Romeo and Juliet''), Leabhar Breac, 2016. *Jonathan Swift, ''Camchuairt Ghuilivéir'' (trans. of ''Gulliver's Travels''), Leabhar Breac, 2016. *Hugo Pratt, ''Corto Maltese'' '''''Flag of Bones (Bratach na gCnámh) Series''''' Leabhar Breac published the Bratach na gCnámh series of books for young readers. Written in French by Alain Surget, illustrated by Annette Marnat and translated by Darach Ó Scolaí, this series uses the history of Caribbean Sea pirates<ref>{{Cite web|url=https://leabharbreac.com/en/product-category/alain-surget/|title=Alain Surget Archives|website=Leabhar Breac|language=en-US|access-date=2025-09-30}}</ref>: *Alain Surget, ''Éalú as Páras'' (''Escape from Paris''), Annette Marnat (Illustr.), Leabhar Breac, 2011. * Alain Surget, ''Oilean na Siorcanna'' (''Shark Island''), Annette Marnat (Illustr.), Leabhar Breac, 2011. * Alain Surget, ''Long na dTaibhsi'' (''Ship of the Ghosts''), Annette Marnat (Illustr.), Leabhar Breac, 2011. * Alain Surget, ''San Ochtapas Dubh'' (''In the Black Octopus''), Annette Marnat (Illustr.), Leabhar Breac, 2013. * Alain Surget, ''San Ionsai ar Veracruz'' (''The Attack on Veracruz''), Annette Marnat (Illustr.), Leabhar Breac, 2013. '''''For "First Readers" (children to 6 years old or so)''''' These books were written originally in Catalan by Spanish author Enric Lluch Girbés and translated into Irish by Ó ScolaÍ: *Enric Lluch, ''Ag Péinteáil an Tí'' (''Painting the House''), Anna Clariana (Illustr.), Leabhar Breac, 2017. *Enric Lluch, ''An Colúr Bacach'' (''The Lazy Dove''), Anna Clariana (Illustr.), Leabhar Breac, 2017. *Enric Lluch, ''An Phluais'' (''The Cave''), Anna Clariana (Illustr.), Leabhar Breac, 2017. *Enric Lluch, ''Madra Dhaideo'' (''Grandpa's Dog''), Anna Clariana (Illustr.), Leabhar Breac, 2017. *Enric Lluch, ''Fiacail Mháire'' (''Mary's Tooth''), Anna Clariana (Illustr.), Leabhar Breac, 2017. '''''Bruno Heitz''''' Leabhar Breac published a series of 3 Heitz books for small children. Published originally in French, this series of three comic books is about a blind mole named Cáitín Chaoch in Irish (and ''Louisette la taupe'' in French).<ref>{{Cite web|url=https://leabharbreac.com/en/product-category/bruno-heitz-en/|title=Bruno Heitz Archives|website=Leabhar Breac|language=en-US|access-date=2025-10-02}}</ref> Ó Scolaí translated these: *Bruno Heitz (author and illustr.), ''Práinneach'' (''Urgent''), Leabhar Breac, 2020 *Bruno Heitz (author and illustr.), ''Preab san Aer'' (''Bounce in the Air''), Leabhar Breac, 2020. '''''Books for Toddlers''''' Leabhar Breac has published 14 books written by French author Orianne Lallemand's and illustrated by Eleonore Thuillier, about Lallemmand's popular character Loup, Wolf. These are translated by Ó Scolaí: *Orianne Lallemand, ''An Mac Tire a Raibh Faitios an Domhain Air'' (trans. of ''The Son Who Saw the World in His Eyes''), Eleonore Thuillier  Illustr.), Leabhar Breac, 2018. *Orianne Lallemand, ''Macan agus an Goban'' (trans. of ''Macan and the Goblin''), Eleonore Thuillier (Illustr.), Leabhar Breac, 2018. * Orianne Lallemand, ''A Mac Tíre a Chuaigh go Tóin na Farraige'' (trans. of ''The Wolf Who Went to the Bottom of the Sea''), Éléanore Thuillier  (Illustr.), Leabhar Breac, 2019. '''''Board Books (for babies)''''' J. C. (Joan Carles) Girbés Aparisi is a Catalan author and editor. These books were written in Catalan and translated by Ó Scolai. *J. C. Girbés, ''An Phicnic'' (''The Picnic''), Silvia Ortega (Illustr.), Leabhar Breac, 2013. * J. C. Girbés, ''An Chóisir'' (''The Party''), Silvia Ortega (Illustr.), Leabhar Breac, 2013. *J. C. Girbés, ''Lá Mór Fada'' (''A Long Day''), Silvia Ortega (Illustr.), Leabhar Breac, 2014. *J. C. Girbés, ''Tabhair Leat do Leabhar'' (''Bring Your Book''), Silvia Ortega (Illustr.), Leabhar Breac, 2014. ==== Gradam Réics Carló ==== The Réics Carló prize is awarded for the best book in the Irish language for young readers. It is named for one of the characters of 20th-century writer [[wikipedia:Cathal_Ó_Sándair|Cathal Ó Sándair (Charles Saunders)]]. * ''An Bradán Feasa'' was “shortlisted for the Réics Carlo award 2010.”<ref name=":9" /> == References == {{reflist}} 4vgj4ywjij6wnzzgvbgob6rxpxrprqp 2823748 2823747 2026-08-20T21:48:53Z Scogdill 1331941 /* 1870s dress style */ 2823748 wikitext text/x-wiki {{Short description|Dress worn by Queen Victoria at her wedding to Prince Albert in 1840}} = Sandbox = Page to draft revisions for Wikipedia articles. For Gwladys Robinson, see Gwladys Lowther Robinson, [[Social Victorians/People/Ripon|Marchioness of Ripon]] and, earlier, [[Social Victorians/People/Lowther|Countess of Lonsdale]] ==References== {{reflist|2}} [[Category:1840 works]] [[Category:Royal wedding dresses|Victoria Queen]] [[Category:1840s fashion]] [[Category:British royal attire]] [[Category:Dresses in the Royal Collection of the United Kingdom|Victoria, Wedding]] [[Category:Diamond Jubilee of Queen Victoria]] = Victorian fashion = '''Victorian fashion''' consists of the various fashions and trends in [[Culture of the United Kingdom|British culture]] that emerged and developed in the [[United Kingdom of Great Britain and Ireland|United Kingdom]] and the [[British Empire]] throughout the [[Victorian era]], roughly from the 1830s through the 1890s. The period saw many changes in fashion, including changes in styles, fashion technology and the methods of distribution. Various movements in architecture, literature, and the [[decorative arts|decorative]] and [[visual arts]] as well as a changing perception of [[gender roles]] also influenced fashion. Under [[Queen Victoria]]'s reign, England enjoyed a period of growth along with technological advancement. [[Mass production]] of sewing machines in the 1850s as well as the advent of synthetic dyes introduced major changes in fashion.<ref name=":3">{{Cite book|title=The Culture of Fashion|last=Breward|first=Christopher|publisher=Manchester University Press|year=1995|pages=145–180}}</ref> Clothing could be made more quickly and cheaply. Fashion made more extreme and more rapid changes than it had in prior centuries. Advancement in printing and proliferation of fashion magazines allowed the masses to participate in the evolving trends of high fashion, opening the market of mass consumption and advertising. By 1905, clothing was increasingly factory made and often sold in large, fixed-price department stores, spurring an age of consumerism with the rising middle classes, who benefited from the [[Industrial Revolution|industrial revolution]].<ref name=":3" /> ==Women's fashions== [[File:Fashions.jpg|thumb|upright|Illustration depicting fashions throughout the 19th century]]During the [[Victorian era|Victorian Era]], women generally inhabited the private, domestic sphere.<ref>{{Cite web|url=https://www.bl.uk/romantics-and-victorians/articles/gender-roles-in-the-19th-century|title=Gender roles in the 19th century|website=The British Library|access-date=2016-10-21|archive-date=8 July 2022|archive-url=https://web.archive.org/web/20220708075142/https://www.bl.uk/romantics-and-victorians/articles/gender-roles-in-the-19th-century|url-status=dead}}</ref> Unlike in earlier centuries when women labored with their husbands and brothers or worked in family businesses, during the nineteenth century, gender roles became more rigidly defined. Farm labourers was no longer in such a high demand after the [[Industrial Revolution]], and women were more likely to perform domestic work or, if married, give up paid work entirely. Dress reflected these new lifestyles, and was, for the middle and upper classes, less utilitarian.<p> Clothes were seen as an expression of women's place in society<ref>{{Cite book|title=Victorian and Edwardian Fashion - A Photographic Survey|last=Gernsheim|first=Alison|publisher=Dover Publications Inc.|year=1963|location=New York|pages=26}}</ref> and were differentiated by [[social class]]. Most women wore a [[corset]] over a [[chemise]], followed by a gown or [[skirt]] paired with a [[bodice]], [[blouse]], or [[chemisette]]. The shape of the skirt would be supported by layers of petticoats or, later in the period, structured support such as cage crinolines or bustles. The clothing of [[Upper class|upper-class women]], who generally did not do paid labor, was often elaborately decorated with more layers and [[Trim (sewing)|trims]]. [[Middle class|Middle-class women]] wore less complex dress styles with less expensive trim. [[Working class|Working-class]] clothing was simpler still, with less expensive fabric, fewer layers still and little trim. Including the undergarments, the amount of fabric in women's clothing made it much heavier and the construction made it much more restrictive than ours, especially in the waist (due to the boning in the corset) and the shoulders (due to the popularity of dropped shoulder seams). The amount, quality and type of fabric were displays of wealth and status.<p> Throughout the 19th century, journalism targeting women increased enormously and addressed an increasingly more class-diverse audience. According to the ''Dictionary of Nineteenth-Century Journalism'',<blockquote><p> The closely allied fashion and women's journals can be divided into three phases: titles such as the ''Lady's Magazine'' continued eighteenth-century models, addressing readers as "ladies" and catering to a leisured, fashionable elite; a more domesticated format by the 1840s, targeting middle-class women with instructive and entertaining content including dressmaking and etiquette articles ...; finally, from the 1870s, a livelier, more engaging style of fashion reporting influenced by the New Journalism was integrated with an increased amount of imagery, including better quality fashion plates ....<ref>{{Cite book|title=Dictionary of Nineteenth-Century Journalism In Great Britain and Ireland|last=Beetham|first=Margaret Rachel|last2=A|first2=R|publisher=Academia Press and the British Library|year=2009|editor-last=Brake|editor-first=Laurel, and Marysa Demoor|location=Gent|pages=215a–c|chapter=Fashion Journals}}</ref></blockquote>By the end of the century, women's periodicals were including patterns for dressmaking in their pages, reflecting the presence of middle- and working-class readers as well as technological change like sewing machines for home use and mass-produced fabrics and trim.[[File:1837 Dress.jpg|alt=This dress features a low waistline, and the bodice is worn over the hips to further emphasise the silhouette|thumb|upright|An undressed woman In 1837, featuring a fashionable hairstyle, busked corset, and layers of petticoats.]]It is important not to oversimplify the fashion of the Victorian age. The rate of change in fashion accelerated in the 19th century to the point that styles were distinctly different from one decade to the next (see "When Was That Dress in Fashion?", above right). The styles of Elizabethan England, in contrast, changed much less extremely over the course of a century. The most important characteristics for the analysis of 19th-century fashion include silhouette or line, corsets or stays, the neckline and the sleeves. The silhouette in particular but also the color, the variety of available fabrics and the distribution of information and opinion about fashion were the result of [[Social Victorians/People/Gwladys Robinson#Technological advancement|technological changes]] made throughout the century, but centering in the 1850s.[[File:The Engageants sleeves.jpg|thumb|Engageants, worn to fill open sleeves, were made of light fabrics like lace, linen, lawn or cambric.]] * '''Silhouette''': Silhouette changed over time supported by the evolution of the foundation garments. In fact the line or silhouette of garments changed about every ten years. Just as outer clothing changed, foundation garments were also modified to give the wearer a different silhouette. Over the course of the century most Europeans and some in their colonies wore the same kinds of undergarments and similar outer garments. For example, wide skirts were supported by layers of petticoats that used woven horsehair to stiffen them.<ref>{{Cite web |title=Corsets, crinolines and bustles: fashionable Victorian underwear · V&A |url=https://www.vam.ac.uk/articles/corsets-crinolines-and-bustles-fashionable-victorian-underwear |access-date=2025-10-27 |website=Victoria and Albert Museum |language=en}}</ref> By 1856 the [[Crinoline|cage crinoline]] (a domed structure using steel bands and wires) replaced the petticoats, making the skirts lighter in weight and easier to walk in. The line of the outer garments was influenced by how full the skirt was, how small the waist was and its location relative to the natural waistline, how the sleeves were shaped, and how deep the neckline went. * '''Corsets''': [[Corset]]s or stays were ubiquitous, providing adjustable bust and posture support, helping to shape the body into the fashionable silhouette and preventing horizontal creasing in the bodice. Foundation garments were constantly evolving throughout the century. Over the course of the century, almost all women and some men wore corsets. After the late 1850s, an individual could lace a corset without help.<ref name=":24">{{Cite book|title=Victorian Fashions for Women|last=Kay|first=Fiona|last2=Storey|first2=Neil R.|publisher=Pen & Sword History|year=2022|isbn=978 1 39900 416 9|location=Yorkshire and Philadelphia|pages=30-31}}</ref> Most corsets were constructed with a busk, "(a flat length of whalebone, wood or steel) inserted in a channel down the centre to smooth out the front of the dress."<ref>{{Cite book|title=Victorian Fashions for Women|last=Kay|first=Fiona|publisher=Storey|year=Neil R.|isbn=978 1 39900 416 9|location=Yorkshire and Philadelphia|pages=13}}</ref> The drawing of an undressed woman (above right) shows a self-laced corset with what may be a split busk. * '''Neckline''': Necklines changed over the course of the century as bodices and sleeves evolved. The less formal daywear had a higher neckline, regardless of class and decade. For formal wear, which varied widely by class and kind of event, the neckline was often lower and off the shoulder and finished with a [[Collar (clothing)|bertha]] (lace collar or flounce) or multiple bands of fabric pleats. This [[décolletage|décolleté evening style]] popularized shawls or [[cape]]lets and required a [[Corsets|corset]] without shoulder straps. The fashion was for dressmakers to produce two bodices with each skirt, one closed décolletage for day and one décolleté for evening. * '''Sleeves''': Over the course of the century, styles in sleeves changed radically and more than one sleeve style was fashionable at the same time. Some of the most popular styles included gigot, pagoda, ''engageants'' (see right), bishop and leg-of-mutton sleeves. The changes were in the [[armscye]], the wrist treatment, and the fullness at the shoulder, elbow and wrist. For example, as [[crinoline]]s began to appear in the 1850s, sleeves were shaped like large bells known as pagoda sleeves. [[Engageante]]s, or false sleeves, were stitched inside full or open sleeves like pagoda sleeves. They were easy to remove, launder and restitch into position. Even though the changes in fashion over the century were sometimes rapid and extreme, they were also evolutionary.[[File:Dress - MET 1971.47.3a–e.jpg|thumb|English day dress, c. 1836, with bow details and puffed sleeves]] === 1830s dress style === [[File:Princess Victoria and Dash by George Hayter.jpg|alt=Old portrait of a teenage girl in a white formal dress, with a dog|thumb|Princess Victoria and her dog Dash, 1833|left]]During the beginning of Queen Victoria's reign in 1837, the fashionable silhouette was an hourglass shape with wide shoulders, emphasized by puffed [[gigot sleeves]], a full skirt, and a slim waist. Corsets were extended over the abdomen and down towards the hips, and worn with a busk.<ref name=":0">{{Cite book|title=From Queen to Empress - Victorian Dress 1837-1877|last=Goldthorpe|first=Caroline|publisher=The Metropolitan Museum of Art|year=1988|location=New York|pages=23–24}}</ref> A chemise was worn under the corset and cut relatively low in the neck so that it could not be seen. Over the corset was a tight-fitting bodice featuring a high, straight waistline. Under the ankle-length skirt were layers of petticoats<ref name=":0" /> stiffened with horsehair. (Skirts would not be extremely full for another two decades.) To contrast with the narrow waist, necklines were low and wide. Queen Victoria's 1833 white dress (left) shows an off-the-shoulder neckline, a higher waist and an ankle-length skirt held out by horsehair. The c. 1836 yellow day dress (right) shows gigot sleeves, a higher neckline and a skirt held out by petticoats. Always a mark of wealth and status, Princess Victoria's white dress shows that she is formally dressed, perhaps for court, although the pose itself suggests some informality as well. === 1840s dress style === The 1840s saw an increase in domestic magazines targeting women, along with new varieties in the weave of ready-made fabrics as well as new and much more vibrant colors because of the invention of aniline dyes. And the industrial revolution supplied women with more varieties of color and weave in ready-made fabrics. Cotton replaced silk as a basic fabric, especially among middle-class women because silk was expensive, limiting who could afford it. The elements of fashion changed rapidly during this transitional decade.[[File:Magasin för konst, nyheter och moder 1844, illustration nr 8.jpg|thumb|1844 [[fashion plate]] depicting fashionable clothing for men and women, including illustrations of a [[glove]], a fanchon, and [[Bonnet (headgear)|bonnets]]]]At the beginning of the 1840s, skirts began to widen and become dome shaped (because the skirt pieces changed from rectangles to gores, which are wider at the bottom). The waistline lowered with a point formed at the bottom of both the bodice and corset, which gave a rather rigid look to the silhouette. During this decade, the amount of trim decreased in general, although trim was still plentiful. In addition to the flowers, feathers, and ribbons many of the decorations on the dress were made of the fabric of the dress (tucks and pleats, flounces, ruffles). At the end of the decades waists rose to the natural waistline.[[File:Woman's_Dress_LACMA_M.2007.211.744_(1_of_7).jpg|left|thumb|English silk day dress of the second half of the 1840s, with dropped shoulder seams, tight sleeves, and a pointed waist.]]Although corsets narrowed the bodices and gave them a point in the early 1840s, by the end of the decade, they returned to the natural waistline. Corsets lost their straps by the end of the decade.  Busks in the front of the corset were split by Jean Julien Joselin in 1829,<ref name=":24" /> (75 [of 298]) but the corset wouldn’t stay closed until 1848 when Joseph Cooper patented the "slot and stud" which is still in use today.<ref name=":24" /> (75 [of 298]) Necklines remained wide with further use of lace berthas to frame the upper body. At the end of the decade, necklines were raised and remained high. Dresses were stiffer due to boning in the bodice as well as the corset. Skirts lengthened, while in 1847 widths increased with the introduction of the [http://3.bp.blogspot.com/-bOuPyjWzwT8/TuKx-x1R12I/AAAAAAAAAF0/oRs6AyGH0gw/s1600/CI53.51.15_B1870Amer.Horsehair.jpg horsehair crinoline], which was stiffened with horsehair and starch. The petticoats were numerous and became bulky and heavy and sometimes entangled the feet. Petticoats had another disadvantage: the number of waistbands increased with each additional petticoat. Skirts often had one or two flounces at the bottom that increased the look of fullness (see, for example, the 1844 fashion plate, right). To achieve the narrow waist, skirts were attached to bodices using very tight organ [[pleat]]s secured at each fold.<ref name=":1">{{Cite book |last=Goldthorpe |first=Caroline |title=From Queen to Empress - Victorian Dress 1837-1877 |publisher=The Metropolitan Museum of Art |year=1988 |location=New York |pages=32}}</ref> . Sleeves narrowed with smaller decorative additions (see, for example, the English silk day dress, left). They eventually widened at the wrists into open pagoda-type sleeves requiring engageants to cover the forearms. Shawls were used to convert a simple dress into a more formal outfit. The popularity of shawls grew because of the very soft and beautifully dyed and woven cashmere shawls from India with a paisley design (after the Scottish town that manufactured shawls).<ref name=":24" /> (48 [of 298]) Head coverings were ''de regeur'', dominated by poke bonnets.<ref name=":24" /> (51 [of 298]) (The mannequin in the English silk day dress, above left, is wearing a poke bonnet.) Cosmetics became more popular, with instructions The Handbook of the Toilette (anonymous, many editions beginning in 1839. Unfortunately many contained toxic elements like calcium oxide (or quicklime) found hair dye that was recommended to stay in the hair for 3 to 8 hours.<ref name=":24" /> (47 [of 298]) By the end of the 1840s skirts were more dome shaped, necklines were higher and wider and sleeves broadened at the bottom. === 1850s dress style === The 1850s saw revolutionary [[Social Victorians/People/Gwladys Robinson#Technological advancement|changes in technologies]] affecting the manufacture and consumption of clothing, especially * the mass production of fabrics * the invention of synthetic dyes * the manufacture of inexpensive, flexible and lightweight steel * the invention of a sewing machine that could be used in the home * the spread of fashion journalism and journalism for women According to the ''Dictionary of Nineteenth-Century Journalism'', "The 1850s and 1860s saw the eclipse of the older ladies' journals [that began in the 18th century and targeted upper-class women] and the emergence of the magazine for middle-class ... women."<ref>{{Cite book|title=Dictionary of Nineteenth-Century Journalism In Great Britain and Ireland.|last=Beetham|first=Margaret Rachel|publisher=Academia Press and the British Library|year=2009|editor-last=Brake|editor-first=Laurel, and Marysa Demoor|location=Gent|pages=683–684|chapter=Women's Periodicals}}</ref> (684) Nine fashion magazines were being published in London by 1850 and fourteen by 1859 as part of the burgeoning collection of magazines for women, both domestic magazines aimed at middle-class women and journalism focused mostly on fashion.<ref name=":24" /> (63 [of 298]) The journalism aimed at middle-class women introduced haute couture, making the styles, names of couturiers and fashion houses familiar to them for the first time. These technological changes were revolutionary because of the impact they had on fashion over the course of the rest of the century. Their impact on fashion arises largely because most women were taught a wide range of seamstress skills and, due to reforms in education over the century, more women could read.[[File:Ensemble_MET_DT6845.jpg|thumb|A day ensemble c. 1855, featuring tiers of ruffles and pagoda style sleeves.]] ==== Silhouette ==== The 1850s are considered a transitional decade in 19th-century fashion because little changed in the silhouette and appearance of clothing, but technological changes would make increasingly important structural differences in what was available for people to wear. Skirts widened with the disappearance of the many layers of petticoats but did not change their basic shape. Beyond the silhouette, the design elements of the dress (like sleeves, neckline, or skirt) were barely changed as they evolved from the 1840s to the 1860s. While the silhouette and elements of design did not change significantly, the effect of the technological changes related to the manufacture and consumption of clothing was to give individual (and especially middle-class women) more agency over how their dresses got made and who made them, what fabrics their dresses were made of, how broad a range of options they could choose from and how easy it was to move in their dresses. The number of flounces and ruffles on the skirt increased, making the skirt look wider (see the c. 1855 day ensemble, right). ==== Neckline ==== [[File:1850's Evening Dress.jpg|thumb|1850s evening dress with a bertha|left]] With trim and a front closure in the corset and the bodice, the bodice emphasized a distinct V-shape. Necklines of day dresses were sometimes cut into a V-shape, causing a need to cover the bust area with a chemisette. For evening, a wide, low neckline was popular, often with a [[Collar (clothing)|bertha]] (see the 1850s even dress with a bertha, left).<ref name="h608">{{cite book |last=Arnold |first=Janet |title=Patterns of fashion. 2: Englishwomen's dresses and their construction: 1860 - 1940 |date=1993 |publisher=MacMillan |isbn=978-0-89676-027-1 |publication-place=London |page=}}</ref> ==== Sleeves ==== Pagoda sleeves and under sleeves (''engageants'') continued to be popular for most of the decade. ==== Foundations ==== [[File:1856 Cage Crinoline.jpg|alt=1st patented cage crinoline.Fullness of the skirt is even further emphasised.|thumb|1850s fashionable silhouette and the cage crinoline needed to support it.]] In 1856, the invention of the first [[Crinoline|cage crinoline]] allowed for even wider skirts. The cage crinoline was constructed by joining thin metal strips together with wires to form a circular cage-like structure that could support a very wide skirt (see 1950s silhouette and cage crinoline, right). Although often ridiculed by journalists and cartoonists of the time as the crinoline swelled in size, this innovation freed women from the heavy weight of petticoats.<ref name=":4">{{Cite book |last=Steele |first=Valerie |url=https://archive.org/details/fashioneroticism0000stee |title=Victorian Fashion. Fashion and Eroticism: Ideals of Feminine Beauty from the Victorian Era to the Jazz Age |publisher=Oxford University Press |year=1985 |isbn=978-0-19-503530-8 |pages=[https://archive.org/details/fashioneroticism0000stee/page/51 51]–84 |url-access=registration}}</ref> For a description of the [[Social Victorians/People/Gwladys Robinson#Technological advancement|technological advancement]] that made cage crinolines possible, see below.) Not visible on the outside garment, the cage crinoline was the foundation for the huge dome-shaped skirts that dominated the decade. It was safer and easier to walk in a cage because the hoops held the skirt away from the feet and legs of the wearer. Without the innumerable petticoats more women began to wear drawers or "pantalettes" for modesty and warmth. The dome shape made possibly by the cage foundation changed the way skirts were cut. Instead of rectangles, gores were cut with one end of the skirt piece wider than the other end,<ref name="w586">{{cite book |last=Arnold |first=Janet |title=Patterns of fashion. 2: Englishwomen's dresses and their construction: 1860 - 1940 |date=1993 |publisher=MacMillan |isbn=0-333-13607-1 |publication-place=London |page=}}</ref> preventing bulkiness at the waist from gathered fabric and created a skirt bottom much wider than the top. Bloomers, designed by American Amelia Jenks Bloomer,  introduced bifurcated garments for women, essentially trousers or pants with a seam between the legs. Even pantalettes had no seam between the legs; it was simply left open. This experiment failed and women didn’t wear pants until the 20th century. The 1850s saw two other developments that permanently changed the clothing available to Victorian women (and men). Created in 1856, the first synthetic dyes were much more vivid and vibrant than natural dyes and resisted fading.<ref name=":24" /> (92 [of 298]) Because Victorian photography was black and white, we do not typically see the gaudy and saturated colours that many Victorians loved.<ref name=":3" /> Also, although sewing machines had already been invented, changing the accessibility and value of individual articles of clothing, it was the invention of and widespread sale of "lightweight domestic machines" for home sewing that affected large numbers of women.<ref name=":24" /> (91 [of 298]) Cage crinolines remained popular for perhaps 5 years among the fashion forward and perhaps 10 years for the less adventurous.[[File:Woman's_silk_taffeta_dress_c._1865.jpg|thumb|An 1865 English silk morning dress.]] [[File:Mrs_Ellinor_Guthrie_by_Frederic_Leighton.jpg|thumb|English dress, 1864, with simple trim.]] === 1860s dress style === ==== Foundations ==== The cage crenoline reached their greatest width during the 1860s. Photographs show that the fashion-forward Empress Eugénie of France, Empress Elisabeth of Austria and Countess Pauline von Metternich had stopped wearing the very large crinoline cages as early as 1862, but most middle- and upper-class women (including Queen Victoria) wore them for much of the rest of the decade. During the first half of the 1860s, crinolines began decreasing in size at the top, while retaining their volume at the bottom, creating a more pyramidal shape.<ref name=":2">{{Cite book|title=From Queen to Empress - Victorian Dress 1837-1877|last=Goldthorpe|first=Caroline|publisher=The Metropolitan Museum of Art|year=1988|location=New York|pages=}}</ref> (26) Then the fullness began to move to the back while the front became flat and close to the body. As the back fullness increased, skirts sometimes lengthened into trains. (The 1865 English silk dress, above right, shows the flattening of the front at the waist and the development of the train.) In order to emphasize the back, the train was gathered together to form soft folds and [[Drapery|draperies]].<ref>{{Cite book|title=Making Victorian Costumes for Women|last=Audin|first=Heather|publisher=Crowood|year=2015|pages=45}}</ref> This line or silhouette would eventually evolve into a bustle in the next decade. Decoration or trim often appeared only at the bottom of the skirt (see English dress, 1864, below right). Flounces and ruffles diminished as geometric designs in trim gained popularity.<ref name=":24" /> (102 [of 298]) Skirts were also decorated with overskirts of the same fabric or a different shade of the same color. Waistlines were pointed in front below the natural waistline. By mid-century the waist was seated at the natural waistline often with a wide belt and large decorative buckle.   ==== Bodices and Sleeves ==== Bodices often had buttons down the front because both the corset and the bodice opened in the front. Necklines were generally high and rounded. Some dresses were cut without separating the bodice and skirt so it could be buttoned from the neck to the bottom of the skirt. It became popular for dresses to be made as one skirt and two bodices, one for day wear and one for formal wear.<ref name=":0" /> (43) Sleeves narrowed but remained loose on the arms and were wrist length. Sometimes the sleeves were full at the shoulder, but they were not very puffed. ==== General Trends ==== A greater and richer variety of fabrics was available to the always upwardly-aspirational middle class, with silk essential in the dress of wealthy middle- and upper-class women. Dresses were cut and pieced together to accommodate the more active life women had in sports, walking and even riding bicycles. The trends that began in the 1860s continued through the 1870s and into the 1880s; the changes were evolutionary. === 1870s dress style === ==== Silhouette ==== [[File:Black_net_ball_dress_1874.png|thumb|A black net ball dress, 1874]]In 1877, dresses moulded to fit the figure, as increasingly slimmer and more restrictive silhouettes were favored. Although dress styles took on a more natural form, corsetry was still required and the now ''de regueur'' train was often supported with a bustle cage.<ref name=":2" />{{rp|50}} The armscye, for the first time in the Victorian period, moved from a dropped position up to the shoulders and would remain there for the rest of the era. The most famous designer of this conservative, very fitted and restrictive style was British-born Frederick Worth, who designed the “princess” construction for dresses, which we still use today, and who popularized and then “killed,” according to his obituary in ''The Lady’s Treasury'',<ref>“‘Death of the Chief Ruler of the Fashionable World’, The Ladies’ Treasury (1 April 1895), p. 274.” In ''Fashioning the Victorians: A Critical Sourcebook''. Ed., Rebecca N. Mitchell. Dress, Body, Culture Series, gen. ed., Joanne B. Eicher. Bloomsbury Visual Arts, 2018. Pp. 487–491 of 565.</ref> the crinoline cage. The princess construction was named for Alexandra, Princess of Wales, who preferred a lean, tailored style. By 1879 corsets were being built using "princess" seams to support the tailoring of the smooth, straight dresses like the ones designed by Maison Worth. Because Queen Victoria had been in mourning since 1861, the Princess Alexandra was expected to lead in the haute couture of the day. She set a trend for tailored dresses that was quickly picked up by all classes. Unlike the tailored designs, what Maison Worth created was ornate with many decorative elements, including fringe, which was widely used (along with ribbon, braid, ball fringe, ruching, epaulettes, pieces of the same fabric in a lighter or darker shade, pieces of a different-textured fabric like velvet or velveteen, etc.). No single silhouette dominated the 1870s, however, because of the different lines created by the bustle, the overskirt and the layers of the polonaise, or a combination of these three skirt treatments. Foundation garments changed very little, although perhaps the greatest change came in corsets. In 1870 women were wearing corsets that came to just below the waist with a pointed center front. ==== Skirts ==== [[File:Woman's_Polonaise_Dress_LACMA_M.2007.211.777a-f_(1_of_4).jpg|left|thumb|An c. 1875 English polonaise]]The trend for wide skirts slowly disappeared during the 1870s, as women started to prefer a slimmer silhouette. Skirts went from their most extreme width to their most narrow, waists went to a natural level and the backside took the point of interest in the ensemble. The back of the dress became the focal point of the design. The relationship between the various skirt treatments was very complex, in part because skirts became architectural. (The bustle on the 1874 black net ball dress, above right, has been gathered and bunched and would require padding to keep the draping in place. It also has an overskirt.) The skirt began the decade rather flat in front with most of the fabric pulled to the back and pleated. As the skirt evolved, the gathered fabric draped gracefully at the back. In the next fashion the extra fabric was bunched into large poufs below the waist in back. Then a pad supported the extra fabric, and then by the end of the decade a [[tournure]] or bustle kept the elaborate draping of the back of the skirt and train in place. In general, trains were present on every dress, including day dresses, but they were narrower and longer with tiers and drapes. Petticoats, which could be washed separately, kept the longer trains off the ground. [[overskirt|Overskirts]] became extremely popular, often tied up into an apron effect at the front with a [[Polonaise (clothing)|polonaise]] or puffed draperies at the back.<ref name="g4223">{{cite book |last=Cunnington |first=Cecil Willett |title=English Women's Clothing in the Nineteenth Century |date=1990-05-01 |publisher=Courier Corporation |isbn=0-486-26323-1 |publication-place=New York |page=}}</ref> A revival of an 18th-century romanticization of what a milkmaid might have worn, the 1870s polonaise is a garment featuring both an overskirt and bodice often of the same fabric (see c. 1875 English polonaise, left). Over time, the overskirt shortened into a detached [[Basque (clothing)|basque]], resulting in an elongation of the bodice over the hips. (The early 1870s fashion plate, below right, shows an assortment of ways overskirts were worn, including one for a girl.)[[File:1870's Dress.jpg|alt=Dresses featuring the Bustle & Polonaise|thumb|An early 1870s fashion plate]] ==== Neckline ==== Necklines were high, and lines were sleek and fitted. ==== Sleeves ==== Pagoda sleeves began to lose their three-decade-long popularity in 1875,<ref name=":24" />{{rp|102 [of 298]}} but most sleeve treatments were narrow the sleeves and came to the wrist. ==== General Trends ==== An unusual trend occurred during the 1870s in hairstyles, which grew very large with added braids, buns, coils, poufs and strands. The elaborate hairstyles required multiple hair pieces and featured tiny, over-decorated hats fastened almost vertically on the head. Although women had already been supplementing their own hair, these extremely large styles caused enormous demand in the human hair market. () The practice of constructing a dress with one skirt and two bodices (one for day and one for evening wear) continued from the 1860s. === 1880s dress style === [[File:1885 Bustle.jpg|alt=Horizontal protrusion at the back.|thumb|The lobster tail bustle of around 1885.]] The saw the growing popularity of austere, menswear inspired tailoring.<ref name=":4" /> Some credited the change in silhouette to the [[Victorian dress reform]], which consisted of a few movements including the [[Artistic Dress movement|Aesthetic Costume]] Movement and the [[Victorian dress reform|Rational Dress Movement]] in the mid-to-late Victorian Era advocating for a natural silhouette and lightweight underwear, and rejecting [[tightlacing]]. However, these movements did not gain widespread support. Others noted the growth in cycling and tennis as acceptable feminine pursuits that demanded a greater ease of movement in women's clothing.<ref name=":3" /> Still others argued that the growing popularity of tailored semi-masculine suits was simply a fashionable style, and indicated neither advanced views nor the need for practical clothes.<ref name=":4" /> [[File:Edward_Hughes_-_Juliette_Gordon_Low_-_Google_Art_Project.jpg|left|thumb|An 1887 portrait of English evening dress with higher shoulder placement, simple trims, and a V-shaped neckline.]] After a period of slim, train-less skirts with heavy decoration, the bustle made a re-appearance in 1883, and it featured a further exaggerated horizontal protrusion at the back. Due to the additional fullness, drapery moved towards the sides or front panel of the skirt instead. Bodices shortened, now ending above the hips. Skirts were much less full than the last time the bustle was in fashion in the 1870s and instead focused on a slim front with a shelf-like back protrusion. Sleeves of bodices were thinner and tighter, while necklines became higher again, with a high collar being ubiquitous for daytime, a trend that would continue into the 1890s. For the evening, the bertha fell out of favor, replaced by V-shaped necklines or draped styles due to the new higher shoulder.<ref name="g4223"/> Sleeves tightened again during the [[1880s in Western fashion|1880s]] and the armscye moved back up the shoulders.<ref name="y040">{{cite book |last=Severa |first=Joan L. |title=Dressed for the Photographer |date=1995 |publisher=Kent State University Press |isbn=0-87338-512-8 |publication-place=Kent, Ohio |page=}}</ref> === 1890s dress style === [[File:Lady_Beatrice_Pole-Carew.jpg|thumb|English socialite Lady Beatrice Pole-Carew in the mid-1890s, with puffed sleeves.]] By 1890, the crinoline and bustle were fully abandoned, and skirts flared in an A-line. Necklines were high, while sleeves of bodices initially peaked at the shoulders, but increased in size in the middle of the decade to a puffed [[Sleeve|leg-of-mutton]] style.The sleeves grew to a volume rivaling the 1830s and even sometimes required a cushion to retain their fullness. This sleeve style narrowed down towards the end of the decade. Women also adopted the style of the tailored jacket during this period, with menswear influences such as necktie inspired neckwear continuing from the previous decade. == Hats and headwear == [[File:Ford.madox.brown.last.emma.study.jpg|thumb|''Emma Hill'' by [[Ford Madox Brown]] (1853), a woman wearing a later version of the [[poke bonnet]]]] [[File:Hoed,_objectnr_KA_1237.tif|left|thumb|Perched bonnet style of the early 1870s.]] Hats were crucial to a respectable appearance for both men and women. To go bareheaded was simply not proper. The top hat, for example, was standard formal wear for upper- and middle-class men.<ref name=":4" /> For women, the styles of hats changed over time and were designed to match their outfits. During the early Victorian decades, hats were modest in size and design, straw and fabric bonnets being the popular choice. [[Poke bonnet]]s, which had been worn during the late [[Regency period]], had high, small crowns and brims that grew larger until the 1830s, when the face of a woman wearing a poke bonnet could only be seen directly from the front. They had rounded brims, echoing the rounded form of the bell-shaped hoop skirts. Bonnets shrunk at the end of the 1860s and moved to a perched position in the early 1870s as hairstyles grew in scale and intricacy. This led to the popularization of hats, which became the headwear of choice for the remainder of the Victorian era.<ref name="g4223"/> [[File:The_London_and_Paris_ladies'_magazine_(Apr_1885)_03.png|thumb|Flower pot style hat of 1885.]] The 1880s saw a hat inspired by the top hat for women known as the flowerpot hat, and the 1890s saw the popularity of the boater. The hats of the late Victorian era were covered with elaborate creations of silk flowers, ribbons, and above all, exotic plumes; hats sometimes included entire exotic birds that had been stuffed. Many of these plumes came from birds in the Florida everglades, which were nearly made entirely extinct by overhunting. By 1899, early environmentalists like [[Adeline Knapp]] were engaged in efforts to curtail the hunting for plumes. By 1900, more than five million birds a year were being slaughtered, and nearly 95 per cent of Florida's shore birds had been killed by [[Plume hunting|plume hunter]]s.<ref>{{cite web|title=Everglades National Park|url=https://www.pbs.org/nationalparks/parks/everglades/|archive-url=https://web.archive.org/web/20090927085907/http://www.pbs.org/nationalparks/parks/everglades/|url-status=dead|archive-date=27 September 2009|publisher=PBS|access-date=7 November 2011}}</ref> == Shoes == The women's shoes of the early Victorian period were narrow and heelless, in black or white satin. By 1850s and 1860s, they were slightly broader with a low heel and made of leather or cloth. Ankle-length laced or buttoned boots were also popular. From the 1870s to the twentieth century, heels grew higher and toes more pointed. Low-cut pumps were worn for the evening.<ref name=":4" /> == Cosmetics == [[Victorian-era cosmetics]] were typically minimal, as makeup was associated by the middle classes with promiscuity. However, small amounts of pale face powder or powdered blush were more widely used.<ref>{{Cite book |last=Goodman |first=Ruth |title=How to be a Victorian |date=2014 |publisher=Penguin Books |isbn=978-0-670-92136-2 |location=London}}</ref> Some cosmetics contained toxic or caustic ingredients like lead, mercury, ammonia, and arsenic {{Citation needed|date=October 2025}}. Hair color == Men's fashion == [[File:Mens Coats 1872 Fashion Plate.jpg|thumb|upright|Drawing of Victorian men 1870s]] During the [[1840s in fashion|1840s]], men wore tight-fitting, calf length [[frock coat]]s and a [[waistcoat]] or vest. Sleeves were full at the top and waists were tight, creating an hourglass form. Waistcoats were single- or double-breasted, with shawl or notched collars, and might be finished in double points at the lowered waist. For more formal occasions, a cutaway morning coat was worn with light trousers during the daytime, and a dark tail coat and trousers was worn in the evening. Shirts were made of linen or cotton with low collars, occasionally turned down, and were worn with wide [[Cravat (early)|cravat]]s or neck ties. Trousers had fly fronts, and [[breeches]] were used for formal functions and when horseback riding. Men wore [[top hat]]s, with wide brims in sunny weather. During the [[1850s in fashion|1850s]], men started wearing shirts with high upstanding or turnover [[collar (clothing)|collars]] and [[necktie#Four-in-hand|four-in-hand necktie]]s tied in a bow, or tied in a knot with the pointed ends sticking out like "wings". The upper-class continued to wear top hats, and [[bowler hat]]s were worn by the working class. In the [[1860s in fashion|1860s]], men started wearing wider neckties that were tied in a bow or looped into a loose knot and fastened with a stickpin. Frock coats were shortened to knee-length and were worn for business, while the mid-thigh length [[sack coat]] slowly displaced the frock coat for less-formal occasions, with the overall effect of a looser silhouette. Top hats briefly became the very tall "stovepipe" shape, but a variety of other hat shapes were popular. During the [[1870s in fashion|1870s]], three-piece suits grew in popularity along with patterned fabrics for shirts. Neckties were the four-in-hand and, later, the [[Ascot tie]]s. A narrow ribbon tie was an alternative for tropical climates, especially in the Americas. Both frock coats and sack coats became shorter and more form fitting. Flat straw boaters were worn when boating. During the [[1880s in fashion|1880s]], formal evening dress remained a dark tail coat and trousers with a dark waistcoat, a white bow tie, and a shirt with a winged collar. In mid-decade, the dinner jacket or [[tuxedo]], was used in more relaxed formal occasions. The [[Norfolk jacket]] and tweed or woolen breeches were used for rugged outdoor pursuits such as shooting. Knee-length topcoats, often with contrasting velvet or fur collars, and calf-length overcoats were worn in winter. Men's shoes had higher heels and a narrow toe. Starting from the [[1890s in fashion|1890s]], the [[blazer]] was introduced, and was worn for sports, sailing, and other casual activities.<ref>{{cite web|last=Landow|first=George|url=http://www.victorianweb.org/art/costume/90s/2.html|title=Men's informal sporting dress, late 1880s and '90s}}</ref> Throughout much of the Victorian era most men wore fairly short hair. This was often accompanied by various forms of facial hair including moustaches, side-burns, and full beards. A clean-shaven face did not come back into fashion until the end of the 1880s and early 1890s.<ref>{{cite web|url=http://www.victorianweb.org/art/costume/nunn21.html|title=Victorian Men's Fashions, 1850–1900: Hair}}</ref> Distinguishing what men really wore from what was marketed to them in periodicals and advertisements is difficult, as reliable records do not exist.<ref name="shannon597">{{cite journal|last=Shannon|first=Brent|title=Refashioning Men: Fashion, Masculinity, and the Cultivation of the Male Consumer in Britain, 1860–1914|journal=Victorian Studies|year=2004|volume=46|issue=4|pages=597–630|doi=10.1353/vic.2005.0022}}</ref> Influence of Bertie, Albert Edward, Prince of Wales ==Mourning black== {{See also |Mourning stationery}} [[File:The royal children in mourning Mar 1862.jpg|thumb|Victoria's five daughters (Alice, Helena, Beatrice, Victoria and Louise), photographed wearing mourning black beneath a bust of their late father, Prince Albert (1862)]] [[File:Mourning dress MET 50.40.3a-b front CP4.jpg|alt=Black Victorian mourning dress|thumb|Mourning Dress, 1894–95]] In Britain, black is the colour traditionally associated with mourning for the dead. The customs and etiquette expected of men, and especially women, were rigid during much of the Victorian era. The expectations depended on a complex hierarchy of close or distant relationship with the deceased. The closer the relationship, the longer the mourning period and the wearing of black. The wearing of full black was known as First Mourning, which had its own expected attire, including fabrics, and an expected duration of 4 to 18 months. Following the initial period of First Mourning, the mourner would progress to Second Mourning, a transition period of wearing less black, which was followed by Ordinary Mourning, and then Half-mourning. Some of these stages of mourning were shortened or skipped completely if the mourner's relationship to the deceased was more distant. Half-mourning was a transition period when black was replaced by acceptable colours such as lavender and mauve, possibly considered acceptable transition colours because of the tradition of [[Church of England]] (and [[Catholic Church|Catholic]]) clergy wearing lavender or mauve [[Stole (vestment)|stoles]] for funeral services, to represent the [[Passion (Christianity)|Passion of Christ]].<ref>{{cite web|title=The Colors of the Church Year|url=http://fullhomelydivinity.org/articles/colors.htm|publisher=Consortium of Country Churches|access-date=6 November 2011|archive-date=13 November 2011|archive-url=https://web.archive.org/web/20111113075214/http://fullhomelydivinity.org/articles/colors.htm|url-status=dead}}</ref> The mourning dress on the right was worn by Queen Victoria, "it shows the traditional touches of mourning attire, which she wore from the death of her husband, Prince Albert (1819–1861), until her own death."<ref>{{Cite web|url=https://www.metmuseum.org/art/collection/search/155839?&searchField=All&sortBy=Relevance&deptids=8&ft=queen+victoria&offset=0&rpp=20&amp;pos=2|title=Mourning Dress, 1894–95|last=The Metropolitan Museum of Art|date=7 September 2019|website=The Metropolitan Museum of Art|access-date=7 September 2019}}</ref> === Norms for mourning=== ''Manners and Rules of Good Society, or, Solecisms to be Avoided'' (London, Frederick Warne & Co., 1887) gives clear instructions, such as the following:<ref>{{cite book|last=Flanders|first=Judith|title=The Victorian House|year=2003|publisher=Harper Perennial|location=London|isbn=0-00-713189-5|pages=378–83}}</ref> {| class="wikitable" |- ! Relationship to deceased !! First mourning !! Second mourning !! Ordinary mourning !! Half-mourning |- | Wife for husband || 1-year, 1-month; [[bombazine]] fabric covered with [[Crape|crepe]]; [[widow's cap]], [[lawn cuff]]s, collars || 6 months: less crepe || 6 months: no crepe, silk or wool replaces bombazine; in last 3 months jet jewellery and ribbons can be added || 6 months: colours permitted are grey, lavender, mauve, and black-and-grey |- | Daughter for parent || 6 months: black with black or white crepe (for young girls); no linen cuffs and collars; no jewellery for first 2 months || 4 months: less crepe || – || 2 months as above |- | Wife for husband's parents || 18 months in black bombazine with crepe || – || 3 months in black || 3 months as above |- | Parent for son- or daughter-in-law's parent || – Black armband in representation of someone lost || – || 1-month black || – |- | Second wife for parent of a first wife || – || – || 3 months black || – |} The complexity of these etiquette rules extends to specific mourning periods and attire for siblings, step-parents, aunts and uncles distinguished by blood and by marriage, nieces, nephews, first and second cousins, children, infants, and "connections" (who were entitled to ordinary mourning for a period of "1–3 weeks, depending on level of intimacy"). Men were expected to wear mourning black to a lesser extent than women, and for a shorter mourning period. After the mid-19th century, men would wear a black hatband and black suit, but for only half the prescribed period of mourning expected of women. Widowers were expected to mourn for a mere three months, whereas the proper mourning period expected for widows was up to four years.<ref>{{cite book|last=Flanders|first=Judith|title=The Victorian House|year=2003|publisher=Harper Perennial|location=London|isbn=0-00-713189-5|pages=378–9}}</ref> Women who mourned in black for longer periods were accorded great respect in public for their devotion to the departed, the most prominent example being Queen Victoria herself. Women with lesser financial means tried to keep up with the example being set by the middle and upper classes by dyeing their daily dress. Dyers made most of their income during the Victorian period by dyeing clothes black for mourning.<ref>{{cite book|last=Flanders|first=Judith|title=The Victorian House|year=2003|publisher=Harper Perennial|location=London|isbn=0-00-713189-5|page=341}}</ref> == Technological advancement == The technological changes that affected the manufacture and consumption of clothing in the Victorian age included the following: * the mass production of fabrics — for example, "by the early 1850s there were thousands of steam-powered looms churning out millions of miles of fabric every year"  [62] * the invention of aniline dyes, which were much more vibrantly colored and resistant to fading than the natural dyes that had been used. — . Invented by chemist [[William Henry Perkin]] in 1856, the first aniline dye mauveine (or mauve) "wash[ed] the fashionable landscape in a haze of purple."<ref name=":22">{{Cite book|title=The Dress Diary: Secrets from a Victorian Woman's Wardrobe|last=Strasdin|first=Kate|publisher=Pegasus Books|year=2023|location=New York, New York}}</ref> (247) Other intense and, to the Victorians, intensely exciting colors followed, but the new synthetic additions to fabric sometimes included chemicals harmful to their wearers. For example, a "bright-magenta hue was achieved by adding arsenical-based chemicals to existing aniline dyes, brightening the already luminous shades – but these left residues themselves, along with a toxic labour trail in their wake."<ref name=":22" /> (255) Perhaps the most famous of these is arsenic green, used on fabrics, wallpapers, and trim: "The craze for artificial foliage to adorn the heads and dresses of women of fashion in the mid-nineteenth century had seen the proliferation of flower workshops, where young women in their hundreds laboured to produce the lifelike green leaves and blooms that would make a fetching headdress or would trail becomingly across the bodice of a gown. The lushness of the green was achieved by the application of a powder, a pigment that was created by mixing copper and the highly toxic chemical, arsenic trioxide. The physical effects of working with this poisonous compound were horrific. Contemporary medical drawings depict the green hue of the skin and dreadful open lesions on the hands of the maker, whilst the daily gradual ingestion of the powder by the flower girls was eventually fatal."<ref name=":22" /> (255) * the invention of a sewing machine that could be used in the home. Although sewing machines were already in use in the clothing industry, in 1858 Isaac Merritt Singer began to sell "lightweight domestic machines" for home sewing, radically increasing women's control over their own dress.<ref name=":24" /> (91 [of 298]) * the spread of journalism for women and fashion journalism Perhaps not at the same scale as these but as important in 1850s designs was a technology that turned iron into steel, which could then be drawn into fine wires.<ref name=":3" /> Steel was refined to a malleable state so that thin blades could be curved into concentric circles (called hoops) and connected with wires to form the cage. Technological advancements not only influenced the economy but brought a major change in the fashion styles worn by men and women. As the Victorian era was based on the principles of gender, race and class.<ref>{{cite journal|last1=Graham|first1=P|title=The Victorian Era|url=https://archive.org/details/in.ernet.dli.2015.261548|journal=Digital Library of India}}</ref> Much advancement was in favor of the upper class as they were the ones who could afford the latest technology and change their fashion styles accordingly. In 1830s there was introduction of horse hair crinoline that became a symbol of status and wealth as only the upper-class women could wear it. In 1850s there were more fashion technological advancements hence 1850s could rightly be called a revolution in the Victorian fashion industry such as the innovation of artificial cage crinoline that gave women an artificial hourglass silhouette without layers of petticoats, which was lighter and more hygienic.<ref>{{cite book|last1=Shrimpton|first1=J|title=Victorian Fashion|publisher=Bloomsbury Shire Publications}}</ref> Synthetic dyes, such as [[mauveine]] (aniline purple), were introduced in 1856, adding bright colours to garments. In 1855's ''[[Haute couture]]'' was introduced as tailoring became more mainstream in years to follow.<ref>{{cite book|last1=Aspelund|first1=Karl|title=Fashioning Society|publisher=Fairchild Books}}</ref> Charles Frederick Worth, a prominent English designer, became popular amongst the upper class though its city of destiny always is Paris. Haute couture became popular at the same time that sewing machines were invented.<ref name="Haute Couture">{{cite book|last1=Martin|first1=Richard|last2=Koda|first2=Harold|title=Haute Couture|publisher=The Metropolitan Museum of Art}}</ref> Princess [[Eugénie de Montijo|Eugenie]] of France wore the Englishman dressmaker, Charles Frederick Worth's couture and he instantly became famous in France though he had just arrived in Paris a few years ago. In 1855, Queen Victoria and Prince Albert of Britain welcomed [[Napoleon III]] and Eugenie of France to a full state visit to England. Eugenie was considered a fashion icon in France. Queen Victoria, who had been the fashion icon for European high fashion, was inspired by Eugenie's style and the fashions she wore.{{Citation needed|date=October 2025}} Later, Queen Victoria also appointed Charles Frederick Worth as her dress maker and he became a prominent designer amongst the European upper class. Charles Frederick Worth is known as the father of the haute couture as later the concept of labels were also invented in the late 19th century as custom, made to fit tailoring became mainstream.<ref>{{cite book|last1=Saillard|first1=Olivier|last2=Zazzo|first2=Anne|title=Paris Haute Couture|publisher=Skira Flammarion}}</ref> By the 1860s, when made-to-fit tailoring was popular in Europe, crinolines were considered impractical. In the 1870s, women preferred more slimmer silhouettes, hence bodices grew longer and the polonaise, a skirt and bodice made together, was introduced. In 1870s the Cuirass Bodice, a piece of armour that covers the torso and functions like a corset, was invented. Towards the end of Victoria's reign, dresses were flared naturally as crinolines were rejected by middle-class women. Designers such as Charles Frederick Worth were also against them. All these inventions and changes in fashion led to women's liberation as tailored looks improved posture and were more practical.<ref name="Haute Couture"/> dressmakers, couturiers, modistes == Home decor == {{main|Victorian decorative arts}} Home decor started spare, veered into the elaborately draped and decorated style we today regard as Victorian, then embraced the retro-chic of [[William Morris]] as well as pseudo-[[Japonaiserie]]. == Myths and Oversimplifications == === Modesty === {{main|Victorian morality}} {{Original research|section|date=May 2008}} [[File:1868-skirt-lengths-girl-ages-Harpers-Bazar.gif|thumb|upright|"The proper length for little girls' skirts at various ages", from ''[[Harper's Bazaar]]'', showing a 1900 idea of how the hemline should descend towards the ankle as a girl got older]]Many myths and exaggerations about the period persist to the modern day. Examples include the idea of men's clothing is seen as formal and stiff, women's as elaborate and over-done; clothing covered the entire body, and even the glimpse of an ankle was scandalous. Critics contend that [[corset]]s constricted women's bodies and lives. Homes are described as gloomy, dark, cluttered with massive and over-ornate furniture and proliferating [[bric-a-brac]]. Myth has it that even piano legs were scandalous, and covered with tiny [[pantalette]]s. === Tight Lacing === Tight-lacing, which was not possible until the development of the grommet in 1828, was famously controversial in the Victorian age, generating many column inches of profitable newspaper copy, in part because it was (and still is) fetishistic and subversive in that adolescent girls used it as a means of rebellion and upper-working- or lower-middle-class shop girls saw it as a means of upward mobility.<ref name=":21">{{Cite book|title=Fashion and Fetishism: Corsets, Tight-Lacing and Other Forms of Body-sculpture|last=Kunzle|first=David|publisher=History Press|year=2013|isbn=978 0 7524 9545 3|location=Stroud, Gloucestershire|pages=}}</ref> (71 [of 1182]) No evidence exists that tight lacing was widespread or particularly dangerous.<ref name=":21" /> () In truth, men's formal clothing may have been less colourful than it was in the previous century, but brilliant [[waistcoat]]s and [[cummerbund]]s provided a touch of colour, and [[smoking jacket]]s and [[robe|dressing gown]]s were often of rich Oriental [[brocade]]s. This phenomenon was the result of the growing textile manufacturing sector, developing mass production processes, and increasing attempts to market fashion to men.<ref name="shannon597"/> Corsets stressed a woman's sexuality, exaggerating hips and bust by contrast with a tiny waist. Women's [[evening gown]]s bared the shoulders and the tops of the breasts. The [[jersey dress]]es of the 1880s may have covered the body, but the stretchy novel fabric fit the body like a glove.<ref>{{cite book |last=Gernsheim |first=Alison |title=Victorian & Edwardian Fashion: A Photographic Survey |year=1981 |publisher=Dover Publications |location=New York |page=65|edition=New |isbn=0-486-24205-6}}</ref> Home furnishing was not necessarily ornate or overstuffed. However, those who could afford lavish draperies and expensive ornaments, and wanted to display their wealth, would often do so. Since the Victorian era was one of increased social mobility, there were ever more ''[[nouveaux riches]]'' making a rich show. The items used in decoration may also have been darker and heavier than those used today, simply as a matter of practicality. London was noisy and its air was full of [[soot]] from countless coal fires. Hence those who could afford it draped their windows in heavy, sound-muffling curtains, and chose colours that didn't show soot quickly. When all washing was done by hand, curtains were not washed as frequently as they might be today. There is no actual evidence that piano legs were considered scandalous. Pianos and tables were often draped with [[shawl]]s or cloths—but if the shawls hid anything, it was the cheapness of the furniture. There are references to lower-middle-class families covering up their [[pine]] tables rather than show that they couldn't afford [[mahogany]]. The piano leg story seems to have originated in the 1839 book, ''A Diary in America'' written by Captain [[Frederick Marryat]], as a satirical comment on American prissiness.<ref>{{cite book |last1=Marryat |first1=C.B. |title=A Diary in America: With Remarks on Its Institutions |date=1839 |publisher=Longman, Orme, Brown, Green, and Longmans |location=London, England |volume=2 |pages=246–247 |url=https://books.google.com/books?id=2-VEAAAAIAAJ&pg=PA246}} From pp. 246-247: "I was requested by a lady to escort her to a seminary for young ladies, and on being ushered into the reception-room, conceive my astonishment at beholding a square piano-forte with four ''limbs''. However, that the ladies who visited their daughters, might feel in its full force the extreme delicacy of the mistress of the establishment, and her care to preserve in their utmost purity the ideas of the young ladies under her charge, she had dressed all these four limbs in modest little trousers, with frills at the bottom of them!"</ref> Victorian manners may have been as strict as imagined—on the surface. One simply did not speak publicly about sex, childbirth, and such matters, at least in the respectable middle and upper classes. However, as is well known, discretion covered a multitude of sins. Prostitution flourished. Upper-class men and women indulged in [[adultery|adulterous]] liaisons. == Gallery == {{gallery |2=A mid-Victorian interior: ''Hide and Seek'' by [[James Tissot]], c. 1877 Image:Winterhalter Elisabeth.jpg|3=Dress designed by [[Charles Frederick Worth]] for [[Elisabeth of Bavaria|Elisabeth of Austria]] painted by [[Franz Xaver Winterhalter]].|4=File:Frith A Private View detail.jpg|5=[[William Powell Frith]]'s painting of 1883 contrasts women's [[Aesthetic dress]] (left and right) with fashionable attire (center).|6=File:Tissot lilacs 1875.jpg|7=Day dress, c. 1875 [[James Tissot]] painting.|8=File:James Abbot McNeill Whistler 011.jpg|9=[[James McNeill Whistler|Whistler]]'s [[Portrait of Lady Meux]], 1882 Image:Jeanna_Samary-Renoir.png|10=[[Pierre-Auguste Renoir|Renoir]]'s portrait of [[Jeanne Samary]] in an [[evening gown]], 1878|11=File:Melville_-_Queen_Victoria.jpg|12=Portrait by [[Alexander Melville (artist)|Alexander Melville]] of [[Victoria of the United Kingdom|Queen Victoria]], 1845|13=File:Henry Treffry Dunn Rossetti and Dunton at 16 Cheyne Walk.jpg|14=An artistic interior: [[Dante Gabriel Rossetti]] reading to [[Theodore Watts-Dunton]] in the drawing room at No. 16 [[Cheyne Walk]], 1882|15=File:Punch - Masculine beauty retouched1.png|16=Men's swimwear: Cartoon from ''[[Punch (magazine)|Punch]]'' by [[George du Maurier]]}} == See also == * [[Emily Clapham]] * [[Victorian decorative arts]] * [[Victorian dress reform]] * [[Victorian morality]] * [[Victoriana]] * [[Women in the Victorian Era]] * [[Charles Frederick Worth]] === Time periods === * [[1830s in fashion]] * [[1840s in fashion]] * [[1850s in fashion]] * [[1860s in fashion]] * [[1870s in fashion]] * [[1880s in fashion]] * [[1890s in fashion]] === Women's clothing === * [[Corset]] * [[Corset controversy]] * [[Tightlacing]] * [[Bloomers (clothing)|Bloomers]] * [[Bodice]] === Contemporary interpretations === * [[Steampunk]] * [[Neo-Victorian]] * [[Lolita Fashion|Lolita]] == References == {{Reflist}} == Further reading == *{{cite book |author=Phipps, Elena| title= ''From Queen to Empress: Victorian dress 1837-1877'' | location=New York | publisher=The Metropolitan Museum of Art | year=1988 | isbn=0870995340| url= http://libmma.contentdm.oclc.org/cdm/compoundobject/collection/p15324coll10/id/69547/rec/235 | display-authors=etal}} * Sweet, Matthew – ''Inventing the Victorians'', St. Martin's Press, 2001 {{ISBN|0-312-28326-1}} == External links == * [http://www.victorians.co.uk/victorian-fashion Victorian Fashion] {{Webarchive|url=https://web.archive.org/web/20180407223711/http://www.victorians.co.uk/victorian-fashion |date=7 April 2018 }} * [https://www.victorianvoices.net/topics/fashion/index.shtml VictorianVoices.net] – Fashion articles and illustrations from Victorian periodicals; extensive fashion image gallery * [http://www.cracked.com/article_19575_5-ridiculous-sex-myths-from-history-you-probably-believe.html Victorian myths] * [http://www.victorianstation.com/lifestylemenu.htm Victorian fashion, etiquette, and sports] {{Webarchive|url=https://web.archive.org/web/20180103162620/http://www.victorianstation.com/lifestylemenu.htm |date=3 January 2018 }} * [http://www.thesmartset.com/article/article12180701.aspx Background on "A Diary in America"] * [http://www.mccord-museum.qc.ca/en/keys/webtours/VQ_P2_17_EN.html Form and Fashion] — the evolution of women's dress during the 19th century (many photographs) * [http://www.mccord-museum.qc.ca/en/keys/games/jeu2/ Educational Game: Mix and Match] — build a 19th-century dress using a virtual mannequin * {{cite web |publisher= [[Victoria and Albert Museum]] |url= http://www.vam.ac.uk/content/articles/v/victorian-dress-at-v-and-a/ |title= Victorian Dress |work= Fashion, Jewellery & Accessories |date= 14 January 2011 |access-date= 2011-04-03}} *[http://cv.vic.gov.au/stories/creative-life/fashion-detective-fashion-fiction-and-forensics/ Fashion detective: Fashion, Fiction and Forensics in nineteenth century Australian fashion] on Culture Victoria {{Timeline of clothing and fashion|state=collapsed}}{{Victorian era|state=collapsed}} [[Category:Victorian fashion| ]] [[Category:19th-century fashion|*]] [[Category:1900s fashion]] [[Category:History of Western fashion]] [[Category:19th century in the arts]] =From ''Women in the Victorian era''= ===Victorian women's fashion=== {{Multiple issues|{{tone|date=March 2023}} {{more footnotes needed|date=March 2023}}|section=y}}{{Further|Victorian fashion}} The ideal Victorian woman was pure, chaste, refined, and modest. This ideal was supported by etiquette and manners. The etiquette extended to the pretension of never acknowledging the use of undergarments (sometimes generically referred to as "unmentionables"). The discussion of such a topic, it was feared, would gravitate towards unhealthy attention on anatomical details. As one Victorian lady expressed it: "[those] are not things, my dear, that we speak of; indeed, we try not even to think of them", in contrast to current norms.<ref>{{cite book |last=Cunnington |first=C. Willett |title=English Women's Clothing in the Nineteenth Century: A Comprehensive Guide with 1,117 Illustrations |publisher=Dover Publications |year=1990 |isbn=978-0-486-26323-6 |pages=20}}</ref> The pretence of avoiding acknowledgement of anatomical realities met with embarrassing failure on occasion. In 1859, the Hon. Eleanor Stanley wrote about an incident where the [[Louisa Cavendish, Duchess of Devonshire|Duchess of Manchester]] moved too quickly while manoeuvring over a [[stile]], tripping over her large [[hoop skirt]]: {{blockquote|[the Duchess] caught a hoop of her cage in it and went regularly head over heels lighting on her feet with her cage and whole petticoats above, above her head. They say there was never such a thing seen – and the other ladies hardly knew whether to be thankful or not that a part of her undergarments consisted in a pair of scarlet tartan [[knickerbockers (clothing)|knickerbockers]] (the things Charlie shoots in) which were revealed to the view of all the world in general and the [[Aimable Pélissier|Duc de Malakoff]] in particular".<ref>{{cite book|last=Cunnington|first=C. Willett|title=English Women's Clothing in the Nineteenth Century: A Comprehensive Guide with 1,117 Illustrations|year=1990|publisher=Dover Publications|isbn=978-0-486-26323-6|pages=20–1}}</ref>}} However, despite the fact that Victorians considered the mention of women's undergarments in mixed company unacceptable, men's entertainment made great comedic material out of the topic of ladies' [[bloomers (clothing)|bloomers]], including men's magazines and music hall skits.<ref>{{cite book |last=Cunnington |first=C. Willett |title=English Women's Clothing in the Nineteenth Century: A Comprehensive Guide with 1,117 Illustrations |publisher=Dover Publications |year=1990 |isbn=978-0-486-26323-6 |pages=22}}</ref> Victorian women's clothing followed trends that emphasised elaborate dresses, skirts with wide volume created by the use of layered material such as [[crinoline]]s, hoop skirt frames, and heavy fabrics. Because of the impracticality and health impact of the era's fashions, a [[Victorian dress reform|dress reform movement]] began among women. The ideal silhouette of the time demanded a narrow waist, which was accomplished by constricting the abdomen with a laced [[corset]]. While the silhouette was striking, and the dresses themselves were often exquisitely detailed creations, the fashions were cumbersome. At best, they restricted women's movements and at worst, they had a harmful effect on women's health. Physicians turned their attention to the use of corsets and determined that they caused several medical problems: compression of the thorax, restricted breathing, organ displacement, poor circulation, and prolapsed uterus.<ref name="O'Connor"/> Articles advocating the reform of women's clothing by the British National Health Society, the Ladies' Dress Association, and the [[Rational Dress Society]] were reprinted in ''The Canada Lancet'', Canada's medical journal. In 1884, Dr J. Algernon Temple of Toronto even voiced concern that the fashions were having a negative impact on the health of young women from the working classes. He pointed out that a young working-class woman was likely to spend a large part of her earnings on fine hats and shawls, while "her feet are improperly protected, and she wears no flannel petticoat or woollen stockings".<ref name="O'Connor"/> [[File:Bloomers.jpg|thumb|1850s illustration of a woman wearing [[bloomers]]]] [[Florence Pomeroy]], Lady Haberton, was president of the Rational Dress movement in Britain. At a National Health Society exhibition held in 1882, Viscountess Haliburton presented her invention of a "[[divided skirt]]", which was a long skirt that cleared the ground, with separate halves at the bottom made with material attached to the bottom of the skirt. She hoped that her invention would become popular by supporting women's freedom of physical movement, but the British public was not impressed by the invention, perhaps because of the negative "unwomanly" association of the style with the American [[Bloomers]] movement.<ref>{{cite book|last=Murray|first=Janet Horowitz|title=Strong-Minded Women and Other Lost Voices from 19th Century England|year=1982|publisher=Pantheon Books|location=New York|isbn=0-394-71044-4|pages=[https://archive.org/details/strongmindedwome00jane/page/68 68–70]|url=https://archive.org/details/strongmindedwome00jane/page/68}}</ref> [[Amelia Jenks Bloomer]] had encouraged the wearing of visible bloomers by feminists to assert their right to wear comfortable and practical clothing, but it was no more than a passing fashion itself among radical feminists. The movement to reform women's dress would persist and have long-term success, however; by the 1920s, [[Coco Chanel]] was successful at selling a progressive, far less restrictive silhouette that abandoned the corset and raised hemlines. The new silhouette symbolised modernism for trendy young women and became the 20th century standard. Other Paris designers continued reintroducing pants for women and the trend was gradually adopted over the next century. Fashion trends, in one sense, travelled "full circle" over the course of the Victorian era. The popular women's styles during the [[Georgian era]], and at the very beginning of Victoria's reign, emphasized a simple style influenced by flowing gowns worn by women in [[Ancient Greek clothing|Ancient Greece]] and [[Clothing in ancient Rome|Rome]]. The [[Empire waist]] silhouette was replaced by a trend towards ornate styles and an artificial silhouette, with the restrictiveness of women's clothing reaching its low point during the mid-century passion for narrow corseted waists and hoop skirts. The iconic wide-brimmed women's hats of the later Victorian era also followed the trend towards ostentatious display. Hats began the Victorian era as simple [[Bonnet (headgear)|bonnets]]. By the 1880s, milliners were tested by the competition among women to top their outfits with the most creative (and extravagant) hats, designed with expensive materials such as silk flowers and exotic plumes such as ostrich and peacock. As the Victorian era drew to a close, however, fashions were showing indications of a popular backlash against excessive styles. Model, actress and socialite [[Lillie Langtry]] took London by storm in the 1870s, attracting notice for wearing simple black dresses to social events. Combined with her natural beauty, the style appeared dramatic. Fashions followed her example (as well as Queen Victoria's wearing of mourning black later in her reign). According to [[Harold Koda]], the former Curator-in-chief of the [[Costume Institute at The Met|Metropolitan Museum of Art's Costume Institute]],<ref>{{cite web|url=http://www.metmuseum.org/about-the-museum/press-room/exhibitions/2014/death-becomes-her|title=Death Becomes Her: A Century of Mourning Attire : October 21, 2014-February 1, 2015|website=Metmuseuim.org|access-date=7 November 2021}}</ref> "The predominantly black palette of [[mourning]] dramatizes the evolution of period silhouettes and the increasing absorption of fashion ideals into this most codified of etiquettes," said Koda, "The veiled widow could elicit sympathy as well as predatory male advances. As a woman of sexual experience without marital constraints, she was often imagined as a potential threat to the social order." ====Evolution of Victorian women's fashion==== <gallery> File:Fashion plate December 1844.jpg|Ladies' December Fashions (1844). Hand-coloured steel engraving from a women's magazine. File:Thegalleryofhmscalcutta james tissot 1876.jpg|''[[The Gallery of HMS Calcutta]]'' by [[James Tissot]] (1876). [[Bustle]]s were fashionable in the 1870s and 1880s. File:Mrs lillie langtry george frederic watts 1880.jpg|''Mrs. Lillie Langtry'' by [[George Frederic Watts]] (1880). File:Five-women-on-queenslander-steps-r.jpg|Fashionable women in [[Queensland]], Australia around 1900. </gallery> {{Short description|Irish writer (born 1963)}} {{Use Irish English|date=August 2025}} {{Use dmy dates|date=August 2025}} {{Infobox writer | name = Darach Ó Scolaí | image = Darach Ó Scolaí.JPG | alt = Man holding prize-winning book | caption = Ó Scolaí in 2019 | birth_name = Darach Ó Scolaí | birth_date = {{Birth date and age|1963|df=y}} | birth_place = [[County Galway]], The Republic of Ireland | death_date = | death_place = | occupation = Writer, artist, publisher | alma_mater = [[University of Galway]] | years_active = 1998–present | genre = Novel, retelling, translation, play, screenplay, illustrated book for children and adults | other_names = | spouse = | children = 3 | awards = [[Awards and Honors received by Darach Ó Scolaí|Awards and Honors]] | signature = | website = }}[[File:Darach Ó Scolaí.JPG|thumb|Darach Ó Scolaí, holding ''Oileán an Órchiste'' (his translation of Robert Louis Stevenson's ''Treasure Island'')]] == Darach Ó Scolaí == Darach Ó Scolaí (<small>Irish:</small> [/ˈda.rax/ /oː/ /sˠkˠoː/l̪ˠəi/]; born 1963<ref>{{Cite web|url=https://portraidi.ie/en/darach-o-scolai/|title=Darach Ó Scolaí|date=20 October 2017|website=Portráidí (Portraits of Irish-Language Writers)|access-date=1 August 2025}}</ref>) is an Irish author who works in a number of genres, from novels, plays and screenplays to illustrated books for children and adults. He began his literary career in 1998 writing screenplays, stage plays, retellings and translations; he began to publish novels in 2008. Ó Scolaí is widely recognized as a leading figure in contemporary Irish literature, known as “one of the most important Irish language writers of his generation”<ref>{{Cite journal|last=Poirtéir|first=Cathal|date=2022|title=? Suil an Daill: Constant Tensions and Shifting Allegiances|url=https://booksirelandmagazine.com/suil-an-daill-constant-tensions-and-shifting-allegiances/|journal=Books Ireland}}</ref> and "one of the great Irish language novelists [duine d’úrscéalaithe móra na Gaeilge]."<ref name=":17" /> His writing has been called “the high literature of the Irish language.”<ref>Ó Coimín, Maitiú. ''Nós'' 2 February 2018). Qtd. in "Táin Bó Cuailnge." ''Leabhar Breac''. Retrieved 25 August 2025.</ref> Much of his fiction is based on a knowledge of traditional Irish tales and narrative practices as well as Irish history. He specializes in literary and [[wikipedia:Historical_fiction|historical fiction]], or as novelist Alan Titley says, Ó Scolaí’s “peak (for now), or at least his greatest imaginative interest, is the historical novel [tá an chuma air gurb é a bhuaic (go fóill), nó ar a laghad, a mhórspéis samhlaíochta, an t-úrscéal staire].”<ref name=":11">{{Cite journal|last=Titley|first=Alan|date=Fall 2020|title=An Stíl Go Deo!: Soather Dharach Uí Scolaí (The style would be forever!: Worker Darach Ó Scolaí)|url=https://www.jstor.org/stable/27046090|journal=Comhar|volume=80, No. 10|pages=27|via=JSTOR}}</ref> His retellings of old stories and tales from their original Middle and Early-Modern Irish into Modern Irish ([[wikipedia:Irish_language|Gaeilge]]) are respected for their accessibility to students and language learners as well as for their artistry. Ó Scolaí also regularly reviews books and lectures and writes on literature and culture. Beyond his writing, Ó Scolaí is a publisher and has co-produced a number of film, television shows and stage plays. == Life == Ó Scolaí was born in Dublin and raised in the Galway [[wikipedia:Gaeltacht#Galway Gaeltacht|Gaeltacht]] (Irish-speaking) regions of Cois Fharraige on the north shore of Galway Bay, in the Republic of Ireland, where he lives now with his wife and children in Lochán Beag (Indreabhán).<ref name=":7">{{Cite journal|date=30 October 2024|title=Duais don úrscéal liteartha is fearr buaite ag Darach Ó Scolaí ag Oireachtas na Samhna|url=https://tuairisc.ie/duais-don-ursceal-liteartha-is-fearr-buaite-ag-darach-o-scolai-ag-oireachtas-na-samhna/|journal=Tuairisc}}</ref><ref>{{Cite journal|last=Ní Scolaí|first=Aifric|date=2024|title=Darach Ó Scolaí|url=https://www.taiscecf.ie/ealaiontoiri?category=Scr%C3%ADbhneoir|journal=Taisce Chois Fharraige}}</ref> He graduated the [[wikipedia:University_of_Galway|University of Galway]] (then University College Galway) with a B.A. in 1983.<ref>{{Cite web|url=https://www.linkedin.com/in/darach-ó-scolaí-20026920/|title=Darach Ó Scolaí|last=Ó Scolaí|first=Darach|date=August 2025|website=LinkedIn}}</ref> === Writing and Publishing === Ó Scolaí writes in Irish ([[wikipedia:Irish_language|Gaeilge]]), his native language, and lives in an area defined for the predominant presence of Irish as the vernacular language, the language spoken at home. Irish was the language of his parents' home and is the language of children as well. He is fluent in Irish and English and conversant in French. None of his works has been translated into English. ==== Leabhar Breac ==== In 1995 Darach Ó Scolaí and his brother Caomhán Ó Scolaí — a [[wikipedia:Typography|typographer]] and designer — founded the publishing house Leabhar Breac at Indreabhán (Inverin), County Galway. Their father “Séamas Ó Scolaí was an editor at An Gúm and worked on the Irish-English dictionary team [bhí a n-athair Séamas Ó Scolaí ina eagarthóir sa Ghúm agus d’oibrigh sé ar fhoireann an fhoclóra Gaeilge-Béarla].”<ref name=":0">{{Cite web|url=https://leabharbreac.com/en/about-us/|title=About Us|date=2024|website=Leabhar Breac|access-date=1 July 2025}}</ref> Darach Ó Scolaí has been publisher and literary editor at Leabhar Breac since its founding. Named for [[wikipedia:An_Leabhar_Breac|An Leabhar Breac (The Speckled Book)]], Leabhar Breac publishing house has more than 140 books in print.<ref name=":0" /> Leabhar Breac aims to publish Irish-language books that meet “a high literary and artistic standard.”<ref name=":0" /> Besides the content, Leabhar Breac is known for the typically "superb [thar cionn]" quality of the design and production of the "physical book [leabhar fisiciúil]."<ref name=":8">{{Cite journal|last=Ní Mhuilneoir|first=Gráinne|date=30 July 2024|title=‘Bláthnaid’ – leabhar álainn i sraithín álainn faoi mhná|url=https://tuairisc.ie/blathnaid-leabhar-alainn-i-sraithin-alainn-faoi-mhna/|journal=Tuairisc}}</ref> Its books regularly win awards for literary and artistic quality. Leabhar Breac also publishes translations for children and adults from various early versions of Irish as well as from French and English (and has published translations of books for young readers from Spanish, Catalan, and Italian as well). Leabhar Breac prints its books in Ireland. === Stage and Screen === ==== Rosg ==== In 1998 along with Ciarán Ó Cofaigh,<ref name=":1">{{Cite web|url=http://www.rosg.ie/en/about/History_6/|title=About Us: History|date=July 2025|website=Rosg|access-date=1 August 2025}}</ref> Ó Scolaí co-founded the film and television production company [http://www.rosg.ie/en/ Rosg] and was co-director until 2006. Rosg produced Ó ScolaÍ’s films ''Cosa Nite'' (1999), ''An Leabhar'' (2001) and ''Na Cloigne'' (2010). He left Rosg in 2006 to devote his time to other artistic activities. ==== Ealaín ar Oileán ==== In 2004, along with Val Balance, Ó Scolaí co-founded the annual artists' symposium Ealaín ar Oileán (trans., Art on an Island). The Irish-language symposium was held annually in the Áras Éanna arts and cultural center on Inis Oírr ([[wikipedia:Inisheer|Inisheer]], the smallest of the [[wikipedia:Aran_Islands|Aran Islands]]) from 2004 to 2013. Ó Scolaí was its co-director from its founding<ref>{{Cite web|url=https://ga.wikipedia.org/wiki/Darach_Ó_Scolaí.|title=Darach Ó Scolaí|date=3 February 2024|website=Vicipéid|access-date=1 July 2025}}</ref> until 2013. Besides being its co-director, Ó Scolaí has taken part in this conference as an artist<ref>{{Cite journal|date=16 January 2005|title=Darach Ó Scolaí|url=https://web.archive.org/web/20050116163252/http://bliainiris.com/authors/darach_oscolai.html|journal=Bliainiris}}</ref> and writer<ref name=":2">{{Cite web|url=http://ealainaroilean.ie/ealainaroilean.html|title=The Conference|date=7 September 2013|website=Ealaín ar Oileán|archive-url=https://web.archive.org/web/20130907083744/http://ealainaroilean.ie/ealainaroilean.html|archive-date=7 September 2013|access-date=1 August 2025}}</ref>. ==== Salamandar ==== In 2006 Ó Scolaí founded the stage production company Salamandar and directed his own play ''An Braon Aníos''. His plays ''An tSeanbhróg'' (2009) and ''Craos'' (2008) were also produced by Salamandar.<ref name=":19">{{Cite web|url=https://leabharbreac.com/en/product-category/darach-o-scolai/|title=Darach Ó Scolaí|date=2024|website=Leabhar Breac|access-date=1 July 2025}}</ref> == Works == === Novels === * [[wikipedia:An_Cléireach|''An Cléireach'' (trans., ''The Clerk'')]], Leabhar Breac, 2007. The Oireachtas Prize for Literary Fiction, 2007; The Ó Súilleabháin Award (Book of the Year) in 2008, and "named as ‘the best novel since the turn of the Century’ by Comhar."<ref>{{Cite web|url=https://leabharbreac.com/en/shop/fiction/an-cleireach/|title=An Cléireach - Leabhar Breac - Irish language novel|website=Leabhar Breac|language=en-US|access-date=2025-10-24}}</ref> * ''Na Comharthaí'' (trans., ''The Signs''), Leabhar Breac, 2014. * ''Súil an Daill'' (trans., ''The Eye of the Blind''), Leabhar Breac, 2021. The Oireachtas Prize for Literary Fiction, 2019.<ref name=":4">{{Cite web|url=https://leabharbreac.com/en/shop/fiction/suil-an-daill/|title=Súil an Daill|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> * ''Bódléar'', Leabhar Breac, 2024. The Oireachtas Prize for Literary Fiction, 2024<ref name=":7" />; The Ó Súilleabháin Award (Book of the Year) in 2025; featured in the 2025 Listen-Up Irish Summer Challenge for students of the Irish language.<ref>{{Cite news|url=https://connachttribune.ie/novel-approach-helps-people-learn-irish-in-a-creative-way/|title=Novel approach helps people learn Irish in a creative way|last=Murphy|first=Judy|date=3 October 2025|work=Connaught Tribune|access-date=24 October 2025}}</ref> === Retellings, Translations and Editions === The retellings and translations are into modern Irish. * ''Feis Tigh Chonáin'' (trans., ''The Feast of Conán's House''), Leabhar Breac, 2000; a retelling of a 15^th-century tale from the [[wikipedia:Fenian_Cycle|Fenian Cycle]].<ref>{{Cite web|url=https://leabharbreac.com/en/shop/fiction/feis-tigh-chonain/|title=Feis Tigh Chonáin|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> * ''An Ceithearnach Caolriabhach'' (trans., ''The Narrow-Striped Kern''), Leabhar Breac, 2002; a retelling from c. 1500, also illustrated by Darach Ó ScolaÍ.<ref>{{Cite web|url=https://leabharbreac.com/en/shop/fiction/an-ceithearnach-caolriabhach/|title=An Ceithearnach Caolriabhach|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> * ''Táin Bó Cuailnge'' (trans., ''The Cattle Raid of Cooley''), Leabhar Breac, 2017, both a modern edition of an 11th-century epic and an annotated edition.<ref name=":3">{{Cite web|url=https://leabharbreac.com/en/shop/darach-o-scolai/tain-bo-cuailnge-2-2/|title=Táin Bó Cuailnge|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> "''Táin Bó Cuailnge'' won the Aodán Mac Poilín Memorial Prize 2017."<ref name=":19" /> * ''Deirdre'', Leabhar Breac, 2023, a “picture book for adults” with artist Anastasia Melnykova.<ref>{{Cite web|url=https://leabharbreac.com/en/shop/darach-o-scolai/deirdre/|title=Deirdre|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> Part of the [[wikipedia:Ulster_Cycle|Ulster Cycle]], ''Deirdre'' is a retelling of the story of possibly the most widely known Irish figure from the early tales and sagas.<ref>{{Cite book|title=A Dictionary of Celtic Mythology|last=MacKillop|first=James|publisher=Oxford University Press|year=2004|isbn=9780198609674|pages=181}}</ref> * ''Bláthnaid'', Leabhar Breac, 2024, a “picture book for adults” with artist Anastasia Melnykova; “one of the great stories of the [[wikipedia:Ulster_Cycle|Ulster Cycle]].”<ref name=":4" /> * ''Sadhbh,'' Leabhar Breac, 2025, a picture book for adult readers, illustrated by Alé Mercado; a retelling of the medieval tale ''Ceasacht Inghine Ghuile (''trans., ''The Complaint of Guile's Daughter'').<ref name=":5">{{Cite web|url=https://leabharbreac.com/en/tales-of-wonder/|title=Tales of Wonder|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> * ''Eoghan Béal'', Leabhar Breac, 2025, a picture book for adult readers illustrated by Alé Mercado<ref name=":5" />; a retelling of the medieval tale ''[https://ga.wikipedia.org/wiki/Caithr%C3%A9im_Cellaig Cathréim Ceallaigh]'' from ''The Yellow Book of Leacan.''<ref name=":5" /> === For Young Readers === Ó Scolaí has written illustrated books for young readers (8–10 years old) in two series, the Fionn Series and the Scéalta Staire series, and translated a large number of classics and popular books for children of all ages. The number of these written and translated works suggests a commitment to children and their literacy in Irish. The Fionn Series “is a retelling ... of the great legends of the Fianna for the young Irish readers of today.”<ref name=":6">{{Cite web|url=https://leabharbreac.com/en/shop/oige-en/8-9/doiteoir-na-samhna/|title=Dóiteoir na Samhna|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> [[wikipedia:The_Boyhood_Deeds_of_Fionn|Macgnímartha Finn (The Boyhood Deeds of Fionn)]] is a medieval story in the [[wikipedia:Fenian_Cycle|Fenian Cycle]]. * ''An Bradán Feasa'' (trans., ''The Salmon of Knowledge''), Leabhar Breac, 2010, “shortlisted for the Réics Carlo award 2010.”<ref name=":9">{{Cite web|url=https://leabharbreac.com/en/shop/oige-en/8-9/an-bradan-feasa/|title=An Bradán Feasa|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> * ''Dóiteoir na Samhna'' (trans., ''The Halloween Burner''), 2010.<ref name=":6" /> * ''Bodach an Chóta Lachna'' (trans., ''The Churl in the Dun Coat''), 2011.<ref>{{Cite web|url=https://leabharbreac.com/en/shop/oige-en/7-8/bodach-an-chota-lachna/|title=Bodach an Chóta Lachna|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> The Scéalta Staire (Historical Stories) series<ref name=":9" /> * ''Mánas Ó Dónaill'', 2000. * ''Seán Ó Néill'', Leabhar Breac, 2000. * ''Gráinne Mhaol Ní Mháille'', Leabhar Breac, 2003. * ''Tadhg Dall Ó hUiginn'', Leabhar Breac, 2003. ==== Translations ==== * Robert Louis Stevenson, ''Oileán an Órchiste'' (trans. of ''Treasure Island''), Leabhar Breac, 2014.<ref>{{Cite journal|date=2025-06-19|title=Oireachtas na Gaeilge|url=https://en.wikipedia.org/w/index.php?title=Oireachtas_na_Gaeilge&oldid=1296394643|journal=Wikipedia|language=en}}</ref> * Robert Louis Stevenson, ''An Fuadach'' (trans. of ''Kidnapped''), Leabhar Breac, 2016. * Clement Clarke Moore, ''Cuairt San Nioclás'' (trans. of ''A Visit from St. Nicholas'', or "'Twas the Night Before Christmas"), Leabhar Breac, 2022. '''''The Corto Maltese Graphic Novels''''' Written in Italian by Hugo Pratt and translated by Ó Scolaí, both adults and teenagers read this series of Italian adventure graphic novels.<ref>{{Cite journal|date=2025-07-01|title=Corto Maltese|url=https://en.wikipedia.org/w/index.php?title=Corto_Maltese&oldid=1298285365|journal=Wikipedia|language=en}}</ref> Ó Scolaí's '''translation of ''Corto Maltese''''' was listed in 2017 among "The 30 Irish books that Irish people love."<ref>{{Cite journal|last=Ó Murchú|first=Eoin P.|date=09/06/2017|title=Na 30 leabhar Gaeilge is fearr leis na Gaeil [The 30 Irish books that Irish people love]|url=https://nos.ie/cultur/leabhair/an-30-leabhar-gaeilge-is-fearr-leis-na-gaeil/|journal=Nós}}</ref> * Hugo Pratt, ''Corto: Port na Farraige Goirt'', Leabhar Breac, 2013. * Hugo Pratt, ''Corto: The Golden House in Samarkand'', 2014. * Hugo Pratt, ''Corto: Na Liopard-Fhir ó Rufiji'' (trans. of ''Corto: The Leopard Men of Rufiji''), Leabhar Breac, 2014. * Hugo Pratt, ''Corto: In Ainm Dé Uilthrócairigh'' (trans. of ''Corto: In the Name of God All-Merciful''), Leabhar Breac, 2014. * Hugo Pratt, ''Corto: Tóraíocht Eile'' (trans. of ''Corto: Another Quest''), Leabhar Breac, 2014. * Hugo Pratt, ''Corto: Sa tSibéir'' (trans. of ''Corto: In Siberia''), Leabhar Breac, 2016. '''''Other Translations for Children''''' Ó Scolaí has translated into Irish six books from the ''Le Pavillon Noir'' (trans., ''Jolly Roger'') series by Alain Surget; four books from the ''Catalan First Steps'' series by Enric Lluch Girbés and the ''Caitlín & Cormac'' series by Joan Carles; three books from the ''Louisette le Taupe'' series by Bruno Heitz, and three books from the ''Loup'' series by Orianne Lallemand. === Plays and Screenplays === ==== Stage Plays ==== Ó Scolaí was writer and director of the original productions of two plays in the ''Trí Bhraon'' (trans., ''Three Drops'') trilogy; ''Coinneáil Orainn'' was directed by Darach Mac Con Iomaire and staged by An Taibhdhearc. All three plays have been published in book form by Leabhar Breac. * ''Coinneáil Orainn'' (trans., ''We'll Keep Going''), 2005.<ref>{{Cite web|url=https://irishplayography.com/play?playid=32553|title=Coinneáil Orainn|date=2025|website=PlayographyIreland: A Comprehensive Database of New Irish Plays Produced Professionally Since 1904.|access-date=25 August 2025}}</ref> The first play in the ''Trí Bhraon'' (''Three Drops'') trilogy. [[wikipedia:Taibhdhearc_na_Gaillimhe|An Taibhdhearc]], the national Irish-language theatre of Ireland, toured the country in 2005 with ''Coinneáil Orainn''.<ref>{{Cite web|url=https://leabharbreac.com/en/shop/darach-o-scolai/coinneail-orainn/|title=Coinneáil Orainn|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> Walter Macken Prize, 2005; BBC Stewart Parker Award, 2006.<ref>{{Cite web|url=https://irishplayography.com/person/darach-scola|title=Darach Ó Scolaí|date=2025|website=PlayographyIreland: A Comprehensive Database of New Irish Plays Produced Professionally Since 1904.|access-date=25 August 2025}}</ref> * ''Branwen'', 2006, by Darach Ó Scolaí and Ifor ap Glyn, in Irish, Welsh and English, co-produced by Project Arts Centre and Llwyfan Gogledd Cymru, toured the Republic of Ireland and Wales.<ref>{{Cite web|url=https://irishplayography.com/play?playid=32418|title=Branwen|date=2025|website=PlayographyIreland: A Comprehensive Database of New Irish Plays Produced Professionally Since 1904|access-date=25 August 2025}}</ref> * ''An Braon'' Aníos (trans., ''Rising Damp''), 2006, directed by Ó Scolaí.<ref>{{Cite web|url=https://irishplayography.com/play?playid=32461|title=An Braon Aníos|date=2025|website=PlayographyIreland: A Comprehensive Database of New Irish Plays Produced Professionally Since 1904|access-date=25 August 2025}}</ref> The second play in the ''Trí Bhraon'' (''Three Drops'') trilogy. “The Salamandar company toured the country in 2006-07 with this play, and Salamandar also produced a radio version of the play for RTÉ Raidió na Gaeltachta in 2009.”<ref>{{Cite web|url=https://leabharbreac.com/en/shop/darach-o-scolai/an-braon-anios/|title=An Braon Aníos|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> * ''Craos'' (trans., ''Gluttony''), 2008, directed by Ó Scolaí.<ref name=":13">{{Cite web|url=https://irishplayography.com/play?playid=32867|title=Craos|date=2025|website=PlayographyIreland: A Comprehensive Database of New Irish Plays Produced Professionally Since 1904|access-date=25 August 2025}}</ref> The third play in the ''Trí Bhraon'' (''Three Drops'') trilogy, it toured to Cork and Belfast.<ref name=":13" /> A review of the 2008 Salamander performance in the ''Irish Times'' says, “a humorous play which offers plenty to think about, fine acting, and sparklingly witty dialogue.”<ref>{{Cite web|url=https://leabharbreac.com/en/shop/darach-o-scolai/craos-2/|title=Craos|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> * ''A+E'', 2008, by Ríonach Ní Néill and Darach Ó Scolaí, "dance and music drama," co-produced by Ciotóg and Salamandar.<ref>{{Cite web|url=https://irishplayography.com/play?playid=32962|title=A+E|date=2025|website=PlayographyIreland: A Comprehensive Database of New Irish Plays Produced Professionally Since 1904|access-date=25 August 2025}}</ref> * ''An tSeanbhróg'' (trans., ''The Old Shoe''), 2009, produced by Salamander<ref>{{Cite web|url=https://irishplayography.com/play?playid=33042|title=An tSeanbhróg|date=2025|website=PlayographyIreland: A Comprehensive Database of New Irish Plays Produced Professionally Since 1904|access-date=25 August 2025}}</ref> and staged in the Axis Arts Centre, Dublin, and the Letterkenny Arts Centre. * '''In ''Mhuir Fhíondorcha/The Wine-Dark Sea: The Homer Project'', Ó Scolaí's translation of Homer's Cyclops story, performed at the 2019 IMRAM festival'''.<ref>{{Cite news|url=https://www.irishtimes.com/culture/books/imram-a-festival-celebrating-the-irish-language-1.4047610|title=Imram: a festival celebrating the Irish language. Liam Carson reveals the myths and legends appearing in this year’s programme|last=Carson|first=Liam|date=11 October 2019|work=The Irish Times|access-date=15 October 2025}}</ref> ==== Screenplays ==== * ''Cosa Nite'' (trans., ''Washed Feet''), short film, 1998 (dir. Dearbhla Walsh, prod. Ciarán Ó Cofaigh, Rosg); "a prose version of ''Cosa Nite'' was published (Rosg 2000)."<ref name=":9" /> Nominated for an Irish Film and Television Award.<ref>{{Citation|title=Cosa Nite (Short 1998) - Awards - IMDb|url=https://www.imdb.com/title/tt0191917/awards/|accessdate=2025-08-25|language=en-US}}</ref> * ''Na Glúnta'' (trans., ''The Generations''), 2001<ref>{{Cite web|url=https://www.iftn.ie/production/production_companies/production_sub/feature/?act1=record&aid=70&rid=3917&tpl=filmography_dets&only=1&force=1|title=Na Glúnta {{!}} The Irish Film & Television Network|website=www.iftn.ie|access-date=2025-08-25}}</ref>, co-directors Ciarán Ó Cofaigh & Darach Ó Scolaí, prod. Ciarán Ó Cofaigh, Rosg. * ''An Leabhar'' (trans., ''The Book''), short film, 2000, (dir. Robert Quinn, prod. Ciarán Ó Cofaigh, Rosg) Rosg, 2000.<ref>{{Citation|title=An Leabhar|url=https://www.imdb.com/title/tt0963767/|publisher=Bord Scannán na hÉireann / The Irish Film Board, ROSG|accessdate=2025-08-25|first=Robert|last=Quinn|others=Colm O&apos;Maonlai, Peadar O&apos;Treasaigh, Diarmuid Mac an Adhastair}}</ref> * ''Na Cloigne'' [trans., The Heads], 3-episide series, 2010 (dir. Robert Quinn, prod. Ciarán Ó Cofaigh, Rosg), TG4.<ref>{{Cite web|url=https://www.imdb.com/title/tt1607924/|title=Na cloigne|date=2010|website=IMDb|access-date=25 August 2025}}</ref> === Nonfiction === Ó Scolaí's essays and lectures are published and his interviews are broadcast regularly, making for a large body of nonfiction critical and analytical work. Here are a few, almost all published in [https://comhar.ie/iris/scribhneoiri/darach-o-scolai/ Comhar]: * “Ceol Ciúin na nÉagmaise” (trans., “The Silent Music of Absence ['''the Fall?''']”), an essay on the 2014 Nobel Prize winner for literature, [[wikipedia:Patrick_Modiano|Patrick Modiano]], ''Comhar'', December 2014. * The Ó Cadhain Lecture: [https://leachtaiuichadhain.clo.ie/leachtai/2014 “Cuimhne agus Díchuimhne (trans., “Memory & Forgetfulness"]), 2014. * “Rithim agus Réim” ("Rhythm and Register"), a public lecture in the University College Dublin lecture series “Ó Thrácht go Twitter” (trans., "From Talk to Twitter"), 2014. * Review of Pádraig Ó Cíobháin’s ''Dréachta Chrích Fodla'', '''Comhar?, ??'''. * “Na Geilt i mBun an Tí” (trans., "The Madmen in Charge"), a talk at the Merriman Winter School, Comhar April 2012.<ref name=":18">{{Cite web|url=http://darachoscolai.ie/beathaisneis.html|title=Darach Ó Scolaí: Beathaisnéis|website=darachoscolai.ie|access-date=2025-09-26}}</ref> * The EFACIS podcast: Síle Ní Choincheannain talks to Darach Ó Scolaí about the historical novel. == Critical Reception == Ó Scolaí’s style has been called “crisp and elegant, and rich in language while being highly readable,”<ref>{{Cite journal|last=Heussaf|first=Anna|date=Summer 2025|title=Bláthnaid—A tale of love, violence and sorcery retold for readers today|url=https://booksirelandmagazine.com/blathnaid-a-tale-of-love-violence-and-sorcery/|journal=Books Ireland}}</ref> with “an unsurpassed richness and precision of language.”<ref name=":12">{{Cite journal|last=Ó Cróinín|first=Breandán|date=Summer 2025|title=unknown|journal=The Limerick Leader}}</ref> “Whimsical, hilarious, and subtly learned” is how Éilis Ní Dhuibhne described his writing.<ref name=":20" /> === Original Works === Ó Scolaí’s first novel, the 2007 ''An Cléireach'' (''The Clerk'') won two prizes and was described as “one of the great historical novels in the Irish language and among the best books written in the language since the beginning of this century.”<ref name=":12" /> Novelist Alan Titley says, “In ''An Cléireach'' Ó Scolaí creates the Ireland of war in the 17th century more fully than any other Irish writer on the subject of war since ''L’Attaque'' Eoghain Ó Thuairisc around 1798 [In ''An Cléireach'' cruthaíonn Ó Scolaí Éire an chogaidh san 17ú haois níos iomláine ná mar a dhein aon scríbhneoir Gaeilge eile ar ábhar cogaidh ó ''L’Attaque'' Eoghain Uí Thuairisc timpeall ar 1798].”<ref name=":11" />{{rp|25, Col. 1a}} Not all the reviews of this first novel were so positive, however; Proinsias O' Drisceoil says for the Irish Times says,<blockquote>This then is a novel in search of a plot, a story that attempts to attain a significance that eludes it.<ref>{{Cite news|url=https://www.irishtimes.com/news/a-disaffected-clerk-in-the-confederates-1.943070|title=A disaffected clerk in the confederates|last=O' Drisceoil|first=Proinsias|date=5 July 2008|work=The Irish Times|access-date=16 October 2025}}</ref></blockquote> In the ''Oxford Handbook of Modern Irish Fiction'' Pádraig Ó Siadhail analyzes rather than reviews ''An Cléireach'': <blockquote>In ''An Cléireach'', Ó Scolaí revisits the trauma of Cromwellian Ireland. The primary narrative device is once again the first-hand account, in this case by Tadhg Ó Dúbháin, a clerk and quartermaster in the Confederate Army in 1650. We sample the hardships, the friendships, the tensions, the rivalries, and the petty jealousies amongst comrades in arms, including remnants of the Gaelic literary class, as the Confederate soldiers, increasingly a rabble more than a cohesive unit, retreat in advance of Cromwell’s forces. ''An Cléireach'' concludes with the narrator and his family in exile in continental Europe. But along the retreat route, and central to the novel, members of the Confederate army camp, rest up, and tell versions of a story about the keeper of the treasured manuscript "Saltair an Easpaig" (The Bishop’s Psalter). Their versions raise issues about memory construction, the limitations of individual perspectives, personal agendas, and how minor changes in the telling of a story can alter our understanding of history, Thus, ''An Cléireach'' complements ''Fontenoy'' in moving beyond more realistic recreation of a historical event or period to interrogate the notion of history as construct.<ref>{{Cite book|title=The Oxford Handbook of Modern Irish Fiction|last=Ó Siadhail|first=Pádraig|publisher=Oxford University Press|year=2020|isbn=9780198754893|editor-last=Harte|editor-first=Liam|pages=598–99|chapter=Contemporary Irish Fiction}}</ref> </blockquote> Of ''Súil an Daill,'' in ''Nós'', Cathal Seoighe says, "The book deserves a significant place among the collection of high-quality books published in recent years that would make you feel sorry for someone who does not speak Irish [Tá áit shuntasach ag dul don leabhar i measc an chnuasaigh leabhair ar ardchaighdeán a foilsíodh le roinnt blianta anuas a d’fhágfadh trua agat don té atá gan Ghaeilge]."<ref>{{Cite journal|last=Seoighe|first=Cathal|date=09/26/2022|title=‘Dar leathmhagairle an diabhail, is leabhar den scoth é seo!’ ['According to the devil’s half-wit, this is a great book!’]|url=https://nos.ie/cultur/leabhair/dar-leathmhagairle-an-diabhail-is-leabhar-den-scoth-e-seo/|journal=Nós}}</ref> ''Bódléar'', Ó Scolaí's most recent book, is a “beautiful novel. There is magic and craftsmanship in it. A small miracle of a book and it is highly recommended.”<ref>{{Cite web|url=https://leabharbreac.com/bodlear-mioruilt-bheag-de-leabhar/|title=Bódléar: Míorúilt bheag de leabhar (Bódléar: A Small Miracle of a Book)|last=Ní Ghairbhí|first=Róisín|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> Éilis Ní Dhuibhne in the ''Irish Times'' says,<blockquote>what a gem! An affectionately gentle satire of the Irish poetic scene during one creatively fluid 19th-century year, the story focuses on a Maigue poet and schoolteacher who goes on a trip to France and returns with camembert, a cafetiere, ‘Fleurs du Mal’, and a mission to convert the local traditionalists to la modernité. Whimsical, hilarious, and subtly learned, it’s absolutely delightful!<ref name=":20">{{Cite journal|last=Ní Dhuibhne|first=Éilis|date=30 June 2025|title=Éilís Ní Dhuibhne on the best Irish language books of 2025 so far: Including a history of the Gaeltacht Civil Rights Movements, a gem of a novel by Darach Ó Scolaí and Joe McHugh’s entertaining account of learning Irish|url=https://www.irishtimes.com/culture/books/review/2025/06/30/eilis-ni-dhuibhne-on-the-best-irish-language-books-of-2025-so-far/|journal=The Irish Times|pages=22}}</ref></blockquote> === Retellings and Translations === ==== ''Táin Bó Cuailnge'' ==== ''Táin Bó Cuailnge'' [''The Cattle Raid of Cooley''] is a modern edition of an 11th-century epic into modern Irish.<ref name=":3" /> Gearóid Denvir reviewed ''Táin Bó Cuailnge'' for ''Comhar'':<blockquote>Darach Ó Scolaí has ​​achieved a feat in this challenging reworking. He has found a high level of the Irish language to tell his story – as he has done before in his groundbreaking novel An Cléireach (2007, Leabhar Breac) and in his other prose works. This book is a decoration of the language, literature and culture of the Irish language, following the path of the old storytellers and writers and presenting material from the tradition to his own generation according to the understandings of his own time. The book will be a classic that will be of great interest to all readers of the Irish language, both ordinary readers, students, scholars and writers, and there should be a copy in every home in the country. [Tá éacht déanta ag Darach Ó Scolaí san athleagan dúshlánach seo. Tá réim ard den teanga Ghaeilge aimsithe aige lena scéal a inseacht – mar a rinne sé cheana ina úrscéal ceannródaíoch An Cléireach (2007, Leabhar Breac) agus i saothair eile phróis dá chuid. Is maisiú ar an teanga agus ar litríocht agus cultúr na Gaeilge an leabhar seo a leanas conair na seanscéalaithe agus na seanscríobhaithe agus ábhar de chuid an traidisiúin á chur i láthair a ghlúine féin aige de réir thuiscintí a linne féin. Clasaic a bheas sa leabhar a gcuirfidh léitheoirí uilig na Gaeilge, idir ghnáthléitheoirí, mhic léinn, scoláirí agus scríbhneoirí spéis thar na bearta ann, agus ba cheart cóip a bheith i chuile theach sa tír.]<ref name=":15">{{Cite journal|last=Denvir|first=Gearóid|date=April 2018|title=Táin Bó Cuailgne|url=https://comhar.ie/iris/78/4/leirmheas/|journal=Comhar|via=JSTOR}}</ref> </blockquote>Cathal Poirtéir says, "The freshness and richness of Ó Scolaí’s version are a joy …. The author delights us with the linguistic and stylistic richness of the ancient epic in a modern-Irish version that reflects the original’s spirit and language."<ref>{{Cite journal|last=Poirtéir|first=Cathal|date=May/June 2018|title=Leabhair Idir Lámha|url=https://www.jstor.org/stable/26564180|journal=Books Ireland|pages=46–47|via=JSTOR}}</ref>{{rp|47}} Novelist and academic Alan Titley calls Ó Scolaí's "a wonderful gutsy telling" of ''Táin Bó Cuailnge''.<ref>{{Cite news|url=https://www.irishtimes.com/culture/2023/03/11/the-tain-retold-maeve-and-ailills-spat-could-be-out-of-a-soap-opera/|title=The Táin retold: ‘Maeve and Ailill’s spat could be out of a soap opera’|last=Titley|first=Alan|date=11 March 2023|work=The Irish Times|access-date=16 October 2025}}</ref> ==== ''Deirdre'' ==== Marie Whelton, in "Léann Teanga" ("Language Studies"), in the 2024 ''An Reiviú'' says,<blockquote>this version [of ''Deirdre''] by Darach Ó Scolaí succeeds in skillfully capturing and portraying the complexity of gender and power issues in the ‘Deirdre’ tradition [éiríonn leis an leagan seo le Darach Ó Scolaí castacht cheisteanna na hinscne agus na cumhachta i dtraidisiún scéal Dheirdre a ghabháil agus a léiriú go sciliúil]. … There is no doubt that this new version greatly contributes to the legacy of the story and that it revives that legacy thoughtfully and artistically [Níl amhras faoi ach go gcuireann an leagan úr seo go mór le hoidhreacht an scéil agus go ndéanann sé an oidhreacht sin a athbheochan go tuisceanach agus go healaíonta.].<ref name=":16">{{Cite web|url=https://www.tara.tcd.ie/tara8/server/api/core/bitstreams/3c20175a-7631-44b2-8b0f-f454edd712b4/content|title=An Artistic Retelling of Deirdre's Tale and the Defeat of Conor Review of Deirdre or the Ship of Mac Uisnigh by Darach Ó Scolaí [Athinsint Ealaíonta ar Oidhe Dheirdre agus ar Ansmacht Chonchúir Léirmheas ar Deirdre nó Loingeas Mhac Uisnigh le Darach Ó Scolaí]|last=Whelton|first=Marie|date=2024|website=The Review [An Reiviú], Language Studies [Léann Teanga]|access-date=25 September 2025}}</ref></blockquote> === Works for Young Readers === Meadhbh Ní Eadhra said of ''Bodach an Chóta Lachna'' that it was "Beautiful Irish, but easy to understand for young readers."<ref>Ní Eadhra, Meadhbh. In ''Gaelscéal'', qtd. in "Bodach an Chóta Lachna" https://leabharbreac.com/en/shop/oige-en/7-8/bodach-an-chota-lachna/.</ref> == Awards and Honors == Ó Scolaí's works are regularly nominated and make the short list for prizes, an honor in itself, but they are generally not listed here unless they are named as the first-place winner in their category. === Oireachtas Prize === The Oireachtas Prize is the literary prize awarded by [[wikipedia:Oireachtas_na_Gaeilge|Oireachtas na Gaeilge]], the annual arts festival dedicated to Irish language, arts and culture. Darach Ó Scolaí has won the Oireachtas Prize for Literary Fiction three times, once for ''An Cléireach'' (''The Clerk'') in 2007, for ''Súil an Daill'' (''The Eye of the Blind'') in 2021 and for ''Bódléar'' in 2024. * 2007, for ''An Cléireach'' (trans., ''The Clerk'') — “(a special prize commemorating the 400th anniversary of the foundation of Coláiste na nGael in Louvain, awarded under the auspices of the Franciscan Province of Ireland). The prize of €10,000 was the largest prize ever awarded to an Irish language novel [(duais speisialta chomórtha 400 bliain bhunú Choláiste na nGael i Lobháin a bronnadh faoi urraíocht Phroibhinse Phroinsiasach na hÉireann). Ba é an duais €10,000 sin an duais ba mhó a bronnadh riamh ar úrscéal Gaeilge].”<ref name=":18" /> * 2021, for ''Súil an Daill'' (''The Eye of the Blind'') * 2024, for ''Bódléar'' === Ó Shúilleabháin Award, Irish language “Book of the Year” === The first prize of this award includes €5,000 to the publisher and €2,500 to the author of the winning work.<ref name=":10">{{Cite journal|date=15 August 2023|title=20 saothar san iomaíocht do ‘Leabhair Ghaeilge na Bliana 2023’|url=https://tuairisc.ie/20-saothar-san-iomaiocht-do-leabhair-ghaeilge-na-bliana-2023/|journal=Tuairisc}}</ref> * ''An Cléireach'' (''The Clerk'').<ref>{{Cite web|url=http:/www.gaelport.com/uploads/documents/edition19.html|title=Eagrán / Edition 19 - 04 11 2008|date=4/11/2008|website=Internet Archive|archive-url=https://web.archive.org/web/20130525011340/http:/www.gaelport.com/uploads/documents/edition19.html|archive-date=25 May 2013|access-date=25 August 2025}}</ref> * ''Táin Bó Cuailnge'', 2018. * ''Bódléar'', 2025. ==== De Bhaldraithe Award ==== The Gradam de Bhaldraithe is awarded to the best work in translation.<ref name=":10" /> * ''Cuairt San Nioclás,'' a translation of Clement Clarke Moore's ''A Visit from St. Nicholas'', or "'Twas the Night Before Christmas."<ref name=":10" /> ==== Other ==== * Walter Macken Prize, for ''Coinneáil Orainn'' (trans., ''We'll Keep Going''), 2005 * Bháiteir Uí Mhaicín Memorial Award, for ''Coinneáil Orainn'' (trans., ''We'll Keep Going''), 2005<ref>{{Cite news|url=https://www.irishtimes.com/gaeilge/tuarascail/duais-oireachtais-1.501571|title=Oireachtas Prize: Over €50,000 was awarded to writers in the Oireachtas Literary Competitions at an event in Dublin last night. Winners… [Duais Oireachtais: Bronnadh breis agus €50,000 ar scríbhneoirí i gComórtais Liteartha an Oireachtais ar ócáid i mBaile Átha Cliath aréir. Bhuaigh…]|work=5 October 2005|access-date=15 October 2025}}</ref> * BBC Stewart Parker Award, for ''Coinneáil Orainn'' (trans., ''We'll Keep Going''), 2006 * The Aodán Mac Póilín Commemorative Prize, for ''Táin Bó Cuailnge'' (trans., ''The Cattle Raid of Cooley''), 2017 == External Links == * Leabhar Breac website: https://leabharbreac.com/en/ * Leabhar Breac Facebook pages: * Rosg website: [http://www.rosg.ie/en/ <nowiki>http://ww</nowiki>w.rosg.ie/en/] * Art on the Island (Ealaín ar Oileán) website, archived at the Wayback Machine: https://web.archive.org/web/20130601000520/http://ealainaroilean.ie/ 31 March 2012, 1 June 2013 and 8 January 2014 * Darach Ó Scolaí's website Archived 25 September 2015 at the Wayback Machine: https://web.archive.org/web/20150925103456/http://darachoscolai.ie/ * Youtube video of [https://www.youtube.com/watch?v=OlP2AmSBzXc Breandán Ó Cróinin introducing Deirdre at the book launch] in the pub Tigh Mholly (Molly’s House). == Primordial Ooze == * Known for his sensitivity to language and voices. * Finish scanning through JSTOR * Scan through Irish Times, 56 hits * Check Goodreads * Check YouTube (In the spring of 2013, the arts programme Imeall interviewed the author on TG4.) * Check both Wikipedias for pages on the origins of the retold tales (like Deirdre) and link to this article * Propose link from University of Galway page once Darach’s is up * Write Irish National Biography (<nowiki>https://www.dib.ie</nowiki>) to propose an article about Darach once the Wikip article is done? See what they say. * Link to Ó Scolaí from the Wikipedia * Make sure links '''to''' Wikipedia in the actual encyclopedia work right === Not Placed Yet === * "So here are the books that Irish people love the most! [Mar sin seo iad na leabhair is gile leis na Gaeil!]" — "32. An Cléireach – Darach Ó Scolaí (2)" [18 books got 2 votes, and then they're alphabetized by author's last name, so the 32 of 34 doesn't signify the specificity it seems to]<ref name=":14">{{Cite journal|last=Ó Murchú|first=Eoin P.|date=9 June 2017|title=Na 30 leabhar Gaeilge is fearr leis na Gaeil. [The 30 best Irish books for Irish people]|url=https://nos.ie/cultur/leabhair/an-30-leabhar-gaeilge-is-fearr-leis-na-gaeil/|journal=Nós}}</ref> * "Below is a list of those 111 works – a list that shows a great deal of diversity in the reading habits of Irish speakers.Here is a list of those 111 works – a list that shows a great deal of diversity in the reading habits of Irish speakers [Anseo thíos tá liosta den 111 saothar sin – liosta a léiríonn éagsúlacht an-mhór i nósanna léitheoireachta Gaeilgeoirí.Anseo thíos tá liosta den 111 saothar sin – liosta a léiríonn éagsúlacht an-mhór i nósanna léitheoireachta Gaeilgeoirí]." "Corto Maltese – Hugo Pratt (aistrithe ag Darach Ó Scolaí)"<ref name=":14" /> * "Ceann eile de bhuaicphointí na hÉigse a bheidh sa seisiún le Darach Ó Scolaí, duine d’úrscéalaithe móra na Gaeilge, agus duine de chomhbhunaitheoirí teach foilsitheoireachta Leabhar Breac. [Another highlight of the Éigse will be the session with Darach Ó Scolaí, one of the great Irish language novelists, and one of the co-founders of the publishing house Leabhar Breac.]"<ref name=":17">{{Cite journal|last=Nós|date=4 May 2023|title=Éigse na Bruiséile le filleadh i mí na Bealtaine. [Éigse na Bruséile to return in May]|url=https://nos.ie/cultur/eigse-na-bruiseile-le-filleadh-i-mi-na-bealtaine/|journal=Nós}}</ref> === Things Taken Out for Now === “’The play is a comedy about language, lies, bureaucracy and Gaeltacht grants, in the tradition of Myles na Gcopaleen,’ according to Norma-Jean Kenny in the ''Galway Advertizer'', ‘in which the author comments and criticizes the institutions of the Irish language in Ireland without ceasing.’" Supposedly a quotation by Gearóid Denvir reviewing ''Táin Bó Cuailnge'' for ''Comhar'' (but I don't find it in the article): This book has long been needed by Irish language readers and there is no doubt that it will become a classic in time and surpass Thomas Kinsella’s English version. This version remains faithful to the language of the original while at the same time finding an appropriate language in today’s Irish. Ó Scolaí masterfully overcomes the difficulties of the original’s rhetorical difficulties and the versions of the original poetic texts are extremely effective.[supposedly <ref name=":15" />] “The biggest prize ever awarded for a novel in Irish was presented at a special ceremony in the National Concert Hall in Dublin, today (Thursday, 4 October 2007). Darach Ó Scolaí, writer, artist & playwright from Casla, Co. Galway, was awarded €10,000 for his literary novel, ‘An Ardscoil’. This work, under the new title ‘An Cléireach’, will be launched at Oireachtas na Samhna in Westport in November. This is the first novel from his pen, a story set in the late seventeenth century. This competition was sponsored by the Franciscan Province of Ireland.” (archive, Oireachtas na Gaeilge site, 04 October, 2007) ''Súil an Daill'' (trans., ''The Eye of the Blind''), Leabhar Breac, 2021. number 2 in ''Comhar'' literary magazine’s list of best books of 2021. '''{6}.''' *William Shakespeare, ''Romeo agus Juliet'' (trans. of ''Romeo and Juliet''), Leabhar Breac, 2016. *Jonathan Swift, ''Camchuairt Ghuilivéir'' (trans. of ''Gulliver's Travels''), Leabhar Breac, 2016. *Hugo Pratt, ''Corto Maltese'' '''''Flag of Bones (Bratach na gCnámh) Series''''' Leabhar Breac published the Bratach na gCnámh series of books for young readers. Written in French by Alain Surget, illustrated by Annette Marnat and translated by Darach Ó Scolaí, this series uses the history of Caribbean Sea pirates<ref>{{Cite web|url=https://leabharbreac.com/en/product-category/alain-surget/|title=Alain Surget Archives|website=Leabhar Breac|language=en-US|access-date=2025-09-30}}</ref>: *Alain Surget, ''Éalú as Páras'' (''Escape from Paris''), Annette Marnat (Illustr.), Leabhar Breac, 2011. * Alain Surget, ''Oilean na Siorcanna'' (''Shark Island''), Annette Marnat (Illustr.), Leabhar Breac, 2011. * Alain Surget, ''Long na dTaibhsi'' (''Ship of the Ghosts''), Annette Marnat (Illustr.), Leabhar Breac, 2011. * Alain Surget, ''San Ochtapas Dubh'' (''In the Black Octopus''), Annette Marnat (Illustr.), Leabhar Breac, 2013. * Alain Surget, ''San Ionsai ar Veracruz'' (''The Attack on Veracruz''), Annette Marnat (Illustr.), Leabhar Breac, 2013. '''''For "First Readers" (children to 6 years old or so)''''' These books were written originally in Catalan by Spanish author Enric Lluch Girbés and translated into Irish by Ó ScolaÍ: *Enric Lluch, ''Ag Péinteáil an Tí'' (''Painting the House''), Anna Clariana (Illustr.), Leabhar Breac, 2017. *Enric Lluch, ''An Colúr Bacach'' (''The Lazy Dove''), Anna Clariana (Illustr.), Leabhar Breac, 2017. *Enric Lluch, ''An Phluais'' (''The Cave''), Anna Clariana (Illustr.), Leabhar Breac, 2017. *Enric Lluch, ''Madra Dhaideo'' (''Grandpa's Dog''), Anna Clariana (Illustr.), Leabhar Breac, 2017. *Enric Lluch, ''Fiacail Mháire'' (''Mary's Tooth''), Anna Clariana (Illustr.), Leabhar Breac, 2017. '''''Bruno Heitz''''' Leabhar Breac published a series of 3 Heitz books for small children. Published originally in French, this series of three comic books is about a blind mole named Cáitín Chaoch in Irish (and ''Louisette la taupe'' in French).<ref>{{Cite web|url=https://leabharbreac.com/en/product-category/bruno-heitz-en/|title=Bruno Heitz Archives|website=Leabhar Breac|language=en-US|access-date=2025-10-02}}</ref> Ó Scolaí translated these: *Bruno Heitz (author and illustr.), ''Práinneach'' (''Urgent''), Leabhar Breac, 2020 *Bruno Heitz (author and illustr.), ''Preab san Aer'' (''Bounce in the Air''), Leabhar Breac, 2020. '''''Books for Toddlers''''' Leabhar Breac has published 14 books written by French author Orianne Lallemand's and illustrated by Eleonore Thuillier, about Lallemmand's popular character Loup, Wolf. These are translated by Ó Scolaí: *Orianne Lallemand, ''An Mac Tire a Raibh Faitios an Domhain Air'' (trans. of ''The Son Who Saw the World in His Eyes''), Eleonore Thuillier  Illustr.), Leabhar Breac, 2018. *Orianne Lallemand, ''Macan agus an Goban'' (trans. of ''Macan and the Goblin''), Eleonore Thuillier (Illustr.), Leabhar Breac, 2018. * Orianne Lallemand, ''A Mac Tíre a Chuaigh go Tóin na Farraige'' (trans. of ''The Wolf Who Went to the Bottom of the Sea''), Éléanore Thuillier  (Illustr.), Leabhar Breac, 2019. '''''Board Books (for babies)''''' J. C. (Joan Carles) Girbés Aparisi is a Catalan author and editor. These books were written in Catalan and translated by Ó Scolai. *J. C. Girbés, ''An Phicnic'' (''The Picnic''), Silvia Ortega (Illustr.), Leabhar Breac, 2013. * J. C. Girbés, ''An Chóisir'' (''The Party''), Silvia Ortega (Illustr.), Leabhar Breac, 2013. *J. C. Girbés, ''Lá Mór Fada'' (''A Long Day''), Silvia Ortega (Illustr.), Leabhar Breac, 2014. *J. C. Girbés, ''Tabhair Leat do Leabhar'' (''Bring Your Book''), Silvia Ortega (Illustr.), Leabhar Breac, 2014. ==== Gradam Réics Carló ==== The Réics Carló prize is awarded for the best book in the Irish language for young readers. It is named for one of the characters of 20th-century writer [[wikipedia:Cathal_Ó_Sándair|Cathal Ó Sándair (Charles Saunders)]]. * ''An Bradán Feasa'' was “shortlisted for the Réics Carlo award 2010.”<ref name=":9" /> == References == {{reflist}} ojkugftpc8hl9ei5svwqln0gubsvj4y 2823749 2823748 2026-08-20T22:11:13Z Scogdill 1331941 2823749 wikitext text/x-wiki {{Short description|Dress worn by Queen Victoria at her wedding to Prince Albert in 1840}} = Sandbox = Page to draft revisions for Wikipedia articles. For Gwladys Robinson, see Gwladys Lowther Robinson, [[Social Victorians/People/Ripon|Marchioness of Ripon]] and, earlier, [[Social Victorians/People/Lowther|Countess of Lonsdale]] ==References== {{reflist|2}} [[Category:1840 works]] [[Category:Royal wedding dresses|Victoria Queen]] [[Category:1840s fashion]] [[Category:British royal attire]] [[Category:Dresses in the Royal Collection of the United Kingdom|Victoria, Wedding]] [[Category:Diamond Jubilee of Queen Victoria]] = Victorian fashion = '''Victorian fashion''' consists of the various fashions and trends in [[Culture of the United Kingdom|British culture]] that emerged and developed in the [[United Kingdom of Great Britain and Ireland|United Kingdom]] and the [[British Empire]] throughout the [[Victorian era]], roughly from the 1830s through the 1890s. The period saw many changes in fashion, including changes in styles, fashion technology and the methods of distribution. Various movements in architecture, literature, and the [[decorative arts|decorative]] and [[visual arts]] as well as a changing perception of [[gender roles]] also influenced fashion. Under [[Queen Victoria]]'s reign, England enjoyed a period of growth along with technological advancement. [[Mass production]] of sewing machines in the 1850s as well as the advent of synthetic dyes introduced major changes in fashion.<ref name=":3">{{Cite book|title=The Culture of Fashion|last=Breward|first=Christopher|publisher=Manchester University Press|year=1995|pages=145–180}}</ref> Clothing could be made more quickly and cheaply. Fashion made more extreme and more rapid changes than it had in prior centuries. Advancement in printing and proliferation of fashion magazines allowed the masses to participate in the evolving trends of high fashion, opening the market of mass consumption and advertising. By 1905, clothing was increasingly factory made and often sold in large, fixed-price department stores, spurring an age of consumerism with the rising middle classes, who benefited from the [[Industrial Revolution|industrial revolution]].<ref name=":3" /> ==Women's fashions== [[File:Fashions.jpg|thumb|upright|Illustration depicting fashions throughout the 19th century]]During the [[Victorian era|Victorian Era]], women generally inhabited the private, domestic sphere.<ref>{{Cite web|url=https://www.bl.uk/romantics-and-victorians/articles/gender-roles-in-the-19th-century|title=Gender roles in the 19th century|website=The British Library|access-date=2016-10-21|archive-date=8 July 2022|archive-url=https://web.archive.org/web/20220708075142/https://www.bl.uk/romantics-and-victorians/articles/gender-roles-in-the-19th-century|url-status=dead}}</ref> Unlike in earlier centuries when women labored with their husbands and brothers or worked in family businesses, during the nineteenth century, gender roles became more rigidly defined. Farm labourers was no longer in such a high demand after the [[Industrial Revolution]], and women were more likely to perform domestic work or, if married, give up paid work entirely. Dress reflected these new lifestyles, and was, for the middle and upper classes, less utilitarian.<p> Clothes were seen as an expression of women's place in society<ref>{{Cite book|title=Victorian and Edwardian Fashion - A Photographic Survey|last=Gernsheim|first=Alison|publisher=Dover Publications Inc.|year=1963|location=New York|pages=26}}</ref> and were differentiated by [[social class]]. Most women wore a [[corset]] over a [[chemise]], followed by a gown or [[skirt]] paired with a [[bodice]], [[blouse]], or [[chemisette]]. The shape of the skirt would be supported by layers of petticoats or, later in the period, structured support such as cage crinolines or bustles. The clothing of [[Upper class|upper-class women]], who generally did not do paid labor, was often elaborately decorated with more layers and [[Trim (sewing)|trims]]. [[Middle class|Middle-class women]] wore less complex dress styles with less expensive trim. [[Working class|Working-class]] clothing was simpler still, with less expensive fabric, fewer layers still and little trim. Including the undergarments, the amount of fabric in women's clothing made it much heavier and the construction made it much more restrictive than ours, especially in the waist (due to the boning in the corset) and the shoulders (due to the popularity of dropped shoulder seams). The amount, quality and type of fabric were displays of wealth and status.<p> Throughout the 19th century, journalism targeting women increased enormously and addressed an increasingly more class-diverse audience. According to the ''Dictionary of Nineteenth-Century Journalism'',<blockquote><p> The closely allied fashion and women's journals can be divided into three phases: titles such as the ''Lady's Magazine'' continued eighteenth-century models, addressing readers as "ladies" and catering to a leisured, fashionable elite; a more domesticated format by the 1840s, targeting middle-class women with instructive and entertaining content including dressmaking and etiquette articles ...; finally, from the 1870s, a livelier, more engaging style of fashion reporting influenced by the New Journalism was integrated with an increased amount of imagery, including better quality fashion plates ....<ref>{{Cite book|title=Dictionary of Nineteenth-Century Journalism In Great Britain and Ireland|last=Beetham|first=Margaret Rachel|last2=A|first2=R|publisher=Academia Press and the British Library|year=2009|editor-last=Brake|editor-first=Laurel, and Marysa Demoor|location=Gent|pages=215a–c|chapter=Fashion Journals}}</ref></blockquote>By the end of the century, women's periodicals were including patterns for dressmaking in their pages, reflecting the presence of middle- and working-class readers as well as technological change like sewing machines for home use and mass-produced fabrics and trim.[[File:1837 Dress.jpg|alt=This dress features a low waistline, and the bodice is worn over the hips to further emphasise the silhouette|thumb|upright|An undressed woman In 1837, featuring a fashionable hairstyle, busked corset, and layers of petticoats.]]It is important not to oversimplify the fashion of the Victorian age. The rate of change in fashion accelerated in the 19th century to the point that styles were distinctly different from one decade to the next (see "When Was That Dress in Fashion?", above right). The styles of Elizabethan England, in contrast, changed much less extremely over the course of a century. The most important characteristics for the analysis of 19th-century fashion include silhouette or line, corsets or stays, the neckline and the sleeves. The silhouette in particular but also the color, the variety of available fabrics and the distribution of information and opinion about fashion were the result of [[Social Victorians/People/Gwladys Robinson#Technological advancement|technological changes]] made throughout the century, but centering in the 1850s.[[File:The Engageants sleeves.jpg|thumb|Engageants, worn to fill open sleeves, were made of light fabrics like lace, linen, lawn or cambric.]] * '''Silhouette''': Silhouette changed over time supported by the evolution of the foundation garments. In fact the line or silhouette of garments changed about every ten years. Just as outer clothing changed, foundation garments were also modified to give the wearer a different silhouette. Over the course of the century most Europeans and some in their colonies wore the same kinds of undergarments and similar outer garments. For example, wide skirts were supported by layers of petticoats that used woven horsehair to stiffen them.<ref>{{Cite web |title=Corsets, crinolines and bustles: fashionable Victorian underwear · V&A |url=https://www.vam.ac.uk/articles/corsets-crinolines-and-bustles-fashionable-victorian-underwear |access-date=2025-10-27 |website=Victoria and Albert Museum |language=en}}</ref> By 1856 the [[Crinoline|cage crinoline]] (a domed structure using steel bands and wires) replaced the petticoats, making the skirts lighter in weight and easier to walk in. The line of the outer garments was influenced by how full the skirt was, how small the waist was and its location relative to the natural waistline, how the sleeves were shaped, and how deep the neckline went. * '''Corsets''': [[Corset]]s or stays were ubiquitous, providing adjustable bust and posture support, helping to shape the body into the fashionable silhouette and preventing horizontal creasing in the bodice. Foundation garments were constantly evolving throughout the century. Over the course of the century, almost all women and some men wore corsets. After the late 1850s, an individual could lace a corset without help.<ref name=":24">{{Cite book|title=Victorian Fashions for Women|last=Kay|first=Fiona|last2=Storey|first2=Neil R.|publisher=Pen & Sword History|year=2022|isbn=978 1 39900 416 9|location=Yorkshire and Philadelphia|pages=30-31}}</ref> Most corsets were constructed with a busk, "(a flat length of whalebone, wood or steel) inserted in a channel down the centre to smooth out the front of the dress."<ref>{{Cite book|title=Victorian Fashions for Women|last=Kay|first=Fiona|publisher=Storey|year=Neil R.|isbn=978 1 39900 416 9|location=Yorkshire and Philadelphia|pages=13}}</ref> The drawing of an undressed woman (above right) shows a self-laced corset with what may be a split busk. * '''Neckline''': Necklines changed over the course of the century as bodices and sleeves evolved. The less formal daywear had a higher neckline, regardless of class and decade. For formal wear, which varied widely by class and kind of event, the neckline was often lower and off the shoulder and finished with a [[Collar (clothing)|bertha]] (lace collar or flounce) or multiple bands of fabric pleats. This [[décolletage|décolleté evening style]] popularized shawls or [[cape]]lets and required a [[Corsets|corset]] without shoulder straps. The fashion was for dressmakers to produce two bodices with each skirt, one closed décolletage for day and one décolleté for evening. * '''Sleeves''': Over the course of the century, styles in sleeves changed radically and more than one sleeve style was fashionable at the same time. Some of the most popular styles included gigot, pagoda, ''engageants'' (see right), bishop and leg-of-mutton sleeves. The changes were in the [[armscye]], the wrist treatment, and the fullness at the shoulder, elbow and wrist. For example, as [[crinoline]]s began to appear in the 1850s, sleeves were shaped like large bells known as pagoda sleeves. [[Engageante]]s, or false sleeves, were stitched inside full or open sleeves like pagoda sleeves. They were easy to remove, launder and restitch into position. Even though the changes in fashion over the century were sometimes rapid and extreme, they were also evolutionary.[[File:Dress - MET 1971.47.3a–e.jpg|thumb|English day dress, c. 1836, with bow details and puffed sleeves]] === 1830s dress style === [[File:Princess Victoria and Dash by George Hayter.jpg|alt=Old portrait of a teenage girl in a white formal dress, with a dog|thumb|Princess Victoria and her dog Dash, 1833|left]]During the beginning of Queen Victoria's reign in 1837, the fashionable silhouette was an hourglass shape with wide shoulders, emphasized by puffed [[gigot sleeves]], a full skirt, and a slim waist. Corsets were extended over the abdomen and down towards the hips, and worn with a busk.<ref name=":0">{{Cite book|title=From Queen to Empress - Victorian Dress 1837-1877|last=Goldthorpe|first=Caroline|publisher=The Metropolitan Museum of Art|year=1988|location=New York|pages=23–24}}</ref> A chemise was worn under the corset and cut relatively low in the neck so that it could not be seen. Over the corset was a tight-fitting bodice featuring a high, straight waistline. Under the ankle-length skirt were layers of petticoats<ref name=":0" /> stiffened with horsehair. (Skirts would not be extremely full for another two decades.) To contrast with the narrow waist, necklines were low and wide. Queen Victoria's 1833 white dress (left) shows an off-the-shoulder neckline, a higher waist and an ankle-length skirt held out by horsehair. The c. 1836 yellow day dress (right) shows gigot sleeves, a higher neckline and a skirt held out by petticoats. Always a mark of wealth and status, Princess Victoria's white dress shows that she is formally dressed, perhaps for court, although the pose itself suggests some informality as well. === 1840s dress style === The 1840s saw an increase in domestic magazines targeting women, along with new varieties in the weave of ready-made fabrics as well as new and much more vibrant colors because of the invention of aniline dyes. And the industrial revolution supplied women with more varieties of color and weave in ready-made fabrics. Cotton replaced silk as a basic fabric, especially among middle-class women because silk was expensive, limiting who could afford it. The elements of fashion changed rapidly during this transitional decade.[[File:Magasin för konst, nyheter och moder 1844, illustration nr 8.jpg|thumb|1844 [[fashion plate]] depicting fashionable clothing for men and women, including illustrations of a [[glove]], a fanchon, and [[Bonnet (headgear)|bonnets]]]]At the beginning of the 1840s, skirts began to widen and become dome shaped (because the skirt pieces changed from rectangles to gores, which are wider at the bottom). The waistline lowered with a point formed at the bottom of both the bodice and corset, which gave a rather rigid look to the silhouette. During this decade, the amount of trim decreased in general, although trim was still plentiful. In addition to the flowers, feathers, and ribbons many of the decorations on the dress were made of the fabric of the dress (tucks and pleats, flounces, ruffles). At the end of the decades waists rose to the natural waistline.[[File:Woman's_Dress_LACMA_M.2007.211.744_(1_of_7).jpg|left|thumb|English silk day dress of the second half of the 1840s, with dropped shoulder seams, tight sleeves, and a pointed waist.]]Although corsets narrowed the bodices and gave them a point in the early 1840s, by the end of the decade, they returned to the natural waistline. Corsets lost their straps by the end of the decade.  Busks in the front of the corset were split by Jean Julien Joselin in 1829,<ref name=":24" /> (75 [of 298]) but the corset wouldn’t stay closed until 1848 when Joseph Cooper patented the "slot and stud" which is still in use today.<ref name=":24" /> (75 [of 298]) Necklines remained wide with further use of lace berthas to frame the upper body. At the end of the decade, necklines were raised and remained high. Dresses were stiffer due to boning in the bodice as well as the corset. Skirts lengthened, while in 1847 widths increased with the introduction of the [http://3.bp.blogspot.com/-bOuPyjWzwT8/TuKx-x1R12I/AAAAAAAAAF0/oRs6AyGH0gw/s1600/CI53.51.15_B1870Amer.Horsehair.jpg horsehair crinoline], which was stiffened with horsehair and starch. The petticoats were numerous and became bulky and heavy and sometimes entangled the feet. Petticoats had another disadvantage: the number of waistbands increased with each additional petticoat. Skirts often had one or two flounces at the bottom that increased the look of fullness (see, for example, the 1844 fashion plate, right). To achieve the narrow waist, skirts were attached to bodices using very tight organ [[pleat]]s secured at each fold.<ref name=":1">{{Cite book |last=Goldthorpe |first=Caroline |title=From Queen to Empress - Victorian Dress 1837-1877 |publisher=The Metropolitan Museum of Art |year=1988 |location=New York |pages=32}}</ref> . Sleeves narrowed with smaller decorative additions (see, for example, the English silk day dress, left). They eventually widened at the wrists into open pagoda-type sleeves requiring engageants to cover the forearms. Shawls were used to convert a simple dress into a more formal outfit. The popularity of shawls grew because of the very soft and beautifully dyed and woven cashmere shawls from India with a paisley design (after the Scottish town that manufactured shawls).<ref name=":24" /> (48 [of 298]) Head coverings were ''de regeur'', dominated by poke bonnets.<ref name=":24" /> (51 [of 298]) (The mannequin in the English silk day dress, above left, is wearing a poke bonnet.) Cosmetics became more popular, with instructions The Handbook of the Toilette (anonymous, many editions beginning in 1839. Unfortunately many contained toxic elements like calcium oxide (or quicklime) found hair dye that was recommended to stay in the hair for 3 to 8 hours.<ref name=":24" /> (47 [of 298]) By the end of the 1840s skirts were more dome shaped, necklines were higher and wider and sleeves broadened at the bottom. === 1850s dress style === The 1850s saw revolutionary [[Social Victorians/People/Gwladys Robinson#Technological advancement|changes in technologies]] affecting the manufacture and consumption of clothing, especially * the mass production of fabrics * the invention of synthetic dyes * the manufacture of inexpensive, flexible and lightweight steel * the invention of a sewing machine that could be used in the home * the spread of fashion journalism and journalism for women According to the ''Dictionary of Nineteenth-Century Journalism'', "The 1850s and 1860s saw the eclipse of the older ladies' journals [that began in the 18th century and targeted upper-class women] and the emergence of the magazine for middle-class ... women."<ref>{{Cite book|title=Dictionary of Nineteenth-Century Journalism In Great Britain and Ireland.|last=Beetham|first=Margaret Rachel|publisher=Academia Press and the British Library|year=2009|editor-last=Brake|editor-first=Laurel, and Marysa Demoor|location=Gent|pages=683–684|chapter=Women's Periodicals}}</ref> (684) Nine fashion magazines were being published in London by 1850 and fourteen by 1859 as part of the burgeoning collection of magazines for women, both domestic magazines aimed at middle-class women and journalism focused mostly on fashion.<ref name=":24" /> (63 [of 298]) The journalism aimed at middle-class women introduced haute couture, making the styles, names of couturiers and fashion houses familiar to them for the first time. These technological changes were revolutionary because of the impact they had on fashion over the course of the rest of the century. Their impact on fashion arises largely because most women were taught a wide range of seamstress skills and, due to reforms in education over the century, more women could read.[[File:Ensemble_MET_DT6845.jpg|thumb|A day ensemble c. 1855, featuring tiers of ruffles and pagoda style sleeves.]] ==== Silhouette ==== The 1850s are considered a transitional decade in 19th-century fashion because little changed in the silhouette and appearance of clothing, but technological changes would make increasingly important structural differences in what was available for people to wear. Skirts widened with the disappearance of the many layers of petticoats but did not change their basic shape. Beyond the silhouette, the design elements of the dress (like sleeves, neckline, or skirt) were barely changed as they evolved from the 1840s to the 1860s. While the silhouette and elements of design did not change significantly, the effect of the technological changes related to the manufacture and consumption of clothing was to give individual (and especially middle-class women) more agency over how their dresses got made and who made them, what fabrics their dresses were made of, how broad a range of options they could choose from and how easy it was to move in their dresses. The number of flounces and ruffles on the skirt increased, making the skirt look wider (see the c. 1855 day ensemble, right). ==== Neckline ==== [[File:1850's Evening Dress.jpg|thumb|1850s evening dress with a bertha|left]] With trim and a front closure in the corset and the bodice, the bodice emphasized a distinct V-shape. Necklines of day dresses were sometimes cut into a V-shape, causing a need to cover the bust area with a chemisette. For evening, a wide, low neckline was popular, often with a [[Collar (clothing)|bertha]] (see the 1850s even dress with a bertha, left).<ref name="h608">{{cite book |last=Arnold |first=Janet |title=Patterns of fashion. 2: Englishwomen's dresses and their construction: 1860 - 1940 |date=1993 |publisher=MacMillan |isbn=978-0-89676-027-1 |publication-place=London |page=}}</ref> ==== Sleeves ==== Pagoda sleeves and under sleeves (''engageants'') continued to be popular for most of the decade. ==== Foundations ==== [[File:1856 Cage Crinoline.jpg|alt=1st patented cage crinoline.Fullness of the skirt is even further emphasised.|thumb|1850s fashionable silhouette and the cage crinoline needed to support it.]] In 1856, the invention of the first [[Crinoline|cage crinoline]] allowed for even wider skirts. The cage crinoline was constructed by joining thin metal strips together with wires to form a circular cage-like structure that could support a very wide skirt (see 1950s silhouette and cage crinoline, right). Although often ridiculed by journalists and cartoonists of the time as the crinoline swelled in size, this innovation freed women from the heavy weight of petticoats.<ref name=":4">{{Cite book |last=Steele |first=Valerie |url=https://archive.org/details/fashioneroticism0000stee |title=Victorian Fashion. Fashion and Eroticism: Ideals of Feminine Beauty from the Victorian Era to the Jazz Age |publisher=Oxford University Press |year=1985 |isbn=978-0-19-503530-8 |pages=[https://archive.org/details/fashioneroticism0000stee/page/51 51]–84 |url-access=registration}}</ref> For a description of the [[Social Victorians/People/Gwladys Robinson#Technological advancement|technological advancement]] that made cage crinolines possible, see below.) Not visible on the outside garment, the cage crinoline was the foundation for the huge dome-shaped skirts that dominated the decade. It was safer and easier to walk in a cage because the hoops held the skirt away from the feet and legs of the wearer. Without the innumerable petticoats more women began to wear drawers or "pantalettes" for modesty and warmth. The dome shape made possibly by the cage foundation changed the way skirts were cut. Instead of rectangles, gores were cut with one end of the skirt piece wider than the other end,<ref name="w586">{{cite book |last=Arnold |first=Janet |title=Patterns of fashion. 2: Englishwomen's dresses and their construction: 1860 - 1940 |date=1993 |publisher=MacMillan |isbn=0-333-13607-1 |publication-place=London |page=}}</ref> preventing bulkiness at the waist from gathered fabric and created a skirt bottom much wider than the top. Bloomers, designed by American Amelia Jenks Bloomer,  introduced bifurcated garments for women, essentially trousers or pants with a seam between the legs. Even pantalettes had no seam between the legs; it was simply left open. This experiment failed and women didn’t wear pants until the 20th century. The 1850s saw two other developments that permanently changed the clothing available to Victorian women (and men). Created in 1856, the first synthetic dyes were much more vivid and vibrant than natural dyes and resisted fading.<ref name=":24" /> (92 [of 298]) Because Victorian photography was black and white, we do not typically see the gaudy and saturated colours that many Victorians loved.<ref name=":3" /> Also, although sewing machines had already been invented, changing the accessibility and value of individual articles of clothing, it was the invention of and widespread sale of "lightweight domestic machines" for home sewing that affected large numbers of women.<ref name=":24" /> (91 [of 298]) Cage crinolines remained popular for perhaps 5 years among the fashion forward and perhaps 10 years for the less adventurous.[[File:Woman's_silk_taffeta_dress_c._1865.jpg|thumb|An 1865 English silk morning dress.]] [[File:Mrs_Ellinor_Guthrie_by_Frederic_Leighton.jpg|thumb|English dress, 1864, with simple trim.]] === 1860s dress style === ==== Foundations ==== The cage crenoline reached their greatest width during the 1860s. Photographs show that the fashion-forward Empress Eugénie of France, Empress Elisabeth of Austria and Countess Pauline von Metternich had stopped wearing the very large crinoline cages as early as 1862, but most middle- and upper-class women (including Queen Victoria) wore them for much of the rest of the decade. During the first half of the 1860s, crinolines began decreasing in size at the top, while retaining their volume at the bottom, creating a more pyramidal shape.<ref name=":2">{{Cite book|title=From Queen to Empress - Victorian Dress 1837-1877|last=Goldthorpe|first=Caroline|publisher=The Metropolitan Museum of Art|year=1988|location=New York|pages=}}</ref> (26) Then the fullness began to move to the back while the front became flat and close to the body. As the back fullness increased, skirts sometimes lengthened into trains. (The 1865 English silk dress, above right, shows the flattening of the front at the waist and the development of the train.) In order to emphasize the back, the train was gathered together to form soft folds and [[Drapery|draperies]].<ref>{{Cite book|title=Making Victorian Costumes for Women|last=Audin|first=Heather|publisher=Crowood|year=2015|pages=45}}</ref> This line or silhouette would eventually evolve into a bustle in the next decade. Decoration or trim often appeared only at the bottom of the skirt (see English dress, 1864, below right). Flounces and ruffles diminished as geometric designs in trim gained popularity.<ref name=":24" /> (102 [of 298]) Skirts were also decorated with overskirts of the same fabric or a different shade of the same color. Waistlines were pointed in front below the natural waistline. By mid-century the waist was seated at the natural waistline often with a wide belt and large decorative buckle.   ==== Bodices and Sleeves ==== Bodices often had buttons down the front because both the corset and the bodice opened in the front. Necklines were generally high and rounded. Some dresses were cut without separating the bodice and skirt so it could be buttoned from the neck to the bottom of the skirt. It became popular for dresses to be made as one skirt and two bodices, one for day wear and one for formal wear.<ref name=":0" /> (43) Sleeves narrowed but remained loose on the arms and were wrist length. Sometimes the sleeves were full at the shoulder, but they were not very puffed. ==== General Trends ==== A greater and richer variety of fabrics was available to the always upwardly-aspirational middle class, with silk essential in the dress of wealthy middle- and upper-class women. Dresses were cut and pieced together to accommodate the more active life women had in sports, walking and even riding bicycles. The trends that began in the 1860s continued through the 1870s and into the 1880s; the changes were evolutionary. === 1870s dress style === ==== Silhouette ==== [[File:Black_net_ball_dress_1874.png|thumb|A black net ball dress, 1874]]In 1877, dresses moulded to fit the figure, as increasingly slimmer and more restrictive silhouettes were favored. Although dress styles took on a more natural form, corsetry was still required and the now ''de regueur'' train was often supported with a bustle cage.<ref name=":2" />{{rp|50}} The armscye, for the first time in the Victorian period, moved from a dropped position up to the shoulders and would remain there for the rest of the era. The most famous designer of this conservative, very fitted and restrictive style was British-born Frederick Worth, who designed the “princess” construction for dresses, which we still use today, and who popularized and then “killed,” according to his obituary in ''The Lady’s Treasury'',<ref>“‘Death of the Chief Ruler of the Fashionable World’, The Ladies’ Treasury (1 April 1895), p. 274.” In ''Fashioning the Victorians: A Critical Sourcebook''. Ed., Rebecca N. Mitchell. Dress, Body, Culture Series, gen. ed., Joanne B. Eicher. Bloomsbury Visual Arts, 2018. Pp. 487–491 of 565.</ref> the crinoline cage. The princess construction was named for Alexandra, Princess of Wales, who preferred a lean, tailored style. By 1879 corsets were being built using "princess" seams to support the tailoring of the smooth, straight dresses like the ones designed by Maison Worth. Because Queen Victoria had been in mourning since 1861, the Princess Alexandra was expected to lead in the haute couture of the day. She set a trend for tailored dresses that was quickly picked up by all classes. Unlike the tailored designs, what Maison Worth created was ornate with many decorative elements, including fringe, which was widely used (along with ribbon, braid, ball fringe, ruching, epaulettes, pieces of the same fabric in a lighter or darker shade, pieces of a different-textured fabric like velvet or velveteen, etc.). No single silhouette dominated the 1870s, however, because of the different lines created by the bustle, the overskirt and the layers of the polonaise, or a combination of these three skirt treatments. Foundation garments changed very little, although perhaps the greatest change came in corsets. In 1870 women were wearing corsets that came to just below the waist with a pointed center front. ==== Skirts ==== [[File:Woman's_Polonaise_Dress_LACMA_M.2007.211.777a-f_(1_of_4).jpg|left|thumb|An c. 1875 English polonaise]]The trend for wide skirts slowly disappeared during the 1870s, as women started to prefer a slimmer silhouette. Skirts went from their most extreme width to their most narrow, waists went to a natural level and the backside took the point of interest in the ensemble. The back of the dress became the focal point of the design. The relationship between the various skirt treatments was very complex, in part because skirts became architectural. (The bustle on the 1874 black net ball dress, above right, has been gathered and bunched and would require padding to keep the draping in place. It also has an overskirt.) The skirt began the decade rather flat in front with most of the fabric pulled to the back and pleated. As the skirt evolved, the gathered fabric draped gracefully at the back. In the next fashion the extra fabric was bunched into large poufs below the waist in back. Then a pad supported the extra fabric, and then by the end of the decade a [[tournure]] or bustle kept the elaborate draping of the back of the skirt and train in place. In general, trains were present on every dress, including day dresses, but they were narrower and longer with tiers and drapes. Petticoats, which could be washed separately, kept the longer trains off the ground. [[overskirt|Overskirts]] became extremely popular, often tied up into an apron effect at the front with a [[Polonaise (clothing)|polonaise]] or puffed draperies at the back.<ref name="g4223">{{cite book |last=Cunnington |first=Cecil Willett |title=English Women's Clothing in the Nineteenth Century |date=1990-05-01 |publisher=Courier Corporation |isbn=0-486-26323-1 |publication-place=New York |page=}}</ref> A revival of an 18th-century romanticization of what a milkmaid might have worn, the 1870s polonaise is a garment featuring both an overskirt and bodice often of the same fabric (see c. 1875 English polonaise, left). Over time, the overskirt shortened into a detached [[Basque (clothing)|basque]], resulting in an elongation of the bodice over the hips. (The early 1870s fashion plate, below right, shows an assortment of ways overskirts were worn, including one for a girl.)[[File:1870's Dress.jpg|alt=Dresses featuring the Bustle & Polonaise|thumb|An early 1870s fashion plate]] ==== Neckline ==== Necklines were high, and lines were sleek and fitted. ==== Sleeves ==== Pagoda sleeves began to lose their three-decade-long popularity in 1875,<ref name=":24" />{{rp|102 [of 298]}} but most sleeve treatments were narrow and came to the wrist. ==== General Trends ==== An unusual trend occurred during the 1870s in hairstyles, which grew very large with added braids, buns, coils, poufs and strands. The elaborate hairstyles required multiple hair pieces and featured tiny, over-decorated hats fastened almost vertically on the head. Although women had already been supplementing their own hair, these extremely large styles caused enormous demand in the human hair market. () The practice of constructing a dress with one skirt and two bodices (one for day and one for evening wear) continued from the 1860s. === 1880s dress style === The Second Bustle Era lasted through the 1880s. Bustles had been seen in the 1870s but those in the 1880s were quite different from the evolving bustles of the 1870s. Dress reform was supported by several movements or organizations. ==== Silhouette ==== At the beginning of the 1880s day dresses were very fitted – narrow sleeves, tight bodice, straight skirt – no excess fabric for decorations. Some dresses were in one piece and most often buttoned down the front usually from neckline to hemline. Some dresses had overskirts and separate bodices. The massive hair pieces gave way to a simple chignon at the base of the neck that later moved to the top of the head. ==== Foundation ==== The smoothness of the dress required a corset to maintain a wrinkle-free garment. Corsets extended below the waist and had the same “princess” seams to keep the line straight.  If the bodice was made like a jacket, it was tailored for each woman. ==== Skirts ==== Along with the smoothly tailored ensembles, women wore narrow, decorative bustles that “were more pronounced, projecting sharply outwards” and had no train. In fact, the new bustles were their own garment. 162 of 298 They looked like a highly decorated shelf coming out of the backside. ==== Necklines and Sleeves ==== Bodices looked more like a suit jacket with a high neckline and a white blouse with a ruffled collar or some kind of feminine neck treatment. Sleeves remained tight fitting to the arm but near the end of the decade sleeves developed more fullness at the shoulder. ==== Dress Reform ==== During the 1880s many people believed that there needed to be dress reform. Some of the societies formed include:  the Rational Dress Society, Aesthetic Dress Movement and the Artistic Dress Movement. These groups wanted to simplify and get rid of some of the layers and restrictions current fashion dictated.  While the 1880s had no significant inventions or events that impacted the fashion or clothing industries. ==== Old Version ==== [[File:1885 Bustle.jpg|alt=Horizontal protrusion at the back.|thumb|The lobster tail bustle of around 1885.]] The 1880s saw the growing popularity of austere, menswear inspired tailoring like that preferred by Alexandra, Princess of Wales.<ref name=":4" /> Some credited the change in silhouette to the [[Victorian dress reform]], which consisted of a few movements including the [[Artistic Dress movement|Aesthetic Costume]] Movement and the [[Victorian dress reform|Rational Dress Movement]] in the mid-to-late Victorian Era advocating for a natural silhouette and lightweight underwear, and rejecting [[tightlacing]]. However, these movements did not gain widespread support. Others noted the growth in cycling and tennis as acceptable feminine pursuits that demanded a greater ease of movement in women's clothing.<ref name=":3" /> Still others argued that the growing popularity of tailored semi-masculine suits was simply a fashionable style, and indicated neither advanced views nor the need for practical clothes.<ref name=":4" /> [[File:Edward_Hughes_-_Juliette_Gordon_Low_-_Google_Art_Project.jpg|left|thumb|An 1887 portrait of English evening dress with higher shoulder placement, simple trims, and a V-shaped neckline.]] After a period of slim, train-less skirts with heavy decoration, the bustle made a re-appearance in 1883, and it featured a further exaggerated horizontal protrusion at the back. Due to the additional fullness, drapery moved towards the sides or front panel of the skirt instead. Bodices shortened, now ending above the hips. Skirts were much less full than the last time the bustle was in fashion in the 1870s and instead focused on a slim front with a shelf-like back protrusion. Sleeves of bodices were thinner and tighter, while necklines became higher again, with a high collar being ubiquitous for daytime, a trend that would continue into the 1890s. For the evening, the bertha fell out of favor, replaced by V-shaped necklines or draped styles due to the new higher shoulder.<ref name="g4223"/> Sleeves tightened again during the [[1880s in Western fashion|1880s]] and the armscye moved back up the shoulders.<ref name="y040">{{cite book |last=Severa |first=Joan L. |title=Dressed for the Photographer |date=1995 |publisher=Kent State University Press |isbn=0-87338-512-8 |publication-place=Kent, Ohio |page=}}</ref> === 1890s dress style === ==== Silhouette ==== At the beginning of the 1890s a small puff of fullness was seen at the shoulders. By 1896 sleeves had reached the peak of fullness while skirts fitted the body more closely, flaring out towards the bottom. The fullness of the sleeves stopped at the elbow and sleeves were tightly fitted to the arm below the elbow. ==== Foundations ==== Corsets were still worn to keep the dress smooth and support the bust. Larger busts were more fashionable, leading to a variety of different kinds of padding to place in the corset and make the bust look bigger.  Corsets continued to reach well beyond the waist, smoothing the front of the dress. ==== Skirts ==== Bustles were left behind in the 1880s and skirts, cut in gores, were smooth, fitted close to the waist and hips until they flared outward.  Away from the knees, the  gores widened the skirts into an A-line.   ==== Necklines and Sleeves ==== Daywear dresses had very high necks with a kind of Mandarin collar or military band of fabric around the neck. A large brooch could be worn on such a collar. If bustles were the focal point of the ensemble in the 1880s, then sleeves were the focal point in the 1890s.  They were huge and round from the natural shoulder line to the elbow and required stuffing or padding to maintain the fullness. From the elbow to the wrist or onto the hand, sleeves were tight fitting. This type of sleeve was known colloquially as “lego-mutton.” 197 of 298  They reached their widest around 1896 and began to deflate. By 1900 the entire sleeve was  “straight and narrow again.” 198 of 298 Much of the excess trim disappeared in the 1890s and dresses had a softer, more feminine look. Although they closely fitted the body, dresses were not tight, allowing more freedom of movement. Many more women were participating in sports and other physical activities that required a less structured fit. The new century would let go of boned foundation garments and shorten skirts to a shocking length. The 20th century brought even more radical changes to feminine attire. ==== Old Version ==== [[File:Lady_Beatrice_Pole-Carew.jpg|thumb|English socialite Lady Beatrice Pole-Carew in the mid-1890s, with puffed sleeves.]] By 1890, the crinoline and bustle were fully abandoned, and skirts flared in an A-line. Necklines were high, while sleeves of bodices initially peaked at the shoulders, but increased in size in the middle of the decade to a puffed [[Sleeve|leg-of-mutton]] style.The sleeves grew to a volume rivaling the 1830s and even sometimes required a cushion to retain their fullness. This sleeve style narrowed down towards the end of the decade. Women also adopted the style of the tailored jacket during this period, with menswear influences such as necktie inspired neckwear continuing from the previous decade. == Hats and headwear == [[File:Ford.madox.brown.last.emma.study.jpg|thumb|''Emma Hill'' by [[Ford Madox Brown]] (1853), a woman wearing a later version of the [[poke bonnet]]]] [[File:Hoed,_objectnr_KA_1237.tif|left|thumb|Perched bonnet style of the early 1870s.]] Hats were crucial to a respectable appearance for both men and women. To go bareheaded was simply not proper. The top hat, for example, was standard formal wear for upper- and middle-class men.<ref name=":4" /> For women, the styles of hats changed over time and were designed to match their outfits. During the early Victorian decades, hats were modest in size and design, straw and fabric bonnets being the popular choice. [[Poke bonnet]]s, which had been worn during the late [[Regency period]], had high, small crowns and brims that grew larger until the 1830s, when the face of a woman wearing a poke bonnet could only be seen directly from the front. They had rounded brims, echoing the rounded form of the bell-shaped hoop skirts. Bonnets shrunk at the end of the 1860s and moved to a perched position in the early 1870s as hairstyles grew in scale and intricacy. This led to the popularization of hats, which became the headwear of choice for the remainder of the Victorian era.<ref name="g4223"/> [[File:The_London_and_Paris_ladies'_magazine_(Apr_1885)_03.png|thumb|Flower pot style hat of 1885.]] The 1880s saw a hat inspired by the top hat for women known as the flowerpot hat, and the 1890s saw the popularity of the boater. The hats of the late Victorian era were covered with elaborate creations of silk flowers, ribbons, and above all, exotic plumes; hats sometimes included entire exotic birds that had been stuffed. Many of these plumes came from birds in the Florida everglades, which were nearly made entirely extinct by overhunting. By 1899, early environmentalists like [[Adeline Knapp]] were engaged in efforts to curtail the hunting for plumes. By 1900, more than five million birds a year were being slaughtered, and nearly 95 per cent of Florida's shore birds had been killed by [[Plume hunting|plume hunter]]s.<ref>{{cite web|title=Everglades National Park|url=https://www.pbs.org/nationalparks/parks/everglades/|archive-url=https://web.archive.org/web/20090927085907/http://www.pbs.org/nationalparks/parks/everglades/|url-status=dead|archive-date=27 September 2009|publisher=PBS|access-date=7 November 2011}}</ref> == Shoes == The women's shoes of the early Victorian period were narrow and heelless, in black or white satin. By 1850s and 1860s, they were slightly broader with a low heel and made of leather or cloth. Ankle-length laced or buttoned boots were also popular. From the 1870s to the twentieth century, heels grew higher and toes more pointed. Low-cut pumps were worn for the evening.<ref name=":4" /> == Cosmetics == [[Victorian-era cosmetics]] were typically minimal, as makeup was associated by the middle classes with promiscuity. However, small amounts of pale face powder or powdered blush were more widely used.<ref>{{Cite book |last=Goodman |first=Ruth |title=How to be a Victorian |date=2014 |publisher=Penguin Books |isbn=978-0-670-92136-2 |location=London}}</ref> Some cosmetics contained toxic or caustic ingredients like lead, mercury, ammonia, and arsenic {{Citation needed|date=October 2025}}. Hair color == Men's fashion == [[File:Mens Coats 1872 Fashion Plate.jpg|thumb|upright|Drawing of Victorian men 1870s]] During the [[1840s in fashion|1840s]], men wore tight-fitting, calf length [[frock coat]]s and a [[waistcoat]] or vest. Sleeves were full at the top and waists were tight, creating an hourglass form. Waistcoats were single- or double-breasted, with shawl or notched collars, and might be finished in double points at the lowered waist. For more formal occasions, a cutaway morning coat was worn with light trousers during the daytime, and a dark tail coat and trousers was worn in the evening. Shirts were made of linen or cotton with low collars, occasionally turned down, and were worn with wide [[Cravat (early)|cravat]]s or neck ties. Trousers had fly fronts, and [[breeches]] were used for formal functions and when horseback riding. Men wore [[top hat]]s, with wide brims in sunny weather. During the [[1850s in fashion|1850s]], men started wearing shirts with high upstanding or turnover [[collar (clothing)|collars]] and [[necktie#Four-in-hand|four-in-hand necktie]]s tied in a bow, or tied in a knot with the pointed ends sticking out like "wings". The upper-class continued to wear top hats, and [[bowler hat]]s were worn by the working class. In the [[1860s in fashion|1860s]], men started wearing wider neckties that were tied in a bow or looped into a loose knot and fastened with a stickpin. Frock coats were shortened to knee-length and were worn for business, while the mid-thigh length [[sack coat]] slowly displaced the frock coat for less-formal occasions, with the overall effect of a looser silhouette. Top hats briefly became the very tall "stovepipe" shape, but a variety of other hat shapes were popular. During the [[1870s in fashion|1870s]], three-piece suits grew in popularity along with patterned fabrics for shirts. Neckties were the four-in-hand and, later, the [[Ascot tie]]s. A narrow ribbon tie was an alternative for tropical climates, especially in the Americas. Both frock coats and sack coats became shorter and more form fitting. Flat straw boaters were worn when boating. During the [[1880s in fashion|1880s]], formal evening dress remained a dark tail coat and trousers with a dark waistcoat, a white bow tie, and a shirt with a winged collar. In mid-decade, the dinner jacket or [[tuxedo]], was used in more relaxed formal occasions. The [[Norfolk jacket]] and tweed or woolen breeches were used for rugged outdoor pursuits such as shooting. Knee-length topcoats, often with contrasting velvet or fur collars, and calf-length overcoats were worn in winter. Men's shoes had higher heels and a narrow toe. Starting from the [[1890s in fashion|1890s]], the [[blazer]] was introduced, and was worn for sports, sailing, and other casual activities.<ref>{{cite web|last=Landow|first=George|url=http://www.victorianweb.org/art/costume/90s/2.html|title=Men's informal sporting dress, late 1880s and '90s}}</ref> Throughout much of the Victorian era most men wore fairly short hair. This was often accompanied by various forms of facial hair including moustaches, side-burns, and full beards. A clean-shaven face did not come back into fashion until the end of the 1880s and early 1890s.<ref>{{cite web|url=http://www.victorianweb.org/art/costume/nunn21.html|title=Victorian Men's Fashions, 1850–1900: Hair}}</ref> Distinguishing what men really wore from what was marketed to them in periodicals and advertisements is difficult, as reliable records do not exist.<ref name="shannon597">{{cite journal|last=Shannon|first=Brent|title=Refashioning Men: Fashion, Masculinity, and the Cultivation of the Male Consumer in Britain, 1860–1914|journal=Victorian Studies|year=2004|volume=46|issue=4|pages=597–630|doi=10.1353/vic.2005.0022}}</ref> Influence of Bertie, Albert Edward, Prince of Wales ==Mourning black== {{See also |Mourning stationery}} [[File:The royal children in mourning Mar 1862.jpg|thumb|Victoria's five daughters (Alice, Helena, Beatrice, Victoria and Louise), photographed wearing mourning black beneath a bust of their late father, Prince Albert (1862)]] [[File:Mourning dress MET 50.40.3a-b front CP4.jpg|alt=Black Victorian mourning dress|thumb|Mourning Dress, 1894–95]] In Britain, black is the colour traditionally associated with mourning for the dead. The customs and etiquette expected of men, and especially women, were rigid during much of the Victorian era. The expectations depended on a complex hierarchy of close or distant relationship with the deceased. The closer the relationship, the longer the mourning period and the wearing of black. The wearing of full black was known as First Mourning, which had its own expected attire, including fabrics, and an expected duration of 4 to 18 months. Following the initial period of First Mourning, the mourner would progress to Second Mourning, a transition period of wearing less black, which was followed by Ordinary Mourning, and then Half-mourning. Some of these stages of mourning were shortened or skipped completely if the mourner's relationship to the deceased was more distant. Half-mourning was a transition period when black was replaced by acceptable colours such as lavender and mauve, possibly considered acceptable transition colours because of the tradition of [[Church of England]] (and [[Catholic Church|Catholic]]) clergy wearing lavender or mauve [[Stole (vestment)|stoles]] for funeral services, to represent the [[Passion (Christianity)|Passion of Christ]].<ref>{{cite web|title=The Colors of the Church Year|url=http://fullhomelydivinity.org/articles/colors.htm|publisher=Consortium of Country Churches|access-date=6 November 2011|archive-date=13 November 2011|archive-url=https://web.archive.org/web/20111113075214/http://fullhomelydivinity.org/articles/colors.htm|url-status=dead}}</ref> The mourning dress on the right was worn by Queen Victoria, "it shows the traditional touches of mourning attire, which she wore from the death of her husband, Prince Albert (1819–1861), until her own death."<ref>{{Cite web|url=https://www.metmuseum.org/art/collection/search/155839?&searchField=All&sortBy=Relevance&deptids=8&ft=queen+victoria&offset=0&rpp=20&amp;pos=2|title=Mourning Dress, 1894–95|last=The Metropolitan Museum of Art|date=7 September 2019|website=The Metropolitan Museum of Art|access-date=7 September 2019}}</ref> === Norms for mourning=== ''Manners and Rules of Good Society, or, Solecisms to be Avoided'' (London, Frederick Warne & Co., 1887) gives clear instructions, such as the following:<ref>{{cite book|last=Flanders|first=Judith|title=The Victorian House|year=2003|publisher=Harper Perennial|location=London|isbn=0-00-713189-5|pages=378–83}}</ref> {| class="wikitable" |- ! Relationship to deceased !! First mourning !! Second mourning !! Ordinary mourning !! Half-mourning |- | Wife for husband || 1-year, 1-month; [[bombazine]] fabric covered with [[Crape|crepe]]; [[widow's cap]], [[lawn cuff]]s, collars || 6 months: less crepe || 6 months: no crepe, silk or wool replaces bombazine; in last 3 months jet jewellery and ribbons can be added || 6 months: colours permitted are grey, lavender, mauve, and black-and-grey |- | Daughter for parent || 6 months: black with black or white crepe (for young girls); no linen cuffs and collars; no jewellery for first 2 months || 4 months: less crepe || – || 2 months as above |- | Wife for husband's parents || 18 months in black bombazine with crepe || – || 3 months in black || 3 months as above |- | Parent for son- or daughter-in-law's parent || – Black armband in representation of someone lost || – || 1-month black || – |- | Second wife for parent of a first wife || – || – || 3 months black || – |} The complexity of these etiquette rules extends to specific mourning periods and attire for siblings, step-parents, aunts and uncles distinguished by blood and by marriage, nieces, nephews, first and second cousins, children, infants, and "connections" (who were entitled to ordinary mourning for a period of "1–3 weeks, depending on level of intimacy"). Men were expected to wear mourning black to a lesser extent than women, and for a shorter mourning period. After the mid-19th century, men would wear a black hatband and black suit, but for only half the prescribed period of mourning expected of women. Widowers were expected to mourn for a mere three months, whereas the proper mourning period expected for widows was up to four years.<ref>{{cite book|last=Flanders|first=Judith|title=The Victorian House|year=2003|publisher=Harper Perennial|location=London|isbn=0-00-713189-5|pages=378–9}}</ref> Women who mourned in black for longer periods were accorded great respect in public for their devotion to the departed, the most prominent example being Queen Victoria herself. Women with lesser financial means tried to keep up with the example being set by the middle and upper classes by dyeing their daily dress. Dyers made most of their income during the Victorian period by dyeing clothes black for mourning.<ref>{{cite book|last=Flanders|first=Judith|title=The Victorian House|year=2003|publisher=Harper Perennial|location=London|isbn=0-00-713189-5|page=341}}</ref> == Technological advancement == The technological changes that affected the manufacture and consumption of clothing in the Victorian age included the following: * the mass production of fabrics — for example, "by the early 1850s there were thousands of steam-powered looms churning out millions of miles of fabric every year"  [62] * the invention of aniline dyes, which were much more vibrantly colored and resistant to fading than the natural dyes that had been used. — . Invented by chemist [[William Henry Perkin]] in 1856, the first aniline dye mauveine (or mauve) "wash[ed] the fashionable landscape in a haze of purple."<ref name=":22">{{Cite book|title=The Dress Diary: Secrets from a Victorian Woman's Wardrobe|last=Strasdin|first=Kate|publisher=Pegasus Books|year=2023|location=New York, New York}}</ref> (247) Other intense and, to the Victorians, intensely exciting colors followed, but the new synthetic additions to fabric sometimes included chemicals harmful to their wearers. For example, a "bright-magenta hue was achieved by adding arsenical-based chemicals to existing aniline dyes, brightening the already luminous shades – but these left residues themselves, along with a toxic labour trail in their wake."<ref name=":22" /> (255) Perhaps the most famous of these is arsenic green, used on fabrics, wallpapers, and trim: "The craze for artificial foliage to adorn the heads and dresses of women of fashion in the mid-nineteenth century had seen the proliferation of flower workshops, where young women in their hundreds laboured to produce the lifelike green leaves and blooms that would make a fetching headdress or would trail becomingly across the bodice of a gown. The lushness of the green was achieved by the application of a powder, a pigment that was created by mixing copper and the highly toxic chemical, arsenic trioxide. The physical effects of working with this poisonous compound were horrific. Contemporary medical drawings depict the green hue of the skin and dreadful open lesions on the hands of the maker, whilst the daily gradual ingestion of the powder by the flower girls was eventually fatal."<ref name=":22" /> (255) * the invention of a sewing machine that could be used in the home. Although sewing machines were already in use in the clothing industry, in 1858 Isaac Merritt Singer began to sell "lightweight domestic machines" for home sewing, radically increasing women's control over their own dress.<ref name=":24" /> (91 [of 298]) * the spread of journalism for women and fashion journalism Perhaps not at the same scale as these but as important in 1850s designs was a technology that turned iron into steel, which could then be drawn into fine wires.<ref name=":3" /> Steel was refined to a malleable state so that thin blades could be curved into concentric circles (called hoops) and connected with wires to form the cage. Technological advancements not only influenced the economy but brought a major change in the fashion styles worn by men and women. As the Victorian era was based on the principles of gender, race and class.<ref>{{cite journal|last1=Graham|first1=P|title=The Victorian Era|url=https://archive.org/details/in.ernet.dli.2015.261548|journal=Digital Library of India}}</ref> Much advancement was in favor of the upper class as they were the ones who could afford the latest technology and change their fashion styles accordingly. In 1830s there was introduction of horse hair crinoline that became a symbol of status and wealth as only the upper-class women could wear it. In 1850s there were more fashion technological advancements hence 1850s could rightly be called a revolution in the Victorian fashion industry such as the innovation of artificial cage crinoline that gave women an artificial hourglass silhouette without layers of petticoats, which was lighter and more hygienic.<ref>{{cite book|last1=Shrimpton|first1=J|title=Victorian Fashion|publisher=Bloomsbury Shire Publications}}</ref> Synthetic dyes, such as [[mauveine]] (aniline purple), were introduced in 1856, adding bright colours to garments. In 1855's ''[[Haute couture]]'' was introduced as tailoring became more mainstream in years to follow.<ref>{{cite book|last1=Aspelund|first1=Karl|title=Fashioning Society|publisher=Fairchild Books}}</ref> Charles Frederick Worth, a prominent English designer, became popular amongst the upper class though its city of destiny always is Paris. Haute couture became popular at the same time that sewing machines were invented.<ref name="Haute Couture">{{cite book|last1=Martin|first1=Richard|last2=Koda|first2=Harold|title=Haute Couture|publisher=The Metropolitan Museum of Art}}</ref> Princess [[Eugénie de Montijo|Eugenie]] of France wore the Englishman dressmaker, Charles Frederick Worth's couture and he instantly became famous in France though he had just arrived in Paris a few years ago. In 1855, Queen Victoria and Prince Albert of Britain welcomed [[Napoleon III]] and Eugenie of France to a full state visit to England. Eugenie was considered a fashion icon in France. Queen Victoria, who had been the fashion icon for European high fashion, was inspired by Eugenie's style and the fashions she wore.{{Citation needed|date=October 2025}} Later, Queen Victoria also appointed Charles Frederick Worth as her dress maker and he became a prominent designer amongst the European upper class. Charles Frederick Worth is known as the father of the haute couture as later the concept of labels were also invented in the late 19th century as custom, made to fit tailoring became mainstream.<ref>{{cite book|last1=Saillard|first1=Olivier|last2=Zazzo|first2=Anne|title=Paris Haute Couture|publisher=Skira Flammarion}}</ref> By the 1860s, when made-to-fit tailoring was popular in Europe, crinolines were considered impractical. In the 1870s, women preferred more slimmer silhouettes, hence bodices grew longer and the polonaise, a skirt and bodice made together, was introduced. In 1870s the Cuirass Bodice, a piece of armour that covers the torso and functions like a corset, was invented. Towards the end of Victoria's reign, dresses were flared naturally as crinolines were rejected by middle-class women. Designers such as Charles Frederick Worth were also against them. All these inventions and changes in fashion led to women's liberation as tailored looks improved posture and were more practical.<ref name="Haute Couture"/> dressmakers, couturiers, modistes == Home decor == {{main|Victorian decorative arts}} Home decor started spare, veered into the elaborately draped and decorated style we today regard as Victorian, then embraced the retro-chic of [[William Morris]] as well as pseudo-[[Japonaiserie]]. == Myths and Oversimplifications == === Modesty === {{main|Victorian morality}} {{Original research|section|date=May 2008}} [[File:1868-skirt-lengths-girl-ages-Harpers-Bazar.gif|thumb|upright|"The proper length for little girls' skirts at various ages", from ''[[Harper's Bazaar]]'', showing a 1900 idea of how the hemline should descend towards the ankle as a girl got older]]Many myths and exaggerations about the period persist to the modern day. Examples include the idea of men's clothing is seen as formal and stiff, women's as elaborate and over-done; clothing covered the entire body, and even the glimpse of an ankle was scandalous. Critics contend that [[corset]]s constricted women's bodies and lives. Homes are described as gloomy, dark, cluttered with massive and over-ornate furniture and proliferating [[bric-a-brac]]. Myth has it that even piano legs were scandalous, and covered with tiny [[pantalette]]s. === Tight Lacing === Tight-lacing, which was not possible until the development of the grommet in 1828, was famously controversial in the Victorian age, generating many column inches of profitable newspaper copy, in part because it was (and still is) fetishistic and subversive in that adolescent girls used it as a means of rebellion and upper-working- or lower-middle-class shop girls saw it as a means of upward mobility.<ref name=":21">{{Cite book|title=Fashion and Fetishism: Corsets, Tight-Lacing and Other Forms of Body-sculpture|last=Kunzle|first=David|publisher=History Press|year=2013|isbn=978 0 7524 9545 3|location=Stroud, Gloucestershire|pages=}}</ref> (71 [of 1182]) No evidence exists that tight lacing was widespread or particularly dangerous.<ref name=":21" /> () In truth, men's formal clothing may have been less colourful than it was in the previous century, but brilliant [[waistcoat]]s and [[cummerbund]]s provided a touch of colour, and [[smoking jacket]]s and [[robe|dressing gown]]s were often of rich Oriental [[brocade]]s. This phenomenon was the result of the growing textile manufacturing sector, developing mass production processes, and increasing attempts to market fashion to men.<ref name="shannon597"/> Corsets stressed a woman's sexuality, exaggerating hips and bust by contrast with a tiny waist. Women's [[evening gown]]s bared the shoulders and the tops of the breasts. The [[jersey dress]]es of the 1880s may have covered the body, but the stretchy novel fabric fit the body like a glove.<ref>{{cite book |last=Gernsheim |first=Alison |title=Victorian & Edwardian Fashion: A Photographic Survey |year=1981 |publisher=Dover Publications |location=New York |page=65|edition=New |isbn=0-486-24205-6}}</ref> Home furnishing was not necessarily ornate or overstuffed. However, those who could afford lavish draperies and expensive ornaments, and wanted to display their wealth, would often do so. Since the Victorian era was one of increased social mobility, there were ever more ''[[nouveaux riches]]'' making a rich show. The items used in decoration may also have been darker and heavier than those used today, simply as a matter of practicality. London was noisy and its air was full of [[soot]] from countless coal fires. Hence those who could afford it draped their windows in heavy, sound-muffling curtains, and chose colours that didn't show soot quickly. When all washing was done by hand, curtains were not washed as frequently as they might be today. There is no actual evidence that piano legs were considered scandalous. Pianos and tables were often draped with [[shawl]]s or cloths—but if the shawls hid anything, it was the cheapness of the furniture. There are references to lower-middle-class families covering up their [[pine]] tables rather than show that they couldn't afford [[mahogany]]. The piano leg story seems to have originated in the 1839 book, ''A Diary in America'' written by Captain [[Frederick Marryat]], as a satirical comment on American prissiness.<ref>{{cite book |last1=Marryat |first1=C.B. |title=A Diary in America: With Remarks on Its Institutions |date=1839 |publisher=Longman, Orme, Brown, Green, and Longmans |location=London, England |volume=2 |pages=246–247 |url=https://books.google.com/books?id=2-VEAAAAIAAJ&pg=PA246}} From pp. 246-247: "I was requested by a lady to escort her to a seminary for young ladies, and on being ushered into the reception-room, conceive my astonishment at beholding a square piano-forte with four ''limbs''. However, that the ladies who visited their daughters, might feel in its full force the extreme delicacy of the mistress of the establishment, and her care to preserve in their utmost purity the ideas of the young ladies under her charge, she had dressed all these four limbs in modest little trousers, with frills at the bottom of them!"</ref> Victorian manners may have been as strict as imagined—on the surface. One simply did not speak publicly about sex, childbirth, and such matters, at least in the respectable middle and upper classes. However, as is well known, discretion covered a multitude of sins. Prostitution flourished. Upper-class men and women indulged in [[adultery|adulterous]] liaisons. == Gallery == {{gallery |2=A mid-Victorian interior: ''Hide and Seek'' by [[James Tissot]], c. 1877 Image:Winterhalter Elisabeth.jpg|3=Dress designed by [[Charles Frederick Worth]] for [[Elisabeth of Bavaria|Elisabeth of Austria]] painted by [[Franz Xaver Winterhalter]].|4=File:Frith A Private View detail.jpg|5=[[William Powell Frith]]'s painting of 1883 contrasts women's [[Aesthetic dress]] (left and right) with fashionable attire (center).|6=File:Tissot lilacs 1875.jpg|7=Day dress, c. 1875 [[James Tissot]] painting.|8=File:James Abbot McNeill Whistler 011.jpg|9=[[James McNeill Whistler|Whistler]]'s [[Portrait of Lady Meux]], 1882 Image:Jeanna_Samary-Renoir.png|10=[[Pierre-Auguste Renoir|Renoir]]'s portrait of [[Jeanne Samary]] in an [[evening gown]], 1878|11=File:Melville_-_Queen_Victoria.jpg|12=Portrait by [[Alexander Melville (artist)|Alexander Melville]] of [[Victoria of the United Kingdom|Queen Victoria]], 1845|13=File:Henry Treffry Dunn Rossetti and Dunton at 16 Cheyne Walk.jpg|14=An artistic interior: [[Dante Gabriel Rossetti]] reading to [[Theodore Watts-Dunton]] in the drawing room at No. 16 [[Cheyne Walk]], 1882|15=File:Punch - Masculine beauty retouched1.png|16=Men's swimwear: Cartoon from ''[[Punch (magazine)|Punch]]'' by [[George du Maurier]]}} == See also == * [[Emily Clapham]] * [[Victorian decorative arts]] * [[Victorian dress reform]] * [[Victorian morality]] * [[Victoriana]] * [[Women in the Victorian Era]] * [[Charles Frederick Worth]] === Time periods === * [[1830s in fashion]] * [[1840s in fashion]] * [[1850s in fashion]] * [[1860s in fashion]] * [[1870s in fashion]] * [[1880s in fashion]] * [[1890s in fashion]] === Women's clothing === * [[Corset]] * [[Corset controversy]] * [[Tightlacing]] * [[Bloomers (clothing)|Bloomers]] * [[Bodice]] === Contemporary interpretations === * [[Steampunk]] * [[Neo-Victorian]] * [[Lolita Fashion|Lolita]] == References == {{Reflist}} == Further reading == *{{cite book |author=Phipps, Elena| title= ''From Queen to Empress: Victorian dress 1837-1877'' | location=New York | publisher=The Metropolitan Museum of Art | year=1988 | isbn=0870995340| url= http://libmma.contentdm.oclc.org/cdm/compoundobject/collection/p15324coll10/id/69547/rec/235 | display-authors=etal}} * Sweet, Matthew – ''Inventing the Victorians'', St. Martin's Press, 2001 {{ISBN|0-312-28326-1}} == External links == * [http://www.victorians.co.uk/victorian-fashion Victorian Fashion] {{Webarchive|url=https://web.archive.org/web/20180407223711/http://www.victorians.co.uk/victorian-fashion |date=7 April 2018 }} * [https://www.victorianvoices.net/topics/fashion/index.shtml VictorianVoices.net] – Fashion articles and illustrations from Victorian periodicals; extensive fashion image gallery * [http://www.cracked.com/article_19575_5-ridiculous-sex-myths-from-history-you-probably-believe.html Victorian myths] * [http://www.victorianstation.com/lifestylemenu.htm Victorian fashion, etiquette, and sports] {{Webarchive|url=https://web.archive.org/web/20180103162620/http://www.victorianstation.com/lifestylemenu.htm |date=3 January 2018 }} * [http://www.thesmartset.com/article/article12180701.aspx Background on "A Diary in America"] * [http://www.mccord-museum.qc.ca/en/keys/webtours/VQ_P2_17_EN.html Form and Fashion] — the evolution of women's dress during the 19th century (many photographs) * [http://www.mccord-museum.qc.ca/en/keys/games/jeu2/ Educational Game: Mix and Match] — build a 19th-century dress using a virtual mannequin * {{cite web |publisher= [[Victoria and Albert Museum]] |url= http://www.vam.ac.uk/content/articles/v/victorian-dress-at-v-and-a/ |title= Victorian Dress |work= Fashion, Jewellery & Accessories |date= 14 January 2011 |access-date= 2011-04-03}} *[http://cv.vic.gov.au/stories/creative-life/fashion-detective-fashion-fiction-and-forensics/ Fashion detective: Fashion, Fiction and Forensics in nineteenth century Australian fashion] on Culture Victoria {{Timeline of clothing and fashion|state=collapsed}}{{Victorian era|state=collapsed}} [[Category:Victorian fashion| ]] [[Category:19th-century fashion|*]] [[Category:1900s fashion]] [[Category:History of Western fashion]] [[Category:19th century in the arts]] =From ''Women in the Victorian era''= ===Victorian women's fashion=== {{Multiple issues|{{tone|date=March 2023}} {{more footnotes needed|date=March 2023}}|section=y}}{{Further|Victorian fashion}} The ideal Victorian woman was pure, chaste, refined, and modest. This ideal was supported by etiquette and manners. The etiquette extended to the pretension of never acknowledging the use of undergarments (sometimes generically referred to as "unmentionables"). The discussion of such a topic, it was feared, would gravitate towards unhealthy attention on anatomical details. As one Victorian lady expressed it: "[those] are not things, my dear, that we speak of; indeed, we try not even to think of them", in contrast to current norms.<ref>{{cite book |last=Cunnington |first=C. Willett |title=English Women's Clothing in the Nineteenth Century: A Comprehensive Guide with 1,117 Illustrations |publisher=Dover Publications |year=1990 |isbn=978-0-486-26323-6 |pages=20}}</ref> The pretence of avoiding acknowledgement of anatomical realities met with embarrassing failure on occasion. In 1859, the Hon. Eleanor Stanley wrote about an incident where the [[Louisa Cavendish, Duchess of Devonshire|Duchess of Manchester]] moved too quickly while manoeuvring over a [[stile]], tripping over her large [[hoop skirt]]: {{blockquote|[the Duchess] caught a hoop of her cage in it and went regularly head over heels lighting on her feet with her cage and whole petticoats above, above her head. They say there was never such a thing seen – and the other ladies hardly knew whether to be thankful or not that a part of her undergarments consisted in a pair of scarlet tartan [[knickerbockers (clothing)|knickerbockers]] (the things Charlie shoots in) which were revealed to the view of all the world in general and the [[Aimable Pélissier|Duc de Malakoff]] in particular".<ref>{{cite book|last=Cunnington|first=C. Willett|title=English Women's Clothing in the Nineteenth Century: A Comprehensive Guide with 1,117 Illustrations|year=1990|publisher=Dover Publications|isbn=978-0-486-26323-6|pages=20–1}}</ref>}} However, despite the fact that Victorians considered the mention of women's undergarments in mixed company unacceptable, men's entertainment made great comedic material out of the topic of ladies' [[bloomers (clothing)|bloomers]], including men's magazines and music hall skits.<ref>{{cite book |last=Cunnington |first=C. Willett |title=English Women's Clothing in the Nineteenth Century: A Comprehensive Guide with 1,117 Illustrations |publisher=Dover Publications |year=1990 |isbn=978-0-486-26323-6 |pages=22}}</ref> Victorian women's clothing followed trends that emphasised elaborate dresses, skirts with wide volume created by the use of layered material such as [[crinoline]]s, hoop skirt frames, and heavy fabrics. Because of the impracticality and health impact of the era's fashions, a [[Victorian dress reform|dress reform movement]] began among women. The ideal silhouette of the time demanded a narrow waist, which was accomplished by constricting the abdomen with a laced [[corset]]. While the silhouette was striking, and the dresses themselves were often exquisitely detailed creations, the fashions were cumbersome. At best, they restricted women's movements and at worst, they had a harmful effect on women's health. Physicians turned their attention to the use of corsets and determined that they caused several medical problems: compression of the thorax, restricted breathing, organ displacement, poor circulation, and prolapsed uterus.<ref name="O'Connor"/> Articles advocating the reform of women's clothing by the British National Health Society, the Ladies' Dress Association, and the [[Rational Dress Society]] were reprinted in ''The Canada Lancet'', Canada's medical journal. In 1884, Dr J. Algernon Temple of Toronto even voiced concern that the fashions were having a negative impact on the health of young women from the working classes. He pointed out that a young working-class woman was likely to spend a large part of her earnings on fine hats and shawls, while "her feet are improperly protected, and she wears no flannel petticoat or woollen stockings".<ref name="O'Connor"/> [[File:Bloomers.jpg|thumb|1850s illustration of a woman wearing [[bloomers]]]] [[Florence Pomeroy]], Lady Haberton, was president of the Rational Dress movement in Britain. At a National Health Society exhibition held in 1882, Viscountess Haliburton presented her invention of a "[[divided skirt]]", which was a long skirt that cleared the ground, with separate halves at the bottom made with material attached to the bottom of the skirt. She hoped that her invention would become popular by supporting women's freedom of physical movement, but the British public was not impressed by the invention, perhaps because of the negative "unwomanly" association of the style with the American [[Bloomers]] movement.<ref>{{cite book|last=Murray|first=Janet Horowitz|title=Strong-Minded Women and Other Lost Voices from 19th Century England|year=1982|publisher=Pantheon Books|location=New York|isbn=0-394-71044-4|pages=[https://archive.org/details/strongmindedwome00jane/page/68 68–70]|url=https://archive.org/details/strongmindedwome00jane/page/68}}</ref> [[Amelia Jenks Bloomer]] had encouraged the wearing of visible bloomers by feminists to assert their right to wear comfortable and practical clothing, but it was no more than a passing fashion itself among radical feminists. The movement to reform women's dress would persist and have long-term success, however; by the 1920s, [[Coco Chanel]] was successful at selling a progressive, far less restrictive silhouette that abandoned the corset and raised hemlines. The new silhouette symbolised modernism for trendy young women and became the 20th century standard. Other Paris designers continued reintroducing pants for women and the trend was gradually adopted over the next century. Fashion trends, in one sense, travelled "full circle" over the course of the Victorian era. The popular women's styles during the [[Georgian era]], and at the very beginning of Victoria's reign, emphasized a simple style influenced by flowing gowns worn by women in [[Ancient Greek clothing|Ancient Greece]] and [[Clothing in ancient Rome|Rome]]. The [[Empire waist]] silhouette was replaced by a trend towards ornate styles and an artificial silhouette, with the restrictiveness of women's clothing reaching its low point during the mid-century passion for narrow corseted waists and hoop skirts. The iconic wide-brimmed women's hats of the later Victorian era also followed the trend towards ostentatious display. Hats began the Victorian era as simple [[Bonnet (headgear)|bonnets]]. By the 1880s, milliners were tested by the competition among women to top their outfits with the most creative (and extravagant) hats, designed with expensive materials such as silk flowers and exotic plumes such as ostrich and peacock. As the Victorian era drew to a close, however, fashions were showing indications of a popular backlash against excessive styles. Model, actress and socialite [[Lillie Langtry]] took London by storm in the 1870s, attracting notice for wearing simple black dresses to social events. Combined with her natural beauty, the style appeared dramatic. Fashions followed her example (as well as Queen Victoria's wearing of mourning black later in her reign). According to [[Harold Koda]], the former Curator-in-chief of the [[Costume Institute at The Met|Metropolitan Museum of Art's Costume Institute]],<ref>{{cite web|url=http://www.metmuseum.org/about-the-museum/press-room/exhibitions/2014/death-becomes-her|title=Death Becomes Her: A Century of Mourning Attire : October 21, 2014-February 1, 2015|website=Metmuseuim.org|access-date=7 November 2021}}</ref> "The predominantly black palette of [[mourning]] dramatizes the evolution of period silhouettes and the increasing absorption of fashion ideals into this most codified of etiquettes," said Koda, "The veiled widow could elicit sympathy as well as predatory male advances. As a woman of sexual experience without marital constraints, she was often imagined as a potential threat to the social order." ====Evolution of Victorian women's fashion==== <gallery> File:Fashion plate December 1844.jpg|Ladies' December Fashions (1844). Hand-coloured steel engraving from a women's magazine. File:Thegalleryofhmscalcutta james tissot 1876.jpg|''[[The Gallery of HMS Calcutta]]'' by [[James Tissot]] (1876). [[Bustle]]s were fashionable in the 1870s and 1880s. File:Mrs lillie langtry george frederic watts 1880.jpg|''Mrs. Lillie Langtry'' by [[George Frederic Watts]] (1880). File:Five-women-on-queenslander-steps-r.jpg|Fashionable women in [[Queensland]], Australia around 1900. </gallery> {{Short description|Irish writer (born 1963)}} {{Use Irish English|date=August 2025}} {{Use dmy dates|date=August 2025}} {{Infobox writer | name = Darach Ó Scolaí | image = Darach Ó Scolaí.JPG | alt = Man holding prize-winning book | caption = Ó Scolaí in 2019 | birth_name = Darach Ó Scolaí | birth_date = {{Birth date and age|1963|df=y}} | birth_place = [[County Galway]], The Republic of Ireland | death_date = | death_place = | occupation = Writer, artist, publisher | alma_mater = [[University of Galway]] | years_active = 1998–present | genre = Novel, retelling, translation, play, screenplay, illustrated book for children and adults | other_names = | spouse = | children = 3 | awards = [[Awards and Honors received by Darach Ó Scolaí|Awards and Honors]] | signature = | website = }}[[File:Darach Ó Scolaí.JPG|thumb|Darach Ó Scolaí, holding ''Oileán an Órchiste'' (his translation of Robert Louis Stevenson's ''Treasure Island'')]] == Darach Ó Scolaí == Darach Ó Scolaí (<small>Irish:</small> [/ˈda.rax/ /oː/ /sˠkˠoː/l̪ˠəi/]; born 1963<ref>{{Cite web|url=https://portraidi.ie/en/darach-o-scolai/|title=Darach Ó Scolaí|date=20 October 2017|website=Portráidí (Portraits of Irish-Language Writers)|access-date=1 August 2025}}</ref>) is an Irish author who works in a number of genres, from novels, plays and screenplays to illustrated books for children and adults. He began his literary career in 1998 writing screenplays, stage plays, retellings and translations; he began to publish novels in 2008. Ó Scolaí is widely recognized as a leading figure in contemporary Irish literature, known as “one of the most important Irish language writers of his generation”<ref>{{Cite journal|last=Poirtéir|first=Cathal|date=2022|title=? Suil an Daill: Constant Tensions and Shifting Allegiances|url=https://booksirelandmagazine.com/suil-an-daill-constant-tensions-and-shifting-allegiances/|journal=Books Ireland}}</ref> and "one of the great Irish language novelists [duine d’úrscéalaithe móra na Gaeilge]."<ref name=":17" /> His writing has been called “the high literature of the Irish language.”<ref>Ó Coimín, Maitiú. ''Nós'' 2 February 2018). Qtd. in "Táin Bó Cuailnge." ''Leabhar Breac''. Retrieved 25 August 2025.</ref> Much of his fiction is based on a knowledge of traditional Irish tales and narrative practices as well as Irish history. He specializes in literary and [[wikipedia:Historical_fiction|historical fiction]], or as novelist Alan Titley says, Ó Scolaí’s “peak (for now), or at least his greatest imaginative interest, is the historical novel [tá an chuma air gurb é a bhuaic (go fóill), nó ar a laghad, a mhórspéis samhlaíochta, an t-úrscéal staire].”<ref name=":11">{{Cite journal|last=Titley|first=Alan|date=Fall 2020|title=An Stíl Go Deo!: Soather Dharach Uí Scolaí (The style would be forever!: Worker Darach Ó Scolaí)|url=https://www.jstor.org/stable/27046090|journal=Comhar|volume=80, No. 10|pages=27|via=JSTOR}}</ref> His retellings of old stories and tales from their original Middle and Early-Modern Irish into Modern Irish ([[wikipedia:Irish_language|Gaeilge]]) are respected for their accessibility to students and language learners as well as for their artistry. Ó Scolaí also regularly reviews books and lectures and writes on literature and culture. Beyond his writing, Ó Scolaí is a publisher and has co-produced a number of film, television shows and stage plays. == Life == Ó Scolaí was born in Dublin and raised in the Galway [[wikipedia:Gaeltacht#Galway Gaeltacht|Gaeltacht]] (Irish-speaking) regions of Cois Fharraige on the north shore of Galway Bay, in the Republic of Ireland, where he lives now with his wife and children in Lochán Beag (Indreabhán).<ref name=":7">{{Cite journal|date=30 October 2024|title=Duais don úrscéal liteartha is fearr buaite ag Darach Ó Scolaí ag Oireachtas na Samhna|url=https://tuairisc.ie/duais-don-ursceal-liteartha-is-fearr-buaite-ag-darach-o-scolai-ag-oireachtas-na-samhna/|journal=Tuairisc}}</ref><ref>{{Cite journal|last=Ní Scolaí|first=Aifric|date=2024|title=Darach Ó Scolaí|url=https://www.taiscecf.ie/ealaiontoiri?category=Scr%C3%ADbhneoir|journal=Taisce Chois Fharraige}}</ref> He graduated the [[wikipedia:University_of_Galway|University of Galway]] (then University College Galway) with a B.A. in 1983.<ref>{{Cite web|url=https://www.linkedin.com/in/darach-ó-scolaí-20026920/|title=Darach Ó Scolaí|last=Ó Scolaí|first=Darach|date=August 2025|website=LinkedIn}}</ref> === Writing and Publishing === Ó Scolaí writes in Irish ([[wikipedia:Irish_language|Gaeilge]]), his native language, and lives in an area defined for the predominant presence of Irish as the vernacular language, the language spoken at home. Irish was the language of his parents' home and is the language of children as well. He is fluent in Irish and English and conversant in French. None of his works has been translated into English. ==== Leabhar Breac ==== In 1995 Darach Ó Scolaí and his brother Caomhán Ó Scolaí — a [[wikipedia:Typography|typographer]] and designer — founded the publishing house Leabhar Breac at Indreabhán (Inverin), County Galway. Their father “Séamas Ó Scolaí was an editor at An Gúm and worked on the Irish-English dictionary team [bhí a n-athair Séamas Ó Scolaí ina eagarthóir sa Ghúm agus d’oibrigh sé ar fhoireann an fhoclóra Gaeilge-Béarla].”<ref name=":0">{{Cite web|url=https://leabharbreac.com/en/about-us/|title=About Us|date=2024|website=Leabhar Breac|access-date=1 July 2025}}</ref> Darach Ó Scolaí has been publisher and literary editor at Leabhar Breac since its founding. Named for [[wikipedia:An_Leabhar_Breac|An Leabhar Breac (The Speckled Book)]], Leabhar Breac publishing house has more than 140 books in print.<ref name=":0" /> Leabhar Breac aims to publish Irish-language books that meet “a high literary and artistic standard.”<ref name=":0" /> Besides the content, Leabhar Breac is known for the typically "superb [thar cionn]" quality of the design and production of the "physical book [leabhar fisiciúil]."<ref name=":8">{{Cite journal|last=Ní Mhuilneoir|first=Gráinne|date=30 July 2024|title=‘Bláthnaid’ – leabhar álainn i sraithín álainn faoi mhná|url=https://tuairisc.ie/blathnaid-leabhar-alainn-i-sraithin-alainn-faoi-mhna/|journal=Tuairisc}}</ref> Its books regularly win awards for literary and artistic quality. Leabhar Breac also publishes translations for children and adults from various early versions of Irish as well as from French and English (and has published translations of books for young readers from Spanish, Catalan, and Italian as well). Leabhar Breac prints its books in Ireland. === Stage and Screen === ==== Rosg ==== In 1998 along with Ciarán Ó Cofaigh,<ref name=":1">{{Cite web|url=http://www.rosg.ie/en/about/History_6/|title=About Us: History|date=July 2025|website=Rosg|access-date=1 August 2025}}</ref> Ó Scolaí co-founded the film and television production company [http://www.rosg.ie/en/ Rosg] and was co-director until 2006. Rosg produced Ó ScolaÍ’s films ''Cosa Nite'' (1999), ''An Leabhar'' (2001) and ''Na Cloigne'' (2010). He left Rosg in 2006 to devote his time to other artistic activities. ==== Ealaín ar Oileán ==== In 2004, along with Val Balance, Ó Scolaí co-founded the annual artists' symposium Ealaín ar Oileán (trans., Art on an Island). The Irish-language symposium was held annually in the Áras Éanna arts and cultural center on Inis Oírr ([[wikipedia:Inisheer|Inisheer]], the smallest of the [[wikipedia:Aran_Islands|Aran Islands]]) from 2004 to 2013. Ó Scolaí was its co-director from its founding<ref>{{Cite web|url=https://ga.wikipedia.org/wiki/Darach_Ó_Scolaí.|title=Darach Ó Scolaí|date=3 February 2024|website=Vicipéid|access-date=1 July 2025}}</ref> until 2013. Besides being its co-director, Ó Scolaí has taken part in this conference as an artist<ref>{{Cite journal|date=16 January 2005|title=Darach Ó Scolaí|url=https://web.archive.org/web/20050116163252/http://bliainiris.com/authors/darach_oscolai.html|journal=Bliainiris}}</ref> and writer<ref name=":2">{{Cite web|url=http://ealainaroilean.ie/ealainaroilean.html|title=The Conference|date=7 September 2013|website=Ealaín ar Oileán|archive-url=https://web.archive.org/web/20130907083744/http://ealainaroilean.ie/ealainaroilean.html|archive-date=7 September 2013|access-date=1 August 2025}}</ref>. ==== Salamandar ==== In 2006 Ó Scolaí founded the stage production company Salamandar and directed his own play ''An Braon Aníos''. His plays ''An tSeanbhróg'' (2009) and ''Craos'' (2008) were also produced by Salamandar.<ref name=":19">{{Cite web|url=https://leabharbreac.com/en/product-category/darach-o-scolai/|title=Darach Ó Scolaí|date=2024|website=Leabhar Breac|access-date=1 July 2025}}</ref> == Works == === Novels === * [[wikipedia:An_Cléireach|''An Cléireach'' (trans., ''The Clerk'')]], Leabhar Breac, 2007. The Oireachtas Prize for Literary Fiction, 2007; The Ó Súilleabháin Award (Book of the Year) in 2008, and "named as ‘the best novel since the turn of the Century’ by Comhar."<ref>{{Cite web|url=https://leabharbreac.com/en/shop/fiction/an-cleireach/|title=An Cléireach - Leabhar Breac - Irish language novel|website=Leabhar Breac|language=en-US|access-date=2025-10-24}}</ref> * ''Na Comharthaí'' (trans., ''The Signs''), Leabhar Breac, 2014. * ''Súil an Daill'' (trans., ''The Eye of the Blind''), Leabhar Breac, 2021. The Oireachtas Prize for Literary Fiction, 2019.<ref name=":4">{{Cite web|url=https://leabharbreac.com/en/shop/fiction/suil-an-daill/|title=Súil an Daill|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> * ''Bódléar'', Leabhar Breac, 2024. The Oireachtas Prize for Literary Fiction, 2024<ref name=":7" />; The Ó Súilleabháin Award (Book of the Year) in 2025; featured in the 2025 Listen-Up Irish Summer Challenge for students of the Irish language.<ref>{{Cite news|url=https://connachttribune.ie/novel-approach-helps-people-learn-irish-in-a-creative-way/|title=Novel approach helps people learn Irish in a creative way|last=Murphy|first=Judy|date=3 October 2025|work=Connaught Tribune|access-date=24 October 2025}}</ref> === Retellings, Translations and Editions === The retellings and translations are into modern Irish. * ''Feis Tigh Chonáin'' (trans., ''The Feast of Conán's House''), Leabhar Breac, 2000; a retelling of a 15^th-century tale from the [[wikipedia:Fenian_Cycle|Fenian Cycle]].<ref>{{Cite web|url=https://leabharbreac.com/en/shop/fiction/feis-tigh-chonain/|title=Feis Tigh Chonáin|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> * ''An Ceithearnach Caolriabhach'' (trans., ''The Narrow-Striped Kern''), Leabhar Breac, 2002; a retelling from c. 1500, also illustrated by Darach Ó ScolaÍ.<ref>{{Cite web|url=https://leabharbreac.com/en/shop/fiction/an-ceithearnach-caolriabhach/|title=An Ceithearnach Caolriabhach|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> * ''Táin Bó Cuailnge'' (trans., ''The Cattle Raid of Cooley''), Leabhar Breac, 2017, both a modern edition of an 11th-century epic and an annotated edition.<ref name=":3">{{Cite web|url=https://leabharbreac.com/en/shop/darach-o-scolai/tain-bo-cuailnge-2-2/|title=Táin Bó Cuailnge|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> "''Táin Bó Cuailnge'' won the Aodán Mac Poilín Memorial Prize 2017."<ref name=":19" /> * ''Deirdre'', Leabhar Breac, 2023, a “picture book for adults” with artist Anastasia Melnykova.<ref>{{Cite web|url=https://leabharbreac.com/en/shop/darach-o-scolai/deirdre/|title=Deirdre|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> Part of the [[wikipedia:Ulster_Cycle|Ulster Cycle]], ''Deirdre'' is a retelling of the story of possibly the most widely known Irish figure from the early tales and sagas.<ref>{{Cite book|title=A Dictionary of Celtic Mythology|last=MacKillop|first=James|publisher=Oxford University Press|year=2004|isbn=9780198609674|pages=181}}</ref> * ''Bláthnaid'', Leabhar Breac, 2024, a “picture book for adults” with artist Anastasia Melnykova; “one of the great stories of the [[wikipedia:Ulster_Cycle|Ulster Cycle]].”<ref name=":4" /> * ''Sadhbh,'' Leabhar Breac, 2025, a picture book for adult readers, illustrated by Alé Mercado; a retelling of the medieval tale ''Ceasacht Inghine Ghuile (''trans., ''The Complaint of Guile's Daughter'').<ref name=":5">{{Cite web|url=https://leabharbreac.com/en/tales-of-wonder/|title=Tales of Wonder|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> * ''Eoghan Béal'', Leabhar Breac, 2025, a picture book for adult readers illustrated by Alé Mercado<ref name=":5" />; a retelling of the medieval tale ''[https://ga.wikipedia.org/wiki/Caithr%C3%A9im_Cellaig Cathréim Ceallaigh]'' from ''The Yellow Book of Leacan.''<ref name=":5" /> === For Young Readers === Ó Scolaí has written illustrated books for young readers (8–10 years old) in two series, the Fionn Series and the Scéalta Staire series, and translated a large number of classics and popular books for children of all ages. The number of these written and translated works suggests a commitment to children and their literacy in Irish. The Fionn Series “is a retelling ... of the great legends of the Fianna for the young Irish readers of today.”<ref name=":6">{{Cite web|url=https://leabharbreac.com/en/shop/oige-en/8-9/doiteoir-na-samhna/|title=Dóiteoir na Samhna|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> [[wikipedia:The_Boyhood_Deeds_of_Fionn|Macgnímartha Finn (The Boyhood Deeds of Fionn)]] is a medieval story in the [[wikipedia:Fenian_Cycle|Fenian Cycle]]. * ''An Bradán Feasa'' (trans., ''The Salmon of Knowledge''), Leabhar Breac, 2010, “shortlisted for the Réics Carlo award 2010.”<ref name=":9">{{Cite web|url=https://leabharbreac.com/en/shop/oige-en/8-9/an-bradan-feasa/|title=An Bradán Feasa|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> * ''Dóiteoir na Samhna'' (trans., ''The Halloween Burner''), 2010.<ref name=":6" /> * ''Bodach an Chóta Lachna'' (trans., ''The Churl in the Dun Coat''), 2011.<ref>{{Cite web|url=https://leabharbreac.com/en/shop/oige-en/7-8/bodach-an-chota-lachna/|title=Bodach an Chóta Lachna|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> The Scéalta Staire (Historical Stories) series<ref name=":9" /> * ''Mánas Ó Dónaill'', 2000. * ''Seán Ó Néill'', Leabhar Breac, 2000. * ''Gráinne Mhaol Ní Mháille'', Leabhar Breac, 2003. * ''Tadhg Dall Ó hUiginn'', Leabhar Breac, 2003. ==== Translations ==== * Robert Louis Stevenson, ''Oileán an Órchiste'' (trans. of ''Treasure Island''), Leabhar Breac, 2014.<ref>{{Cite journal|date=2025-06-19|title=Oireachtas na Gaeilge|url=https://en.wikipedia.org/w/index.php?title=Oireachtas_na_Gaeilge&oldid=1296394643|journal=Wikipedia|language=en}}</ref> * Robert Louis Stevenson, ''An Fuadach'' (trans. of ''Kidnapped''), Leabhar Breac, 2016. * Clement Clarke Moore, ''Cuairt San Nioclás'' (trans. of ''A Visit from St. Nicholas'', or "'Twas the Night Before Christmas"), Leabhar Breac, 2022. '''''The Corto Maltese Graphic Novels''''' Written in Italian by Hugo Pratt and translated by Ó Scolaí, both adults and teenagers read this series of Italian adventure graphic novels.<ref>{{Cite journal|date=2025-07-01|title=Corto Maltese|url=https://en.wikipedia.org/w/index.php?title=Corto_Maltese&oldid=1298285365|journal=Wikipedia|language=en}}</ref> Ó Scolaí's '''translation of ''Corto Maltese''''' was listed in 2017 among "The 30 Irish books that Irish people love."<ref>{{Cite journal|last=Ó Murchú|first=Eoin P.|date=09/06/2017|title=Na 30 leabhar Gaeilge is fearr leis na Gaeil [The 30 Irish books that Irish people love]|url=https://nos.ie/cultur/leabhair/an-30-leabhar-gaeilge-is-fearr-leis-na-gaeil/|journal=Nós}}</ref> * Hugo Pratt, ''Corto: Port na Farraige Goirt'', Leabhar Breac, 2013. * Hugo Pratt, ''Corto: The Golden House in Samarkand'', 2014. * Hugo Pratt, ''Corto: Na Liopard-Fhir ó Rufiji'' (trans. of ''Corto: The Leopard Men of Rufiji''), Leabhar Breac, 2014. * Hugo Pratt, ''Corto: In Ainm Dé Uilthrócairigh'' (trans. of ''Corto: In the Name of God All-Merciful''), Leabhar Breac, 2014. * Hugo Pratt, ''Corto: Tóraíocht Eile'' (trans. of ''Corto: Another Quest''), Leabhar Breac, 2014. * Hugo Pratt, ''Corto: Sa tSibéir'' (trans. of ''Corto: In Siberia''), Leabhar Breac, 2016. '''''Other Translations for Children''''' Ó Scolaí has translated into Irish six books from the ''Le Pavillon Noir'' (trans., ''Jolly Roger'') series by Alain Surget; four books from the ''Catalan First Steps'' series by Enric Lluch Girbés and the ''Caitlín & Cormac'' series by Joan Carles; three books from the ''Louisette le Taupe'' series by Bruno Heitz, and three books from the ''Loup'' series by Orianne Lallemand. === Plays and Screenplays === ==== Stage Plays ==== Ó Scolaí was writer and director of the original productions of two plays in the ''Trí Bhraon'' (trans., ''Three Drops'') trilogy; ''Coinneáil Orainn'' was directed by Darach Mac Con Iomaire and staged by An Taibhdhearc. All three plays have been published in book form by Leabhar Breac. * ''Coinneáil Orainn'' (trans., ''We'll Keep Going''), 2005.<ref>{{Cite web|url=https://irishplayography.com/play?playid=32553|title=Coinneáil Orainn|date=2025|website=PlayographyIreland: A Comprehensive Database of New Irish Plays Produced Professionally Since 1904.|access-date=25 August 2025}}</ref> The first play in the ''Trí Bhraon'' (''Three Drops'') trilogy. [[wikipedia:Taibhdhearc_na_Gaillimhe|An Taibhdhearc]], the national Irish-language theatre of Ireland, toured the country in 2005 with ''Coinneáil Orainn''.<ref>{{Cite web|url=https://leabharbreac.com/en/shop/darach-o-scolai/coinneail-orainn/|title=Coinneáil Orainn|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> Walter Macken Prize, 2005; BBC Stewart Parker Award, 2006.<ref>{{Cite web|url=https://irishplayography.com/person/darach-scola|title=Darach Ó Scolaí|date=2025|website=PlayographyIreland: A Comprehensive Database of New Irish Plays Produced Professionally Since 1904.|access-date=25 August 2025}}</ref> * ''Branwen'', 2006, by Darach Ó Scolaí and Ifor ap Glyn, in Irish, Welsh and English, co-produced by Project Arts Centre and Llwyfan Gogledd Cymru, toured the Republic of Ireland and Wales.<ref>{{Cite web|url=https://irishplayography.com/play?playid=32418|title=Branwen|date=2025|website=PlayographyIreland: A Comprehensive Database of New Irish Plays Produced Professionally Since 1904|access-date=25 August 2025}}</ref> * ''An Braon'' Aníos (trans., ''Rising Damp''), 2006, directed by Ó Scolaí.<ref>{{Cite web|url=https://irishplayography.com/play?playid=32461|title=An Braon Aníos|date=2025|website=PlayographyIreland: A Comprehensive Database of New Irish Plays Produced Professionally Since 1904|access-date=25 August 2025}}</ref> The second play in the ''Trí Bhraon'' (''Three Drops'') trilogy. “The Salamandar company toured the country in 2006-07 with this play, and Salamandar also produced a radio version of the play for RTÉ Raidió na Gaeltachta in 2009.”<ref>{{Cite web|url=https://leabharbreac.com/en/shop/darach-o-scolai/an-braon-anios/|title=An Braon Aníos|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> * ''Craos'' (trans., ''Gluttony''), 2008, directed by Ó Scolaí.<ref name=":13">{{Cite web|url=https://irishplayography.com/play?playid=32867|title=Craos|date=2025|website=PlayographyIreland: A Comprehensive Database of New Irish Plays Produced Professionally Since 1904|access-date=25 August 2025}}</ref> The third play in the ''Trí Bhraon'' (''Three Drops'') trilogy, it toured to Cork and Belfast.<ref name=":13" /> A review of the 2008 Salamander performance in the ''Irish Times'' says, “a humorous play which offers plenty to think about, fine acting, and sparklingly witty dialogue.”<ref>{{Cite web|url=https://leabharbreac.com/en/shop/darach-o-scolai/craos-2/|title=Craos|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> * ''A+E'', 2008, by Ríonach Ní Néill and Darach Ó Scolaí, "dance and music drama," co-produced by Ciotóg and Salamandar.<ref>{{Cite web|url=https://irishplayography.com/play?playid=32962|title=A+E|date=2025|website=PlayographyIreland: A Comprehensive Database of New Irish Plays Produced Professionally Since 1904|access-date=25 August 2025}}</ref> * ''An tSeanbhróg'' (trans., ''The Old Shoe''), 2009, produced by Salamander<ref>{{Cite web|url=https://irishplayography.com/play?playid=33042|title=An tSeanbhróg|date=2025|website=PlayographyIreland: A Comprehensive Database of New Irish Plays Produced Professionally Since 1904|access-date=25 August 2025}}</ref> and staged in the Axis Arts Centre, Dublin, and the Letterkenny Arts Centre. * '''In ''Mhuir Fhíondorcha/The Wine-Dark Sea: The Homer Project'', Ó Scolaí's translation of Homer's Cyclops story, performed at the 2019 IMRAM festival'''.<ref>{{Cite news|url=https://www.irishtimes.com/culture/books/imram-a-festival-celebrating-the-irish-language-1.4047610|title=Imram: a festival celebrating the Irish language. Liam Carson reveals the myths and legends appearing in this year’s programme|last=Carson|first=Liam|date=11 October 2019|work=The Irish Times|access-date=15 October 2025}}</ref> ==== Screenplays ==== * ''Cosa Nite'' (trans., ''Washed Feet''), short film, 1998 (dir. Dearbhla Walsh, prod. Ciarán Ó Cofaigh, Rosg); "a prose version of ''Cosa Nite'' was published (Rosg 2000)."<ref name=":9" /> Nominated for an Irish Film and Television Award.<ref>{{Citation|title=Cosa Nite (Short 1998) - Awards - IMDb|url=https://www.imdb.com/title/tt0191917/awards/|accessdate=2025-08-25|language=en-US}}</ref> * ''Na Glúnta'' (trans., ''The Generations''), 2001<ref>{{Cite web|url=https://www.iftn.ie/production/production_companies/production_sub/feature/?act1=record&aid=70&rid=3917&tpl=filmography_dets&only=1&force=1|title=Na Glúnta {{!}} The Irish Film & Television Network|website=www.iftn.ie|access-date=2025-08-25}}</ref>, co-directors Ciarán Ó Cofaigh & Darach Ó Scolaí, prod. Ciarán Ó Cofaigh, Rosg. * ''An Leabhar'' (trans., ''The Book''), short film, 2000, (dir. Robert Quinn, prod. Ciarán Ó Cofaigh, Rosg) Rosg, 2000.<ref>{{Citation|title=An Leabhar|url=https://www.imdb.com/title/tt0963767/|publisher=Bord Scannán na hÉireann / The Irish Film Board, ROSG|accessdate=2025-08-25|first=Robert|last=Quinn|others=Colm O&apos;Maonlai, Peadar O&apos;Treasaigh, Diarmuid Mac an Adhastair}}</ref> * ''Na Cloigne'' [trans., The Heads], 3-episide series, 2010 (dir. Robert Quinn, prod. Ciarán Ó Cofaigh, Rosg), TG4.<ref>{{Cite web|url=https://www.imdb.com/title/tt1607924/|title=Na cloigne|date=2010|website=IMDb|access-date=25 August 2025}}</ref> === Nonfiction === Ó Scolaí's essays and lectures are published and his interviews are broadcast regularly, making for a large body of nonfiction critical and analytical work. Here are a few, almost all published in [https://comhar.ie/iris/scribhneoiri/darach-o-scolai/ Comhar]: * “Ceol Ciúin na nÉagmaise” (trans., “The Silent Music of Absence ['''the Fall?''']”), an essay on the 2014 Nobel Prize winner for literature, [[wikipedia:Patrick_Modiano|Patrick Modiano]], ''Comhar'', December 2014. * The Ó Cadhain Lecture: [https://leachtaiuichadhain.clo.ie/leachtai/2014 “Cuimhne agus Díchuimhne (trans., “Memory & Forgetfulness"]), 2014. * “Rithim agus Réim” ("Rhythm and Register"), a public lecture in the University College Dublin lecture series “Ó Thrácht go Twitter” (trans., "From Talk to Twitter"), 2014. * Review of Pádraig Ó Cíobháin’s ''Dréachta Chrích Fodla'', '''Comhar?, ??'''. * “Na Geilt i mBun an Tí” (trans., "The Madmen in Charge"), a talk at the Merriman Winter School, Comhar April 2012.<ref name=":18">{{Cite web|url=http://darachoscolai.ie/beathaisneis.html|title=Darach Ó Scolaí: Beathaisnéis|website=darachoscolai.ie|access-date=2025-09-26}}</ref> * The EFACIS podcast: Síle Ní Choincheannain talks to Darach Ó Scolaí about the historical novel. == Critical Reception == Ó Scolaí’s style has been called “crisp and elegant, and rich in language while being highly readable,”<ref>{{Cite journal|last=Heussaf|first=Anna|date=Summer 2025|title=Bláthnaid—A tale of love, violence and sorcery retold for readers today|url=https://booksirelandmagazine.com/blathnaid-a-tale-of-love-violence-and-sorcery/|journal=Books Ireland}}</ref> with “an unsurpassed richness and precision of language.”<ref name=":12">{{Cite journal|last=Ó Cróinín|first=Breandán|date=Summer 2025|title=unknown|journal=The Limerick Leader}}</ref> “Whimsical, hilarious, and subtly learned” is how Éilis Ní Dhuibhne described his writing.<ref name=":20" /> === Original Works === Ó Scolaí’s first novel, the 2007 ''An Cléireach'' (''The Clerk'') won two prizes and was described as “one of the great historical novels in the Irish language and among the best books written in the language since the beginning of this century.”<ref name=":12" /> Novelist Alan Titley says, “In ''An Cléireach'' Ó Scolaí creates the Ireland of war in the 17th century more fully than any other Irish writer on the subject of war since ''L’Attaque'' Eoghain Ó Thuairisc around 1798 [In ''An Cléireach'' cruthaíonn Ó Scolaí Éire an chogaidh san 17ú haois níos iomláine ná mar a dhein aon scríbhneoir Gaeilge eile ar ábhar cogaidh ó ''L’Attaque'' Eoghain Uí Thuairisc timpeall ar 1798].”<ref name=":11" />{{rp|25, Col. 1a}} Not all the reviews of this first novel were so positive, however; Proinsias O' Drisceoil says for the Irish Times says,<blockquote>This then is a novel in search of a plot, a story that attempts to attain a significance that eludes it.<ref>{{Cite news|url=https://www.irishtimes.com/news/a-disaffected-clerk-in-the-confederates-1.943070|title=A disaffected clerk in the confederates|last=O' Drisceoil|first=Proinsias|date=5 July 2008|work=The Irish Times|access-date=16 October 2025}}</ref></blockquote> In the ''Oxford Handbook of Modern Irish Fiction'' Pádraig Ó Siadhail analyzes rather than reviews ''An Cléireach'': <blockquote>In ''An Cléireach'', Ó Scolaí revisits the trauma of Cromwellian Ireland. The primary narrative device is once again the first-hand account, in this case by Tadhg Ó Dúbháin, a clerk and quartermaster in the Confederate Army in 1650. We sample the hardships, the friendships, the tensions, the rivalries, and the petty jealousies amongst comrades in arms, including remnants of the Gaelic literary class, as the Confederate soldiers, increasingly a rabble more than a cohesive unit, retreat in advance of Cromwell’s forces. ''An Cléireach'' concludes with the narrator and his family in exile in continental Europe. But along the retreat route, and central to the novel, members of the Confederate army camp, rest up, and tell versions of a story about the keeper of the treasured manuscript "Saltair an Easpaig" (The Bishop’s Psalter). Their versions raise issues about memory construction, the limitations of individual perspectives, personal agendas, and how minor changes in the telling of a story can alter our understanding of history, Thus, ''An Cléireach'' complements ''Fontenoy'' in moving beyond more realistic recreation of a historical event or period to interrogate the notion of history as construct.<ref>{{Cite book|title=The Oxford Handbook of Modern Irish Fiction|last=Ó Siadhail|first=Pádraig|publisher=Oxford University Press|year=2020|isbn=9780198754893|editor-last=Harte|editor-first=Liam|pages=598–99|chapter=Contemporary Irish Fiction}}</ref> </blockquote> Of ''Súil an Daill,'' in ''Nós'', Cathal Seoighe says, "The book deserves a significant place among the collection of high-quality books published in recent years that would make you feel sorry for someone who does not speak Irish [Tá áit shuntasach ag dul don leabhar i measc an chnuasaigh leabhair ar ardchaighdeán a foilsíodh le roinnt blianta anuas a d’fhágfadh trua agat don té atá gan Ghaeilge]."<ref>{{Cite journal|last=Seoighe|first=Cathal|date=09/26/2022|title=‘Dar leathmhagairle an diabhail, is leabhar den scoth é seo!’ ['According to the devil’s half-wit, this is a great book!’]|url=https://nos.ie/cultur/leabhair/dar-leathmhagairle-an-diabhail-is-leabhar-den-scoth-e-seo/|journal=Nós}}</ref> ''Bódléar'', Ó Scolaí's most recent book, is a “beautiful novel. There is magic and craftsmanship in it. A small miracle of a book and it is highly recommended.”<ref>{{Cite web|url=https://leabharbreac.com/bodlear-mioruilt-bheag-de-leabhar/|title=Bódléar: Míorúilt bheag de leabhar (Bódléar: A Small Miracle of a Book)|last=Ní Ghairbhí|first=Róisín|date=2024|website=Leabhar Breac|access-date=1 August 2025}}</ref> Éilis Ní Dhuibhne in the ''Irish Times'' says,<blockquote>what a gem! An affectionately gentle satire of the Irish poetic scene during one creatively fluid 19th-century year, the story focuses on a Maigue poet and schoolteacher who goes on a trip to France and returns with camembert, a cafetiere, ‘Fleurs du Mal’, and a mission to convert the local traditionalists to la modernité. Whimsical, hilarious, and subtly learned, it’s absolutely delightful!<ref name=":20">{{Cite journal|last=Ní Dhuibhne|first=Éilis|date=30 June 2025|title=Éilís Ní Dhuibhne on the best Irish language books of 2025 so far: Including a history of the Gaeltacht Civil Rights Movements, a gem of a novel by Darach Ó Scolaí and Joe McHugh’s entertaining account of learning Irish|url=https://www.irishtimes.com/culture/books/review/2025/06/30/eilis-ni-dhuibhne-on-the-best-irish-language-books-of-2025-so-far/|journal=The Irish Times|pages=22}}</ref></blockquote> === Retellings and Translations === ==== ''Táin Bó Cuailnge'' ==== ''Táin Bó Cuailnge'' [''The Cattle Raid of Cooley''] is a modern edition of an 11th-century epic into modern Irish.<ref name=":3" /> Gearóid Denvir reviewed ''Táin Bó Cuailnge'' for ''Comhar'':<blockquote>Darach Ó Scolaí has ​​achieved a feat in this challenging reworking. He has found a high level of the Irish language to tell his story – as he has done before in his groundbreaking novel An Cléireach (2007, Leabhar Breac) and in his other prose works. This book is a decoration of the language, literature and culture of the Irish language, following the path of the old storytellers and writers and presenting material from the tradition to his own generation according to the understandings of his own time. The book will be a classic that will be of great interest to all readers of the Irish language, both ordinary readers, students, scholars and writers, and there should be a copy in every home in the country. [Tá éacht déanta ag Darach Ó Scolaí san athleagan dúshlánach seo. Tá réim ard den teanga Ghaeilge aimsithe aige lena scéal a inseacht – mar a rinne sé cheana ina úrscéal ceannródaíoch An Cléireach (2007, Leabhar Breac) agus i saothair eile phróis dá chuid. Is maisiú ar an teanga agus ar litríocht agus cultúr na Gaeilge an leabhar seo a leanas conair na seanscéalaithe agus na seanscríobhaithe agus ábhar de chuid an traidisiúin á chur i láthair a ghlúine féin aige de réir thuiscintí a linne féin. Clasaic a bheas sa leabhar a gcuirfidh léitheoirí uilig na Gaeilge, idir ghnáthléitheoirí, mhic léinn, scoláirí agus scríbhneoirí spéis thar na bearta ann, agus ba cheart cóip a bheith i chuile theach sa tír.]<ref name=":15">{{Cite journal|last=Denvir|first=Gearóid|date=April 2018|title=Táin Bó Cuailgne|url=https://comhar.ie/iris/78/4/leirmheas/|journal=Comhar|via=JSTOR}}</ref> </blockquote>Cathal Poirtéir says, "The freshness and richness of Ó Scolaí’s version are a joy …. The author delights us with the linguistic and stylistic richness of the ancient epic in a modern-Irish version that reflects the original’s spirit and language."<ref>{{Cite journal|last=Poirtéir|first=Cathal|date=May/June 2018|title=Leabhair Idir Lámha|url=https://www.jstor.org/stable/26564180|journal=Books Ireland|pages=46–47|via=JSTOR}}</ref>{{rp|47}} Novelist and academic Alan Titley calls Ó Scolaí's "a wonderful gutsy telling" of ''Táin Bó Cuailnge''.<ref>{{Cite news|url=https://www.irishtimes.com/culture/2023/03/11/the-tain-retold-maeve-and-ailills-spat-could-be-out-of-a-soap-opera/|title=The Táin retold: ‘Maeve and Ailill’s spat could be out of a soap opera’|last=Titley|first=Alan|date=11 March 2023|work=The Irish Times|access-date=16 October 2025}}</ref> ==== ''Deirdre'' ==== Marie Whelton, in "Léann Teanga" ("Language Studies"), in the 2024 ''An Reiviú'' says,<blockquote>this version [of ''Deirdre''] by Darach Ó Scolaí succeeds in skillfully capturing and portraying the complexity of gender and power issues in the ‘Deirdre’ tradition [éiríonn leis an leagan seo le Darach Ó Scolaí castacht cheisteanna na hinscne agus na cumhachta i dtraidisiún scéal Dheirdre a ghabháil agus a léiriú go sciliúil]. … There is no doubt that this new version greatly contributes to the legacy of the story and that it revives that legacy thoughtfully and artistically [Níl amhras faoi ach go gcuireann an leagan úr seo go mór le hoidhreacht an scéil agus go ndéanann sé an oidhreacht sin a athbheochan go tuisceanach agus go healaíonta.].<ref name=":16">{{Cite web|url=https://www.tara.tcd.ie/tara8/server/api/core/bitstreams/3c20175a-7631-44b2-8b0f-f454edd712b4/content|title=An Artistic Retelling of Deirdre's Tale and the Defeat of Conor Review of Deirdre or the Ship of Mac Uisnigh by Darach Ó Scolaí [Athinsint Ealaíonta ar Oidhe Dheirdre agus ar Ansmacht Chonchúir Léirmheas ar Deirdre nó Loingeas Mhac Uisnigh le Darach Ó Scolaí]|last=Whelton|first=Marie|date=2024|website=The Review [An Reiviú], Language Studies [Léann Teanga]|access-date=25 September 2025}}</ref></blockquote> === Works for Young Readers === Meadhbh Ní Eadhra said of ''Bodach an Chóta Lachna'' that it was "Beautiful Irish, but easy to understand for young readers."<ref>Ní Eadhra, Meadhbh. In ''Gaelscéal'', qtd. in "Bodach an Chóta Lachna" https://leabharbreac.com/en/shop/oige-en/7-8/bodach-an-chota-lachna/.</ref> == Awards and Honors == Ó Scolaí's works are regularly nominated and make the short list for prizes, an honor in itself, but they are generally not listed here unless they are named as the first-place winner in their category. === Oireachtas Prize === The Oireachtas Prize is the literary prize awarded by [[wikipedia:Oireachtas_na_Gaeilge|Oireachtas na Gaeilge]], the annual arts festival dedicated to Irish language, arts and culture. Darach Ó Scolaí has won the Oireachtas Prize for Literary Fiction three times, once for ''An Cléireach'' (''The Clerk'') in 2007, for ''Súil an Daill'' (''The Eye of the Blind'') in 2021 and for ''Bódléar'' in 2024. * 2007, for ''An Cléireach'' (trans., ''The Clerk'') — “(a special prize commemorating the 400th anniversary of the foundation of Coláiste na nGael in Louvain, awarded under the auspices of the Franciscan Province of Ireland). The prize of €10,000 was the largest prize ever awarded to an Irish language novel [(duais speisialta chomórtha 400 bliain bhunú Choláiste na nGael i Lobháin a bronnadh faoi urraíocht Phroibhinse Phroinsiasach na hÉireann). Ba é an duais €10,000 sin an duais ba mhó a bronnadh riamh ar úrscéal Gaeilge].”<ref name=":18" /> * 2021, for ''Súil an Daill'' (''The Eye of the Blind'') * 2024, for ''Bódléar'' === Ó Shúilleabháin Award, Irish language “Book of the Year” === The first prize of this award includes €5,000 to the publisher and €2,500 to the author of the winning work.<ref name=":10">{{Cite journal|date=15 August 2023|title=20 saothar san iomaíocht do ‘Leabhair Ghaeilge na Bliana 2023’|url=https://tuairisc.ie/20-saothar-san-iomaiocht-do-leabhair-ghaeilge-na-bliana-2023/|journal=Tuairisc}}</ref> * ''An Cléireach'' (''The Clerk'').<ref>{{Cite web|url=http:/www.gaelport.com/uploads/documents/edition19.html|title=Eagrán / Edition 19 - 04 11 2008|date=4/11/2008|website=Internet Archive|archive-url=https://web.archive.org/web/20130525011340/http:/www.gaelport.com/uploads/documents/edition19.html|archive-date=25 May 2013|access-date=25 August 2025}}</ref> * ''Táin Bó Cuailnge'', 2018. * ''Bódléar'', 2025. ==== De Bhaldraithe Award ==== The Gradam de Bhaldraithe is awarded to the best work in translation.<ref name=":10" /> * ''Cuairt San Nioclás,'' a translation of Clement Clarke Moore's ''A Visit from St. Nicholas'', or "'Twas the Night Before Christmas."<ref name=":10" /> ==== Other ==== * Walter Macken Prize, for ''Coinneáil Orainn'' (trans., ''We'll Keep Going''), 2005 * Bháiteir Uí Mhaicín Memorial Award, for ''Coinneáil Orainn'' (trans., ''We'll Keep Going''), 2005<ref>{{Cite news|url=https://www.irishtimes.com/gaeilge/tuarascail/duais-oireachtais-1.501571|title=Oireachtas Prize: Over €50,000 was awarded to writers in the Oireachtas Literary Competitions at an event in Dublin last night. Winners… [Duais Oireachtais: Bronnadh breis agus €50,000 ar scríbhneoirí i gComórtais Liteartha an Oireachtais ar ócáid i mBaile Átha Cliath aréir. Bhuaigh…]|work=5 October 2005|access-date=15 October 2025}}</ref> * BBC Stewart Parker Award, for ''Coinneáil Orainn'' (trans., ''We'll Keep Going''), 2006 * The Aodán Mac Póilín Commemorative Prize, for ''Táin Bó Cuailnge'' (trans., ''The Cattle Raid of Cooley''), 2017 == External Links == * Leabhar Breac website: https://leabharbreac.com/en/ * Leabhar Breac Facebook pages: * Rosg website: [http://www.rosg.ie/en/ <nowiki>http://ww</nowiki>w.rosg.ie/en/] * Art on the Island (Ealaín ar Oileán) website, archived at the Wayback Machine: https://web.archive.org/web/20130601000520/http://ealainaroilean.ie/ 31 March 2012, 1 June 2013 and 8 January 2014 * Darach Ó Scolaí's website Archived 25 September 2015 at the Wayback Machine: https://web.archive.org/web/20150925103456/http://darachoscolai.ie/ * Youtube video of [https://www.youtube.com/watch?v=OlP2AmSBzXc Breandán Ó Cróinin introducing Deirdre at the book launch] in the pub Tigh Mholly (Molly’s House). == Primordial Ooze == * Known for his sensitivity to language and voices. * Finish scanning through JSTOR * Scan through Irish Times, 56 hits * Check Goodreads * Check YouTube (In the spring of 2013, the arts programme Imeall interviewed the author on TG4.) * Check both Wikipedias for pages on the origins of the retold tales (like Deirdre) and link to this article * Propose link from University of Galway page once Darach’s is up * Write Irish National Biography (<nowiki>https://www.dib.ie</nowiki>) to propose an article about Darach once the Wikip article is done? See what they say. * Link to Ó Scolaí from the Wikipedia * Make sure links '''to''' Wikipedia in the actual encyclopedia work right === Not Placed Yet === * "So here are the books that Irish people love the most! [Mar sin seo iad na leabhair is gile leis na Gaeil!]" — "32. An Cléireach – Darach Ó Scolaí (2)" [18 books got 2 votes, and then they're alphabetized by author's last name, so the 32 of 34 doesn't signify the specificity it seems to]<ref name=":14">{{Cite journal|last=Ó Murchú|first=Eoin P.|date=9 June 2017|title=Na 30 leabhar Gaeilge is fearr leis na Gaeil. [The 30 best Irish books for Irish people]|url=https://nos.ie/cultur/leabhair/an-30-leabhar-gaeilge-is-fearr-leis-na-gaeil/|journal=Nós}}</ref> * "Below is a list of those 111 works – a list that shows a great deal of diversity in the reading habits of Irish speakers.Here is a list of those 111 works – a list that shows a great deal of diversity in the reading habits of Irish speakers [Anseo thíos tá liosta den 111 saothar sin – liosta a léiríonn éagsúlacht an-mhór i nósanna léitheoireachta Gaeilgeoirí.Anseo thíos tá liosta den 111 saothar sin – liosta a léiríonn éagsúlacht an-mhór i nósanna léitheoireachta Gaeilgeoirí]." "Corto Maltese – Hugo Pratt (aistrithe ag Darach Ó Scolaí)"<ref name=":14" /> * "Ceann eile de bhuaicphointí na hÉigse a bheidh sa seisiún le Darach Ó Scolaí, duine d’úrscéalaithe móra na Gaeilge, agus duine de chomhbhunaitheoirí teach foilsitheoireachta Leabhar Breac. [Another highlight of the Éigse will be the session with Darach Ó Scolaí, one of the great Irish language novelists, and one of the co-founders of the publishing house Leabhar Breac.]"<ref name=":17">{{Cite journal|last=Nós|date=4 May 2023|title=Éigse na Bruiséile le filleadh i mí na Bealtaine. [Éigse na Bruséile to return in May]|url=https://nos.ie/cultur/eigse-na-bruiseile-le-filleadh-i-mi-na-bealtaine/|journal=Nós}}</ref> === Things Taken Out for Now === “’The play is a comedy about language, lies, bureaucracy and Gaeltacht grants, in the tradition of Myles na Gcopaleen,’ according to Norma-Jean Kenny in the ''Galway Advertizer'', ‘in which the author comments and criticizes the institutions of the Irish language in Ireland without ceasing.’" Supposedly a quotation by Gearóid Denvir reviewing ''Táin Bó Cuailnge'' for ''Comhar'' (but I don't find it in the article): This book has long been needed by Irish language readers and there is no doubt that it will become a classic in time and surpass Thomas Kinsella’s English version. This version remains faithful to the language of the original while at the same time finding an appropriate language in today’s Irish. Ó Scolaí masterfully overcomes the difficulties of the original’s rhetorical difficulties and the versions of the original poetic texts are extremely effective.[supposedly <ref name=":15" />] “The biggest prize ever awarded for a novel in Irish was presented at a special ceremony in the National Concert Hall in Dublin, today (Thursday, 4 October 2007). Darach Ó Scolaí, writer, artist & playwright from Casla, Co. Galway, was awarded €10,000 for his literary novel, ‘An Ardscoil’. This work, under the new title ‘An Cléireach’, will be launched at Oireachtas na Samhna in Westport in November. This is the first novel from his pen, a story set in the late seventeenth century. This competition was sponsored by the Franciscan Province of Ireland.” (archive, Oireachtas na Gaeilge site, 04 October, 2007) ''Súil an Daill'' (trans., ''The Eye of the Blind''), Leabhar Breac, 2021. number 2 in ''Comhar'' literary magazine’s list of best books of 2021. '''{6}.''' *William Shakespeare, ''Romeo agus Juliet'' (trans. of ''Romeo and Juliet''), Leabhar Breac, 2016. *Jonathan Swift, ''Camchuairt Ghuilivéir'' (trans. of ''Gulliver's Travels''), Leabhar Breac, 2016. *Hugo Pratt, ''Corto Maltese'' '''''Flag of Bones (Bratach na gCnámh) Series''''' Leabhar Breac published the Bratach na gCnámh series of books for young readers. Written in French by Alain Surget, illustrated by Annette Marnat and translated by Darach Ó Scolaí, this series uses the history of Caribbean Sea pirates<ref>{{Cite web|url=https://leabharbreac.com/en/product-category/alain-surget/|title=Alain Surget Archives|website=Leabhar Breac|language=en-US|access-date=2025-09-30}}</ref>: *Alain Surget, ''Éalú as Páras'' (''Escape from Paris''), Annette Marnat (Illustr.), Leabhar Breac, 2011. * Alain Surget, ''Oilean na Siorcanna'' (''Shark Island''), Annette Marnat (Illustr.), Leabhar Breac, 2011. * Alain Surget, ''Long na dTaibhsi'' (''Ship of the Ghosts''), Annette Marnat (Illustr.), Leabhar Breac, 2011. * Alain Surget, ''San Ochtapas Dubh'' (''In the Black Octopus''), Annette Marnat (Illustr.), Leabhar Breac, 2013. * Alain Surget, ''San Ionsai ar Veracruz'' (''The Attack on Veracruz''), Annette Marnat (Illustr.), Leabhar Breac, 2013. '''''For "First Readers" (children to 6 years old or so)''''' These books were written originally in Catalan by Spanish author Enric Lluch Girbés and translated into Irish by Ó ScolaÍ: *Enric Lluch, ''Ag Péinteáil an Tí'' (''Painting the House''), Anna Clariana (Illustr.), Leabhar Breac, 2017. *Enric Lluch, ''An Colúr Bacach'' (''The Lazy Dove''), Anna Clariana (Illustr.), Leabhar Breac, 2017. *Enric Lluch, ''An Phluais'' (''The Cave''), Anna Clariana (Illustr.), Leabhar Breac, 2017. *Enric Lluch, ''Madra Dhaideo'' (''Grandpa's Dog''), Anna Clariana (Illustr.), Leabhar Breac, 2017. *Enric Lluch, ''Fiacail Mháire'' (''Mary's Tooth''), Anna Clariana (Illustr.), Leabhar Breac, 2017. '''''Bruno Heitz''''' Leabhar Breac published a series of 3 Heitz books for small children. Published originally in French, this series of three comic books is about a blind mole named Cáitín Chaoch in Irish (and ''Louisette la taupe'' in French).<ref>{{Cite web|url=https://leabharbreac.com/en/product-category/bruno-heitz-en/|title=Bruno Heitz Archives|website=Leabhar Breac|language=en-US|access-date=2025-10-02}}</ref> Ó Scolaí translated these: *Bruno Heitz (author and illustr.), ''Práinneach'' (''Urgent''), Leabhar Breac, 2020 *Bruno Heitz (author and illustr.), ''Preab san Aer'' (''Bounce in the Air''), Leabhar Breac, 2020. '''''Books for Toddlers''''' Leabhar Breac has published 14 books written by French author Orianne Lallemand's and illustrated by Eleonore Thuillier, about Lallemmand's popular character Loup, Wolf. These are translated by Ó Scolaí: *Orianne Lallemand, ''An Mac Tire a Raibh Faitios an Domhain Air'' (trans. of ''The Son Who Saw the World in His Eyes''), Eleonore Thuillier  Illustr.), Leabhar Breac, 2018. *Orianne Lallemand, ''Macan agus an Goban'' (trans. of ''Macan and the Goblin''), Eleonore Thuillier (Illustr.), Leabhar Breac, 2018. * Orianne Lallemand, ''A Mac Tíre a Chuaigh go Tóin na Farraige'' (trans. of ''The Wolf Who Went to the Bottom of the Sea''), Éléanore Thuillier  (Illustr.), Leabhar Breac, 2019. '''''Board Books (for babies)''''' J. C. (Joan Carles) Girbés Aparisi is a Catalan author and editor. These books were written in Catalan and translated by Ó Scolai. *J. C. Girbés, ''An Phicnic'' (''The Picnic''), Silvia Ortega (Illustr.), Leabhar Breac, 2013. * J. C. Girbés, ''An Chóisir'' (''The Party''), Silvia Ortega (Illustr.), Leabhar Breac, 2013. *J. C. Girbés, ''Lá Mór Fada'' (''A Long Day''), Silvia Ortega (Illustr.), Leabhar Breac, 2014. *J. C. Girbés, ''Tabhair Leat do Leabhar'' (''Bring Your Book''), Silvia Ortega (Illustr.), Leabhar Breac, 2014. ==== Gradam Réics Carló ==== The Réics Carló prize is awarded for the best book in the Irish language for young readers. It is named for one of the characters of 20th-century writer [[wikipedia:Cathal_Ó_Sándair|Cathal Ó Sándair (Charles Saunders)]]. * ''An Bradán Feasa'' was “shortlisted for the Réics Carlo award 2010.”<ref name=":9" /> == References == {{reflist}} s0na8owp01bk0hmdymsy632cefoktez 0 269180 2823833 2820677 2026-08-21T05:43:50Z James500 297601 /* Japanese */ Add 2823833 wikitext text/x-wiki {{Bibliography}} See also [[Universal Bibliography/Bibliography|Bibliography]] This part of the [[Universal Bibliography]] is a bibliography of literature. See [[s:Category:Literature]], [[s:Category:History of literature]], [[w:Bibliography of encyclopedias: literature]] and [[w:Category:Works about literature]] ==World== *Cassell's Encyclopaedia of World Literature. 1953. 2nd Ed: 1973. vol 1 (histories and general articles): [https://books.google.co.uk/books?id=soIYAAAAIAAJ]. vol 3: [https://books.google.co.uk/books?id=AIEYAAAAIAAJ]. Commentary: [https://books.google.co.uk/books?id=Utcb32E7rsMC&pg=PA197#v=onepage&q&f=false]. *Damrosch. What is World Literature? 2003. [https://books.google.co.uk/books?id=yY-17mtp9R8C&pg=PP1#v=onepage&q&f=false] Series: *Edmund Gosse (ed). Literatures of the World. D Appleton and Co [https://en.m.wikisource.org/wiki/Page:A_history_of_Bohemian_literature.pdf/444] ==English== *Bateson. Cambridge Bibliography of English Literature. 1940. Watson, Supplement 1957. *Concise Cambridge Bibliography of English Literature *New Cambridge Bibliography of English Literature *Annual Bibliography of English Language and Literature. Cambridge University *Ewen. Bibliography of Eighteenth Century English Literature. Columbia University. 1935 *Marcuse. A Reference Guide for English Studies. University of Calfornia. 1990 *Bracken. Reference Works in British and American Literature. Libraries Unlimited. 1998 *Kennedy and Sands. A Concise Bibliography for Students of English. Stanford University *Pelican Guide to English Literature *[[w:The Cambridge History of English and American Literature|Cambridge History of English and American Literature]] *[[s:The Cambridge History of English Literature|Cambridge History of English Literature]] *Concise Cambridge History of English Literature *New Cambridge History of English Literature *Oxford History of English Literature *Oxford Illustrated History of English Literature *Short Oxford History of English Literature *Routledge History of Literature in English *Cambridge History of Early Medieval English Literature *Cambridge History of Medieval English Literature *Cambridge History of Early Modern English Literature *Cambridge History of Victorian Literature *Cambridge History of Twentieth Century English Literature *[[s:The Cambridge History of American Literature|Cambridge History of American Literature]] Periodicals *Liverpool Magazine (1890) *Literary Garner (1835) ===United States=== See [[w:Category:American literature by state]] *Dershem. An Outline of American State Literature. 1921 Arizona: *Joseph Amasa Munk, History of Arizona Literature, 1925 *Mary G Boyer, Arizona in Literature, 1935 *Etulain, "Contours of Culture in Arizona and the Modern West" in Luey and Stowe, Arizona at  Seventy-five, 1987 *Diaz, "A Bibliography of Bibliographies Relating to the History and Literature of Arizona and New Mexico" (1958) 14 Arizona Quarterly 197 Colorado: *Eugene Parsons, "Colorado Literature" in Stone, History of Colorado, 1918, volume 1, chapter 42, p 877 [https://books.google.co.uk/books?id=-uVYAAAAMAAJ] *Levette J Davidson, "The Literature of Colorado" in Hafen. Colorado and Its People: A Narrative and Topical History of the Centennial State. Volume 2. Chapter 8. Page 225 [https://books.google.co.uk/books?id=sncXAAAAIAAJ] *Fritz. "Literature". Colorado, the Centennial State. 1941. p 417 [https://books.google.co.uk/books?id=EU0UAAAAYAAJ] *"Books and Writers". Colorado, a Guide to the Highest State. 1941. p 96 [https://books.google.co.uk/books?id=3o8GAQAAIAAJ] *Eugene Parsons, "The Study of Colorado Literature" (1918) Colorado School Journal, vols 34-35, p 24 [https://books.google.co.uk/books?id=QxNRAQAAMAAJ] *"A Plea for the Study of Colorado Literature" (1918) The Trail: A Magazine "for Colorado", vol 11, p 12 [https://books.google.co.uk/books?id=K7QTAAAAYAAJ] Oregon: *Powers, Alfred. History of Oregon Literature. Metropolitan Press. 1935 [https://books.google.co.uk/books?id=JzELAAAAMAAJ] *Horner, John B. Oregon Literature. 1899 [https://books.google.co.uk/books?id=3ecWSpoFMcQC&pg=PA1#v=onepage&q&f=false] ==French== See [[s:Category:French literature]] Bibliographies and bibliographical works: *A Critical Bibliography of French Literature. Syracuse University Press. [https://books.google.co.uk/books?id=IFJQl7eUrg4C&pg=PR3#v=onepage&q&f=false vol 5] *Bassan, Breed and Spinelli. An Annotated Bibliography of French Language and Literature. 2nd Ed: 1976 [https://books.google.co.uk/books?id=BdkaAAAAMAAJ] *French XX Bibliography: A Bibliography for the Study of French Literature and Culture since 1885. [https://books.google.co.uk/books?id=VxVxFxyDOmkC&pg=PA19125#v=onepage&q&f=false] *Foulet. A Bibliography of Medieval French Literature for College Libraries. 1915 [https://books.google.co.uk/books?id=httNAQAAIAAJ] *Kirsop. The Bibliography of French Literary History: Progress, Problems, Projects. 1964. [https://books.google.co.uk/books?id=Xt7nAAAAMAAJ] *Jaffe. Bibliography of French Literature in American Magazines in the 18th Century. Michigan State College Press. 1951. [https://books.google.co.uk/books?id=Cy7GGsr1NI8C] *Raimbert. French Literature in Mauritius (1800-1979): A Select Bibliography in the City Library of Port Louis. 1980 [https://books.google.co.uk/books?id=eQYpAQAAIAAJ] *French Literature in Early American Translation: A Bibliographical Survey of Books and Pamphlets Printed in the United States from 1668 Through 1820. 1977. [https://books.google.co.uk/books?id=CYI0AQAAIAAJ] History: *Cambridge History of French Literature *Coward. A History of French Literature: From Chanson de geste to Cinema. 2002. Paperback 2004. [https://books.google.co.uk/books?id=K8uS9vLpwuYC&lpg=PP1&pg=PR3#v=onepage&q&f=false] *Hollier. A New History of French Literature. 1989. 1994. [https://books.google.co.uk/books?id=nGQOodBVG9YC&pg=PP1#v=onepage&q&f=false] *Cazamian. A History of French Literature. Clarendon Press.1955. Reprinted 1967. [https://books.google.co.uk/books?id=W5PwAAAAMAAJ] *Nitze and Dargan. A History of French Literature: From the Earliest Times to the Present. 1930. [https://books.google.co.uk/books?id=QT0nAAAAMAAJ] *Butler. A History of French Literature. 1923. Reissued 1966. [https://books.google.co.uk/books?id=sPAoAAAAYAAJ] *Dowden. A History of French Literature. (Literatures of the World). 1900 [https://books.google.co.uk/books?id=XWdcAAAAMAAJ] *Wright. A History of French Literature. (Oxford French series). [https://books.google.co.uk/books?id=_O0oAAAAYAAJ] *Schwarz. An Outline History of French Literature. 1924. 1932. [https://books.google.co.uk/books?id=9_fnAAAAMAAJ] *Demogeot. History of French Literature. Adapted from the French by Bridge. 1874. [https://books.google.co.uk/books?id=LgxONYxlEogC&pg=PP9#v=onepage&q&f=false] *Brunetière. Manual of the History of French Literature. 1898. [https://books.google.co.uk/books?id=WOHnAAAAMAAJ] *Brereton. A Short History of French Literature. 1954. 2nd Ed:1976. [https://books.google.co.uk/books?id=DegoAAAAYAAJ] *Bisson. A Short History of French Literature: From the Middle Ages to the Present Day. 1943. [https://books.google.co.uk/books?id=TLQywgEACAAJ] *Hudson and Jack. A Short History of French Literature. 1919 [https://books.google.co.uk/books?id=8xIPAAAAQAAJ] *Saintsbury. A Short History of French Literature. 1882. 2nd Ed: 1884. 7th Ed: 1917 [https://books.google.co.uk/books?id=WDoTAAAAMAAJ] [https://books.google.co.uk/books?id=AWFcAAAAMAAJ] *Finch. French Literature: A Cultural History. 2010. [https://books.google.co.uk/books?id=8L0Z8uYUWj0C&pg=PP1#v=onepage&q&f=false] *Prendergast. History of Modern French Literature: From the Sixteenth Century to the Twentieth Century. 2017. [https://books.google.co.uk/books?id=2QtpDQAAQBAJ&pg=PP1#v=onepage&q&f=false] *Laun. History of French Literature: From the Classical Renaissance until the End of the Reign of Louis XIV. 1883. [https://books.google.co.uk/books?id=bdZEAQAAIAAJ] *Farrant. Introduction to Nineteenth-Century French Literature. 2007. [https://books.google.co.uk/books?id=m4HjBAAAQBAJ&pg=PP1#v=onepage&q&f=false] *Vinet. History of French Literature in the Eighteenth Century. Translated by Bryce. 1854. [https://books.google.co.uk/books?id=5M803wEuBswC&pg=PR1#v=onepage&q&f=false] *Jacqueline Cerquiglini-Toulet. A New History of Medieval French Literature. Translated by Sara Preisig. 2011. [https://books.google.co.uk/books?id=h42MQw6TfAcC&pg=PT3#v=onepage&q&f=false] *Konta. The History of French Literature: From the Oath of Strasburg to Chanticler. 1914. [https://books.google.co.uk/books?id=g2FcAAAAMAAJ] *Cambridge Companion to Medieval French Literature *Holmes. A History of Old French Literature: From the origins to 1300. 1938. Revised Ed: 1962. [https://books.google.co.uk/books?id=0UxcAAAAMAAJ] *Sainstbury. A History of the French Novel (to the Close of the 19th Century). 1919. [https://books.google.co.uk/books?id=GAxJAQAAIAAJ] ==Japanese== *Ryōzō Matsumoto. Japanese Literature New and Old. Hokuseido Press. 1966. [https://books.google.co.uk/books?id=EzftWTtGXzgC] *J Ingram Bryan. The Literature of Japan. 1929. Kennikat Press. Port Washington. Reissued 1970. [https://books.google.co.uk/books?id=BwazAAAAIAAJ] *Clay MacCauley. Japanese Literature. 1898. [https://books.google.co.uk/books?id=9nYuAAAAYAAJ&pg=PP7#v=onepage&q&f=false] *Epiphanius Wilson. Japanese Literature: Including Selections from Genji Monogatari and Classical Poetry and Drama of Japan. 1900. [https://books.google.co.uk/books?id=Iy4NAAAAYAAJ&pg=PP7#v=onepage&q&f=false] *Katsuhiko Takeda. Essays on Japanese Literature. Waseda University Press. 1977. [https://books.google.co.uk/books?id=VKkPAAAAYAAJ] Bibliography *Modern Japanese Literature in Western Translations: A Bibliography. International House of Japan Library. [https://books.google.co.uk/books?id=WZ7QAAAAMAAJ] Periodicals *Japanese Literature Today [https://books.google.co.uk/books?id=NyYHAQAAIAAJ] Kokubungaku and nihonbungaku *Tomoko Aoyama. "From national literature to multicultural literature in Japanese language". Kaori Okano and Yoshio Sugimoto (eds). Rethinking Japanese Studies: Eurocentrism and the Asia-Pacific Region. Routledge Contemporary Japan Series. Chapter 4. pp [https://books.google.co.uk/books?id=sEcrDwAAQBAJ&pg=PA53#v=onepage&q&f=false 53] to 72. Reviewed *Donald Richie. Japanese Literature Reviewed. 2003. [https://books.google.co.uk/books?id=ejJmAAAAMAAJ] History *Shuichi Kato. A History of Japanese Literature: From the Man'yōshū to Modern Times. New Abridged Edition. Japan Library. 1997. [https://books.google.co.uk/books?id=wUxOuD0NS5kC&pg=PP1#v=onepage&q&f=false] *Edward Putzar. Japanese Literature: A Historical Outline. University of Arizona Press. [https://books.google.co.uk/books?id=2kiBAAAAIAAJ] *W G Aston. A History of Japanese Literature. (Literatures of the World). 1903. [https://books.google.co.uk/books?id=T4EMAAAAYAAJ&pg=PR3#v=onepage&q&f=false] *Naomi Fukuda (ed). Literature. (Japanese History: A Guide to Survey Histories, Part 2). Center for Japanese Studies, University of Michigan. 1984. [https://books.google.co.uk/books?id=QsoUAQAAIAAJ] Today *A Survey of Japanese Literature Today. Japan P.E.N. Club. 1984. [https://books.google.co.uk/books?id=OcFDAQAAIAAJ] Contemporary *Kokusai Bunka Shinkokai (Japan Cultural Society). Introduction to Contemporary Japanese Literature: Synopese of Major Works: 1956-1970. University of Tokyo Press. 1972. [https://books.google.co.uk/books?id=XPQkHx6wR4IC] Modern *A Classified Catalogue of Modern Japanese Literature (Meiji, Taisho, Showa). University of Washington Library. 1964. [https://books.google.co.uk/books?id=lD8XAQAAMAAJ] *Routledge Handbook of Modern Japanese Literature. 2016. [https://books.google.co.uk/books?id=EMpJDAAAQBAJ&pg=PP1#v=onepage&q&f=false] *J Thomas Rimer and Van C Gessel (eds). The Columbia Anthology of Modern Japanese Literature. 2007. vol 2. [https://books.google.co.uk/books?id=BAg9tUJR1aEC&pg=PP1#v=onepage&q&f=false] **Abridged. 2011. [https://books.google.co.uk/books?id=VrEYtVFv67oC&pg=PP1#v=onepage&q&f=false vol 1]. *Karatani Kōjin. Origins of Modern Japanese Literature. 1993. [https://books.google.co.uk/books?id=hPJO2vEQgjYC&pg=PP1#v=onepage&q&f=false] *Kan Kikuchi. History and Trends of Modern Japanese Literature. Tokyo. 1936. [https://books.google.co.uk/books?id=TU4DAAAAMAAJ] *Edward Mack. Manufacturing Modern Japanese Literature: Publishing, Prizes, and the Ascription of Literary Value. [https://books.google.co.uk/books?id=WnDI6s9surUC&pg=PP1#v=onepage&q&f=false] *Donald Keene (ed). Modern Japanese Literature: From 1868 to the Present Day. Grove Press. 1956. [https://books.google.co.uk/books?id=5yxkAAAAMAAJ] *Saeki Shōichi. Hidden Dimensions in Modern Japanese Literature. The Japan Foundation, Office for the Japanese Studies Center. [https://books.google.co.uk/books?id=OCYHAQAAIAAJ] Meiji and Taisho *Kimura Ki (editor and compiler). Japanese Literature: Manners and Customs in the Meiji-Taishó Era. Ōbunsha. [https://books.google.co.uk/books?id=rBQrAAAAIAAJ] Early modern *Haruo Shirane (ed). Early Modern Japanese Literature: An Anthology, 1600-1900. Abridged Edition. 2008. [https://books.google.co.uk/books?id=SN72QCVBpVAC&pg=PP1#v=onepage&q&f=false] Classical *The Princeton Companion to Classical Japanese Literature [https://books.google.co.uk/books?id=BSmMbQhafJoC&pg=PP1#v=onepage&q&f=false] *Introduction to Classic Japanese Literature. Kokusai Bunka Shinkokai. 1948. [https://books.google.co.uk/books?id=WJAPAAAAYAAJ] Traditional *Haruo Shirane (ed). Traditional Japanese Literature: An Anthology, Beginnings to 1600. 2007. [https://books.google.co.uk/books?id=LsHfIsIXgEgC&pg=PP1#v=onepage&q&f=false] Literary criticism; Literary studies *Seth Jacobowitz and Jonathan E Abel (eds). Modern Japanese Literary Studies. 2026. [https://books.google.co.uk/books?id=s-_AEQAAQBAJ&pg=PP1#v=onepage&q&f=false] *Studies in Modern Japanese Literature: Essays and Translations in Honor of Edwin McClellan. 1997. [https://books.google.co.uk/books?id=_5EPAAAAYAAJ] Anthology *Donald Keene. Anthology of Japanese Literature from the earliest era to the mid-nineteenth century. Grove Press. 1955. [https://books.google.co.uk/books?id=9h8tAAAAMAAJ] Great Britain. 1956. [https://books.google.co.uk/books?id=LCxkAAAAMAAJ]. Evergreen Ed: 1960. [https://books.google.co.uk/books?id=rumBAAAAIAAJ] Novels Modern novels *Nancy Junko Beauchamp. Modern Japanese Novels in English: A Selected Bibliography. Service Center for Teachers of Asian Studies, Association for Asian Studies, Ohio State University. May 1974. [https://books.google.co.uk/books?id=WltEAAAAIAAJ] *Kinya Tsuruta and Thomas E Swann (eds). Approaches to the Modern Japanese Novel. Sophia University. Tokyo. 1976. [https://books.google.co.uk/books?id=bhdkAAAAMAAJ] Short stories Modern short stories *Thomas E Swann and Kinya Tsuruta (eds). Approaches to the Modern Japanese Short Story. Waseda University Press. 1982. [https://books.google.co.uk/books?id=IJYPAAAAYAAJ] Poetry Modern poetry *A R Davis (ed). Modern Japanese Poetry. University of Queensland Press. 1978. The Open University Press. Milton Keynes. 1979. [https://books.google.co.uk/books?id=v0aBAAAAIAAJ] *Edith Marcombe Shiffert and Yuki Sawa. Anthology of Modern Japanese Poetry. 1972. [https://books.google.co.uk/books?id=OTDRAgAAQBAJ&pg=PP1#v=onepage&q&f=false] *Ichiro Kono and Rikutaro Fukuda. An Anthology of Modern Japanese Poetry. Kenkyusha. Tokyo. 1957. [https://books.google.co.uk/books?id=ZDpkAAAAMAAJ] [[Category:Literature]] klzb854732qswl4jhys7f00tkjiau58 2823834 2823833 2026-08-21T05:44:32Z James500 297601 /* Japanese */ Add 2823834 wikitext text/x-wiki {{Bibliography}} See also [[Universal Bibliography/Bibliography|Bibliography]] This part of the [[Universal Bibliography]] is a bibliography of literature. See [[s:Category:Literature]], [[s:Category:History of literature]], [[w:Bibliography of encyclopedias: literature]] and [[w:Category:Works about literature]] ==World== *Cassell's Encyclopaedia of World Literature. 1953. 2nd Ed: 1973. vol 1 (histories and general articles): [https://books.google.co.uk/books?id=soIYAAAAIAAJ]. vol 3: [https://books.google.co.uk/books?id=AIEYAAAAIAAJ]. Commentary: [https://books.google.co.uk/books?id=Utcb32E7rsMC&pg=PA197#v=onepage&q&f=false]. *Damrosch. What is World Literature? 2003. [https://books.google.co.uk/books?id=yY-17mtp9R8C&pg=PP1#v=onepage&q&f=false] Series: *Edmund Gosse (ed). Literatures of the World. D Appleton and Co [https://en.m.wikisource.org/wiki/Page:A_history_of_Bohemian_literature.pdf/444] ==English== *Bateson. Cambridge Bibliography of English Literature. 1940. Watson, Supplement 1957. *Concise Cambridge Bibliography of English Literature *New Cambridge Bibliography of English Literature *Annual Bibliography of English Language and Literature. Cambridge University *Ewen. Bibliography of Eighteenth Century English Literature. Columbia University. 1935 *Marcuse. A Reference Guide for English Studies. University of Calfornia. 1990 *Bracken. Reference Works in British and American Literature. Libraries Unlimited. 1998 *Kennedy and Sands. A Concise Bibliography for Students of English. Stanford University *Pelican Guide to English Literature *[[w:The Cambridge History of English and American Literature|Cambridge History of English and American Literature]] *[[s:The Cambridge History of English Literature|Cambridge History of English Literature]] *Concise Cambridge History of English Literature *New Cambridge History of English Literature *Oxford History of English Literature *Oxford Illustrated History of English Literature *Short Oxford History of English Literature *Routledge History of Literature in English *Cambridge History of Early Medieval English Literature *Cambridge History of Medieval English Literature *Cambridge History of Early Modern English Literature *Cambridge History of Victorian Literature *Cambridge History of Twentieth Century English Literature *[[s:The Cambridge History of American Literature|Cambridge History of American Literature]] Periodicals *Liverpool Magazine (1890) *Literary Garner (1835) ===United States=== See [[w:Category:American literature by state]] *Dershem. An Outline of American State Literature. 1921 Arizona: *Joseph Amasa Munk, History of Arizona Literature, 1925 *Mary G Boyer, Arizona in Literature, 1935 *Etulain, "Contours of Culture in Arizona and the Modern West" in Luey and Stowe, Arizona at  Seventy-five, 1987 *Diaz, "A Bibliography of Bibliographies Relating to the History and Literature of Arizona and New Mexico" (1958) 14 Arizona Quarterly 197 Colorado: *Eugene Parsons, "Colorado Literature" in Stone, History of Colorado, 1918, volume 1, chapter 42, p 877 [https://books.google.co.uk/books?id=-uVYAAAAMAAJ] *Levette J Davidson, "The Literature of Colorado" in Hafen. Colorado and Its People: A Narrative and Topical History of the Centennial State. Volume 2. Chapter 8. Page 225 [https://books.google.co.uk/books?id=sncXAAAAIAAJ] *Fritz. "Literature". Colorado, the Centennial State. 1941. p 417 [https://books.google.co.uk/books?id=EU0UAAAAYAAJ] *"Books and Writers". Colorado, a Guide to the Highest State. 1941. p 96 [https://books.google.co.uk/books?id=3o8GAQAAIAAJ] *Eugene Parsons, "The Study of Colorado Literature" (1918) Colorado School Journal, vols 34-35, p 24 [https://books.google.co.uk/books?id=QxNRAQAAMAAJ] *"A Plea for the Study of Colorado Literature" (1918) The Trail: A Magazine "for Colorado", vol 11, p 12 [https://books.google.co.uk/books?id=K7QTAAAAYAAJ] Oregon: *Powers, Alfred. History of Oregon Literature. Metropolitan Press. 1935 [https://books.google.co.uk/books?id=JzELAAAAMAAJ] *Horner, John B. Oregon Literature. 1899 [https://books.google.co.uk/books?id=3ecWSpoFMcQC&pg=PA1#v=onepage&q&f=false] ==French== See [[s:Category:French literature]] Bibliographies and bibliographical works: *A Critical Bibliography of French Literature. Syracuse University Press. [https://books.google.co.uk/books?id=IFJQl7eUrg4C&pg=PR3#v=onepage&q&f=false vol 5] *Bassan, Breed and Spinelli. An Annotated Bibliography of French Language and Literature. 2nd Ed: 1976 [https://books.google.co.uk/books?id=BdkaAAAAMAAJ] *French XX Bibliography: A Bibliography for the Study of French Literature and Culture since 1885. [https://books.google.co.uk/books?id=VxVxFxyDOmkC&pg=PA19125#v=onepage&q&f=false] *Foulet. A Bibliography of Medieval French Literature for College Libraries. 1915 [https://books.google.co.uk/books?id=httNAQAAIAAJ] *Kirsop. The Bibliography of French Literary History: Progress, Problems, Projects. 1964. [https://books.google.co.uk/books?id=Xt7nAAAAMAAJ] *Jaffe. Bibliography of French Literature in American Magazines in the 18th Century. Michigan State College Press. 1951. [https://books.google.co.uk/books?id=Cy7GGsr1NI8C] *Raimbert. French Literature in Mauritius (1800-1979): A Select Bibliography in the City Library of Port Louis. 1980 [https://books.google.co.uk/books?id=eQYpAQAAIAAJ] *French Literature in Early American Translation: A Bibliographical Survey of Books and Pamphlets Printed in the United States from 1668 Through 1820. 1977. [https://books.google.co.uk/books?id=CYI0AQAAIAAJ] History: *Cambridge History of French Literature *Coward. A History of French Literature: From Chanson de geste to Cinema. 2002. Paperback 2004. [https://books.google.co.uk/books?id=K8uS9vLpwuYC&lpg=PP1&pg=PR3#v=onepage&q&f=false] *Hollier. A New History of French Literature. 1989. 1994. [https://books.google.co.uk/books?id=nGQOodBVG9YC&pg=PP1#v=onepage&q&f=false] *Cazamian. A History of French Literature. Clarendon Press.1955. Reprinted 1967. [https://books.google.co.uk/books?id=W5PwAAAAMAAJ] *Nitze and Dargan. A History of French Literature: From the Earliest Times to the Present. 1930. [https://books.google.co.uk/books?id=QT0nAAAAMAAJ] *Butler. A History of French Literature. 1923. Reissued 1966. [https://books.google.co.uk/books?id=sPAoAAAAYAAJ] *Dowden. A History of French Literature. (Literatures of the World). 1900 [https://books.google.co.uk/books?id=XWdcAAAAMAAJ] *Wright. A History of French Literature. (Oxford French series). [https://books.google.co.uk/books?id=_O0oAAAAYAAJ] *Schwarz. An Outline History of French Literature. 1924. 1932. [https://books.google.co.uk/books?id=9_fnAAAAMAAJ] *Demogeot. History of French Literature. Adapted from the French by Bridge. 1874. [https://books.google.co.uk/books?id=LgxONYxlEogC&pg=PP9#v=onepage&q&f=false] *Brunetière. Manual of the History of French Literature. 1898. [https://books.google.co.uk/books?id=WOHnAAAAMAAJ] *Brereton. A Short History of French Literature. 1954. 2nd Ed:1976. [https://books.google.co.uk/books?id=DegoAAAAYAAJ] *Bisson. A Short History of French Literature: From the Middle Ages to the Present Day. 1943. [https://books.google.co.uk/books?id=TLQywgEACAAJ] *Hudson and Jack. A Short History of French Literature. 1919 [https://books.google.co.uk/books?id=8xIPAAAAQAAJ] *Saintsbury. A Short History of French Literature. 1882. 2nd Ed: 1884. 7th Ed: 1917 [https://books.google.co.uk/books?id=WDoTAAAAMAAJ] [https://books.google.co.uk/books?id=AWFcAAAAMAAJ] *Finch. French Literature: A Cultural History. 2010. [https://books.google.co.uk/books?id=8L0Z8uYUWj0C&pg=PP1#v=onepage&q&f=false] *Prendergast. History of Modern French Literature: From the Sixteenth Century to the Twentieth Century. 2017. [https://books.google.co.uk/books?id=2QtpDQAAQBAJ&pg=PP1#v=onepage&q&f=false] *Laun. History of French Literature: From the Classical Renaissance until the End of the Reign of Louis XIV. 1883. [https://books.google.co.uk/books?id=bdZEAQAAIAAJ] *Farrant. Introduction to Nineteenth-Century French Literature. 2007. [https://books.google.co.uk/books?id=m4HjBAAAQBAJ&pg=PP1#v=onepage&q&f=false] *Vinet. History of French Literature in the Eighteenth Century. Translated by Bryce. 1854. [https://books.google.co.uk/books?id=5M803wEuBswC&pg=PR1#v=onepage&q&f=false] *Jacqueline Cerquiglini-Toulet. A New History of Medieval French Literature. Translated by Sara Preisig. 2011. [https://books.google.co.uk/books?id=h42MQw6TfAcC&pg=PT3#v=onepage&q&f=false] *Konta. The History of French Literature: From the Oath of Strasburg to Chanticler. 1914. [https://books.google.co.uk/books?id=g2FcAAAAMAAJ] *Cambridge Companion to Medieval French Literature *Holmes. A History of Old French Literature: From the origins to 1300. 1938. Revised Ed: 1962. [https://books.google.co.uk/books?id=0UxcAAAAMAAJ] *Sainstbury. A History of the French Novel (to the Close of the 19th Century). 1919. [https://books.google.co.uk/books?id=GAxJAQAAIAAJ] ==Japanese== *Ryōzō Matsumoto. Japanese Literature New and Old. Hokuseido Press. 1966. [https://books.google.co.uk/books?id=EzftWTtGXzgC] *J Ingram Bryan. The Literature of Japan. 1929. Kennikat Press. Port Washington. Reissued 1970. [https://books.google.co.uk/books?id=BwazAAAAIAAJ] *Clay MacCauley. Japanese Literature. 1898. [https://books.google.co.uk/books?id=9nYuAAAAYAAJ&pg=PP7#v=onepage&q&f=false] *Epiphanius Wilson. Japanese Literature: Including Selections from Genji Monogatari and Classical Poetry and Drama of Japan. 1900. [https://books.google.co.uk/books?id=Iy4NAAAAYAAJ&pg=PP7#v=onepage&q&f=false] *Katsuhiko Takeda. Essays on Japanese Literature. Waseda University Press. 1977. [https://books.google.co.uk/books?id=VKkPAAAAYAAJ] Bibliography *Modern Japanese Literature in Western Translations: A Bibliography. International House of Japan Library. [https://books.google.co.uk/books?id=WZ7QAAAAMAAJ] Periodicals *Japanese Literature Today [https://books.google.co.uk/books?id=NyYHAQAAIAAJ] Kokubungaku and nihonbungaku *Tomoko Aoyama. "From national literature to multicultural literature in Japanese language". Kaori Okano and Yoshio Sugimoto (eds). Rethinking Japanese Studies: Eurocentrism and the Asia-Pacific Region. Routledge Contemporary Japan Series. Chapter 4. pp [https://books.google.co.uk/books?id=sEcrDwAAQBAJ&pg=PA53#v=onepage&q&f=false 53] to 72. Reviewed *Donald Richie. Japanese Literature Reviewed. 2003. [https://books.google.co.uk/books?id=ejJmAAAAMAAJ] History *Shuichi Kato. A History of Japanese Literature: From the Man'yōshū to Modern Times. New Abridged Edition. Japan Library. 1997. [https://books.google.co.uk/books?id=wUxOuD0NS5kC&pg=PP1#v=onepage&q&f=false] *Edward Putzar. Japanese Literature: A Historical Outline. University of Arizona Press. [https://books.google.co.uk/books?id=2kiBAAAAIAAJ] *W G Aston. A History of Japanese Literature. (Literatures of the World). 1903. [https://books.google.co.uk/books?id=T4EMAAAAYAAJ&pg=PR3#v=onepage&q&f=false] *Naomi Fukuda (ed). Literature. (Japanese History: A Guide to Survey Histories, Part 2). Center for Japanese Studies, University of Michigan. 1984. [https://books.google.co.uk/books?id=QsoUAQAAIAAJ] Today *A Survey of Japanese Literature Today. Japan P.E.N. Club. 1984. [https://books.google.co.uk/books?id=OcFDAQAAIAAJ] Contemporary *Kokusai Bunka Shinkokai (Japan Cultural Society). Introduction to Contemporary Japanese Literature: Synopese of Major Works: 1956-1970. University of Tokyo Press. 1972. [https://books.google.co.uk/books?id=XPQkHx6wR4IC] Modern *A Classified Catalogue of Modern Japanese Literature (Meiji, Taisho, Showa). University of Washington Library. 1964. [https://books.google.co.uk/books?id=lD8XAQAAMAAJ] *Routledge Handbook of Modern Japanese Literature. 2016. [https://books.google.co.uk/books?id=EMpJDAAAQBAJ&pg=PP1#v=onepage&q&f=false] *J Thomas Rimer and Van C Gessel (eds). The Columbia Anthology of Modern Japanese Literature. 2007. vol 2. [https://books.google.co.uk/books?id=BAg9tUJR1aEC&pg=PP1#v=onepage&q&f=false] **Abridged. 2011. [https://books.google.co.uk/books?id=VrEYtVFv67oC&pg=PP1#v=onepage&q&f=false vol 1]. *Karatani Kōjin. Origins of Modern Japanese Literature. 1993. [https://books.google.co.uk/books?id=hPJO2vEQgjYC&pg=PP1#v=onepage&q&f=false] *Kan Kikuchi. History and Trends of Modern Japanese Literature. Tokyo. 1936. [https://books.google.co.uk/books?id=TU4DAAAAMAAJ] *Edward Mack. Manufacturing Modern Japanese Literature: Publishing, Prizes, and the Ascription of Literary Value. [https://books.google.co.uk/books?id=WnDI6s9surUC&pg=PP1#v=onepage&q&f=false] *Donald Keene (ed). Modern Japanese Literature: From 1868 to the Present Day. Grove Press. 1956. [https://books.google.co.uk/books?id=5yxkAAAAMAAJ] *Saeki Shōichi. Hidden Dimensions in Modern Japanese Literature. The Japan Foundation, Office for the Japanese Studies Center. [https://books.google.co.uk/books?id=OCYHAQAAIAAJ] Meiji and Taisho *Kimura Ki (editor and compiler). Japanese Literature: Manners and Customs in the Meiji-Taishó Era. Ōbunsha. [https://books.google.co.uk/books?id=rBQrAAAAIAAJ] Early modern *Haruo Shirane (ed). Early Modern Japanese Literature: An Anthology, 1600-1900. Abridged Edition. 2008. [https://books.google.co.uk/books?id=SN72QCVBpVAC&pg=PP1#v=onepage&q&f=false] Classical *The Princeton Companion to Classical Japanese Literature [https://books.google.co.uk/books?id=BSmMbQhafJoC&pg=PP1#v=onepage&q&f=false] *Introduction to Classic Japanese Literature. Kokusai Bunka Shinkokai. 1948. [https://books.google.co.uk/books?id=WJAPAAAAYAAJ] Traditional *Haruo Shirane (ed). Traditional Japanese Literature: An Anthology, Beginnings to 1600. 2007. [https://books.google.co.uk/books?id=LsHfIsIXgEgC&pg=PP1#v=onepage&q&f=false] Literary criticism; Literary studies *Seth Jacobowitz and Jonathan E Abel (eds). Modern Japanese Literary Studies. 2026. [https://books.google.co.uk/books?id=s-_AEQAAQBAJ&pg=PP1#v=onepage&q&f=false] *Studies in Modern Japanese Literature: Essays and Translations in Honor of Edwin McClellan. 1997. [https://books.google.co.uk/books?id=_5EPAAAAYAAJ] Anthology *Donald Keene. Anthology of Japanese Literature from the earliest era to the mid-nineteenth century. Grove Press. 1955. [https://books.google.co.uk/books?id=9h8tAAAAMAAJ] Great Britain. 1956. [https://books.google.co.uk/books?id=LCxkAAAAMAAJ]. Evergreen Ed: 1960. [https://books.google.co.uk/books?id=rumBAAAAIAAJ] Novels Modern novels *Nancy Junko Beauchamp. Modern Japanese Novels in English: A Selected Bibliography. Service Center for Teachers of Asian Studies, Association for Asian Studies, Ohio State University. May 1974. [https://books.google.co.uk/books?id=WltEAAAAIAAJ] *Kinya Tsuruta and Thomas E Swann (eds). Approaches to the Modern Japanese Novel. Sophia University. Tokyo. 1976. [https://books.google.co.uk/books?id=bhdkAAAAMAAJ] Short stories Modern short stories *Thomas E Swann and Kinya Tsuruta (eds). Approaches to the Modern Japanese Short Story. Waseda University Press. 1982. [https://books.google.co.uk/books?id=IJYPAAAAYAAJ] Poetry *J Thomas Rimer and Robert E Morrell. Guide to Japanese Poetry. 1975: [https://books.google.co.uk/books?id=EysyAAAAMAAJ]. 2nd Ed: 1984: [https://books.google.co.uk/books?id=BPEaAAAAMAAJ]. *Miyamori Asatarō. Masterpieces of Japanese Poetry Ancient and Modern. [https://books.google.co.uk/books?id=hnAmAQAAIAAJ] *Yone Noguchi. The Spirit of Japanese Poetry. [https://books.google.co.uk/books?id=5K8PAAAAYAAJ] *Leith Morton. Avant-Garde Japanese Poetry and Poetics: Contemporary Poetry Handbook, 2000–2021. 2026. [https://books.google.co.uk/books?id=7obXEQAAQBAJ&pg=PP1#v=onepage&q&f=false] *Steven D Carter. Traditional Japanese Poetry: An Anthology. Stanford University Press. [https://books.google.co.uk/books?id=dq7TOrkTCP0C&pg=PP3#v=onepage&q&f=false] *Basil Hall Chamberlain. The Classical Poetry of the Japanese. 1880. [https://books.google.co.uk/books?id=-HUuAAAAYAAJ&pg=PR3#v=onepage&q&f=false] *Douglas Kenning. The Romanticism of 17th Century Japanese Poetry. 1998. [https://books.google.co.uk/books?id=1fcZAQAAIAAJ] Modern poetry *A R Davis (ed). Modern Japanese Poetry. University of Queensland Press. 1978. The Open University Press. Milton Keynes. 1979. [https://books.google.co.uk/books?id=v0aBAAAAIAAJ] *Edith Marcombe Shiffert and Yuki Sawa. Anthology of Modern Japanese Poetry. 1972. [https://books.google.co.uk/books?id=OTDRAgAAQBAJ&pg=PP1#v=onepage&q&f=false] *Ichiro Kono and Rikutaro Fukuda. An Anthology of Modern Japanese Poetry. Kenkyusha. Tokyo. 1957. [https://books.google.co.uk/books?id=ZDpkAAAAMAAJ] [[Category:Literature]] s0yb9mp6xczkkd0h77cnj6ms5r93buk 10 283938 2823813 2394793 2026-08-21T04:29:01Z Jtneill 10242 2823813 wikitext text/x-wiki <noinclude>{{center top}}{{tl|Motivation and emotion/Tutorials/Navigation}}{{center bottom}}</noinclude> {{Navbox | name = Motivation and emotion/Tutorials/Navigation | title = [[Motivation and emotion/Tutorials|Tutorials]] | list1 = <div> [[Motivation and emotion/Tutorials/Topic selection|1 Topic selection]] <nowiki>|</nowiki> [[Motivation and emotion/Tutorials/Wiki editing|2 Wiki editing]] <nowiki>|</nowiki> [[Motivation and emotion/Tutorials/Physiological needs|3 Phys needs]] <nowiki>|</nowiki> [[Motivation and emotion/Tutorials/Psychological needs|4 Psych needs]] <nowiki>|</nowiki> [[Motivation and emotion/Tutorials/Functionalist theory and self-tracking|5 Func theory & self-tracking]] <nowiki>|</nowiki> [[Motivation and emotion/Tutorials/Learned optimism|6 Learned optimism]] <nowiki>|</nowiki> [[Motivation and emotion/Tutorials/Core emotions|7 Core emotions]] <nowiki>|</nowiki> [[Motivation and emotion/Tutorials/Measuring emotion|8 Measuring emotion]] <nowiki>|</nowiki> [[Motivation and emotion/Tutorials/20 emotions|9 20 emotions]] <nowiki>|</nowiki> [[Motivation and emotion/Tutorials/Time perspective|10 Time perspective]] <nowiki>|</nowiki> [[Motivation and emotion/Tutorials/Positive psychology|11 Positive psych]] <nowiki>|</nowiki> [[Motivation and emotion/Tutorials/Review|12 Review]] </div> }}<noinclude> [[Category:Motivation and emotion/Tutorials]] [[Category:Motivation and emotion/Templates]] </noinclude> q1fxp363yfhl0m81pkphiam6x83y3zk 0 285380 2823652 2823148 2026-08-20T14:19:03Z Young1lim 21186 /* Applications */ 2823652 wikitext text/x-wiki === Introduction === * Overview ([[Media:C01.Intro1.Overview.1.A.20170925.pdf |A.pdf]], [[Media:C01.Intro1.Overview.1.B.20170901.pdf |B.pdf]], [[Media:C01.Intro1.Overview.1.C.20170904.pdf |C.pdf]]) * Number System ([[Media:C01.Intro2.Number.1.A.20171023.pdf |A.pdf]], [[Media:C01.Intro2.Number.1.B.20170909.pdf |B.pdf]], [[Media:C01.Intro2.Number.1.C.20170914.pdf |C.pdf]]) * Memory System ([[Media:C01.Intro2.Memory.1.A.20170907.pdf |A.pdf]], [[Media:C01.Intro3.Memory.1.B.20170909.pdf |B.pdf]], [[Media:C01.Intro3.Memory.1.C.20170914.pdf |C.pdf]]) === Handling Repetition === * Control ([[Media:C02.Repeat1.Control.1.A.20170925.pdf |A.pdf]], [[Media:C02.Repeat1.Control.1.B.20170918.pdf |B.pdf]], [[Media:C02.Repeat1.Control.1.C.20170926.pdf |C.pdf]]) * Loop ([[Media:C02.Repeat2.Loop.1.A.20170925.pdf |A.pdf]], [[Media:C02.Repeat2.Loop.1.B.20170918.pdf |B.pdf]]) === Handling a Big Work === * Function Overview ([[Media:C03.Func1.Overview.1.A.20171030.pdf |A.pdf]], [[Media:C03.Func1.Oerview.1.B.20161022.pdf |B.pdf]]) * Functions & Variables ([[Media:C03.Func2.Variable.1.A.20161222.pdf |A.pdf]], [[Media:C03.Func2.Variable.1.B.20161222.pdf |B.pdf]]) * Functions & Pointers ([[Media:C03.Func3.Pointer.1.A.20161122.pdf |A.pdf]], [[Media:C03.Func3.Pointer.1.B.20161122.pdf |B.pdf]]) * Functions & Recursions ([[Media:C03.Func4.Recursion.1.A.20161214.pdf |A.pdf]], [[Media:C03.Func4.Recursion.1.B.20161214.pdf |B.pdf]]) === Handling Series of Data === ==== Background ==== * Background ([[Media:C04.Series0.Background.1.A.20180727.pdf |A.pdf]]) ==== Basics ==== * Pointers ([[Media:C04.S1.Pointer.1A.20240524.pdf |A.pdf]], [[Media:C04.Series2.Pointer.1.B.20161115.pdf |B.pdf]]) * Arrays ([[Media:C04.S2.Array.1A.20240514.pdf |A.pdf]], [[Media:C04.Series1.Array.1.B.20161115.pdf |B.pdf]]) * Array Pointers ([[Media:C04.S3.ArrayPointer.1A.20240208.pdf |A.pdf]], [[Media:C04.Series3.ArrayPointer.1.B.20181203.pdf |B.pdf]]) * Multi-dimensional Arrays ([[Media:C04.Series4.MultiDim.1.A.20221130.pdf |A.pdf]], [[Media:C04.Series4.MultiDim.1.B.1111.pdf |B.pdf]]) * Array Access Methods ([[Media:C04.Series4.ArrayAccess.1.A.20190511.pdf |A.pdf]], [[Media:C04.Series3.ArrayPointer.1.B.20181203.pdf |B.pdf]]) * Structures ([[Media:C04.Series3.Structure.1.A.20171204.pdf |A.pdf]], [[Media:C04.Series2.Structure.1.B.20161130.pdf |B.pdf]]) ==== Examples ==== * Spreadsheet Example Programs :: Example 1 ([[Media:C04.Series7.Example.1.A.20171213.pdf |A.pdf]], [[Media:C04.Series7.Example.1.C.20171213.pdf |C.pdf]]) :: Example 2 ([[Media:C04.Series7.Example.2.A.20171213.pdf |A.pdf]], [[Media:C04.Series7.Example.2.C.20171213.pdf |C.pdf]]) :: Example 3 ([[Media:C04.Series7.Example.3.A.20171213.pdf |A.pdf]], [[Media:C04.Series7.Example.3.C.20171213.pdf |C.pdf]]) :: Bubble Sort ([[Media:C04.Series7.BubbleSort.1.A.20171211.pdf |A.pdf]]) ==== Applications ==== * Address-of and de-reference operators ([[Media:C04.SA0.PtrOperator.1A.20260819.pdf |A.pdf]]) * Applications of Pointers ([[Media:C04.SA1.AppPointer.1A.20241121.pdf |A.pdf]]) * Applications of Arrays ([[Media:C04.SA2.AppArray.1A.20240715.pdf |A.pdf]]) * Applications of Array Pointers ([[Media:C04.SA3.AppArrayPointer.1A.20240210.pdf |A.pdf]]) * Applications of Multi-dimensional Arrays ([[Media:C04.Series4App.MultiDim.1.A.20210719.pdf |A.pdf]]) * Applications of Array Access Methods ([[Media:C04.Series9.AppArrAcess.1.A.20190511.pdf |A.pdf]]) * Applications of Structures ([[Media:C04.Series6.AppStruct.1.A.20190423.pdf |A.pdf]]) === Handling Various Kinds of Data === * Types ([[Media:C05.Data1.Type.1.A.20180217.pdf |A.pdf]], [[Media:C05.Data1.Type.1.B.20161212.pdf |B.pdf]]) * Typecasts ([[Media:C05.Data2.TypeCast.1.A.20180217.pdf |A.pdf]], [[Media:C05.Data2.TypeCast.1.B.20161216.pdf |A.pdf]]) * Operators ([[Media:C05.Data3.Operators.1.A.20161219.pdf |A.pdf]], [[Media:C05.Data3.Operators.1.B.20161216.pdf |B.pdf]]) * Files ([[Media:C05.Data4.File.1.A.20161124.pdf |A.pdf]], [[Media:C05.Data4.File.1.B.20161212.pdf |B.pdf]]) === Handling Low Level Operations === * Bitwise Operations ([[Media:BitOp.1.B.20161214.pdf |A.pdf]], [[Media:BitOp.1.B.20161203.pdf |B.pdf]]) * Bit Field ([[Media:BitField.1.A.20161214.pdf |A.pdf]], [[Media:BitField.1.B.20161202.pdf |B.pdf]]) * Union ([[Media:Union.1.A.20161221.pdf |A.pdf]], [[Media:Union.1.B.20161111.pdf |B.pdf]]) * Accessing IO Registers ([[Media:IO.1.A.20141215.pdf |A.pdf]], [[Media:IO.1.B.20161217.pdf |B.pdf]]) === Declarations === * Type Specifiers and Qualifiers ([[Media:C07.Spec1.Type.1.A.20171004.pdf |pdf]]) * Storage Class Specifiers ([[Media:C07.Spec2.Storage.1.A.20171009.pdf |pdf]]) * Scope === Class Notes === * TOC ([[Media:TOC.20171007.pdf |TOC.pdf]]) * Day01 ([[Media:Day01.A.20171007.pdf |A.pdf]], [[Media:Day01.B.20171209.pdf |B.pdf]], [[Media:Day01.C.20171211.pdf |C.pdf]]) ...... Introduction (1) Standard Library * Day02 ([[Media:Day02.A.20171007.pdf |A.pdf]], [[Media:Day02.B.20171209.pdf |B.pdf]], [[Media:Day02.C.20171209.pdf |C.pdf]]) ...... Introduction (2) Basic Elements * Day03 ([[Media:Day03.A.20171007.pdf |A.pdf]], [[Media:Day03.B.20170908.pdf |B.pdf]], [[Media:Day03.C.20171209.pdf |C.pdf]]) ...... Introduction (3) Numbers * Day04 ([[Media:Day04.A.20171007.pdf |A.pdf]], [[Media:Day04.B.20170915.pdf |B.pdf]], [[Media:Day04.C.20171209.pdf |C.pdf]]) ...... Structured Programming (1) Flowcharts * Day05 ([[Media:Day05.A.20171007.pdf |A.pdf]], [[Media:Day05.B.20170915.pdf |B.pdf]], [[Media:Day05.C.20171209.pdf |C.pdf]]) ...... Structured Programming (2) Conditions and Loops * Day06 ([[Media:Day06.A.20171007.pdf |A.pdf]], [[Media:Day06.B.20170923.pdf |B.pdf]], [[Media:Day06.C.20171209.pdf |C.pdf]]) ...... Program Control * Day07 ([[Media:Day07.A.20171007.pdf |A.pdf]], [[Media:Day07.B.20170926.pdf |B.pdf]], [[Media:Day07.C.20171209.pdf |C.pdf]]) ...... Function (1) Definitions * Day08 ([[Media:Day08.A.20171028.pdf |A.pdf]], [[Media:Day08.B.20171016.pdf |B.pdf]], [[Media:Day08.C.20171209.pdf |C.pdf]]) ...... Function (2) Storage Class and Scope * Day09 ([[Media:Day09.A.20171007.pdf |A.pdf]], [[Media:Day09.B.20171017.pdf |B.pdf]], [[Media:Day09.C.20171209.pdf |C.pdf]]) ...... Function (3) Recursion * Day10 ([[Media:Day10.A.20171209.pdf |A.pdf]], [[Media:Day10.B.20171017.pdf |B.pdf]], [[Media:Day10.C.20171209.pdf |C.pdf]]) ...... Arrays (1) Definitions * Day11 ([[Media:Day11.A.20171024.pdf |A.pdf]], [[Media:Day11.B.20171017.pdf |B.pdf]], [[Media:Day11.C.20171212.pdf |C.pdf]]) ...... Arrays (2) Applications * Day12 ([[Media:Day12.A.20171024.pdf |A.pdf]], [[Media:Day12.B.20171020.pdf |B.pdf]], [[Media:Day12.C.20171209.pdf |C.pdf]]) ...... Pointers (1) Definitions * Day13 ([[Media:Day13.A.20171025.pdf |A.pdf]], [[Media:Day13.B.20171024.pdf |B.pdf]], [[Media:Day13.C.20171209.pdf |C.pdf]]) ...... Pointers (2) Applications * Day14 ([[Media:Day14.A.20171226.pdf |A.pdf]], [[Media:Day14.B.20171101.pdf |B.pdf]], [[Media:Day14.C.20171209.pdf |C.pdf]]) ...... C String (1) * Day15 ([[Media:Day15.A.20171209.pdf |A.pdf]], [[Media:Day15.B.20171124.pdf |B.pdf]], [[Media:Day15.C.20171209.pdf |C.pdf]]) ...... C String (2) * Day16 ([[Media:Day16.A.20171208.pdf |A.pdf]], [[Media:Day16.B.20171114.pdf |B.pdf]], [[Media:Day16.C.20171209.pdf |C.pdf]]) ...... C Formatted IO * Day17 ([[Media:Day17.A.20171031.pdf |A.pdf]], [[Media:Day17.B.20171111.pdf |B.pdf]], [[Media:Day17.C.20171209.pdf |C.pdf]]) ...... Structure (1) Definitions * Day18 ([[Media:Day18.A.20171206.pdf |A.pdf]], [[Media:Day18.B.20171128.pdf |B.pdf]], [[Media:Day18.C.20171212.pdf |C.pdf]]) ...... Structure (2) Applications * Day19 ([[Media:Day19.A.20171205.pdf |A.pdf]], [[Media:Day19.B.20171121.pdf |B.pdf]], [[Media:Day19.C.20171209.pdf |C.pdf]]) ...... Union, Bitwise Operators, Enum * Day20 ([[Media:Day20.A.20171205.pdf |A.pdf]], [[Media:Day20.B.20171201.pdf |B.pdf]], [[Media:Day20.C.20171212.pdf |C.pdf]]) ...... Linked List * Day21 ([[Media:Day21.A.20171206.pdf |A.pdf]], [[Media:Day21.B.20171208.pdf |B.pdf]], [[Media:Day21.C.20171212.pdf |C.pdf]]) ...... File Processing * Day22 ([[Media:Day22.A.20171212.pdf |A.pdf]], [[Media:Day22.B.20171213.pdf |B.pdf]], [[Media:Day22.C.20171212.pdf |C.pdf]]) ...... Preprocessing <!----------------------------------------------------------------------> </br> See also https://cprogramex.wordpress.com/ == '''Old Materials '''== until 201201 * Intro.Overview.1.A ([[Media:C.Intro.Overview.1.A.20120107.pdf |pdf]]) * Intro.Memory.1.A ([[Media:C.Intro.Memory.1.A.20120107.pdf |pdf]]) * Intro.Number.1.A ([[Media:C.Intro.Number.1.A.20120107.pdf |pdf]]) * Repeat.Control.1.A ([[Media:C.Repeat.Control.1.A.20120109.pdf |pdf]]) * Repeat.Loop.1.A ([[Media:C.Repeat.Loop.1.A.20120113.pdf |pdf]]) * Work.Function.1.A ([[Media:C.Work.Function.1.A.20120117.pdf |pdf]]) * Work.Scope.1.A ([[Media:C.Work.Scope.1.A.20120117.pdf |pdf]]) * Series.Array.1.A ([[Media:Series.Array.1.A.20110718.pdf |pdf]]) * Series.Pointer.1.A ([[Media:Series.Pointer.1.A.20110719.pdf |pdf]]) * Series.Structure.1.A ([[Media:Series.Structure.1.A.20110805.pdf |pdf]]) * Data.Type.1.A ([[Media:C05.Data2.TypeCast.1.A.20130813.pdf |pdf]]) * Data.TypeCast.1.A ([[Media:Data.TypeCast.1.A.pdf |pdf]]) * Data.Operators.1.A ([[Media:Data.Operators.1.A.20110712.pdf |pdf]]) <br> until 201107 * Intro.1.A ([[Media:Intro.1.A.pdf |pdf]]) * Control.1.A ([[Media:Control.1.A.20110706.pdf |pdf]]) * Iteration.1.A ([[Media:Iteration.1.A.pdf |pdf]]) * Function.1.A ([[Media:Function.1.A.20110705.pdf |pdf]]) * Variable.1.A ([[Media:Variable.1.A.20110708.pdf |pdf]]) * Operators.1.A ([[Media:Operators.1.A.20110712.pdf |pdf]]) * Pointer.1.A ([[Media:Pointer.1.A.pdf |pdf]]) * Pointer.2.A ([[Media:Pointer.2.A.pdf |pdf]]) * Array.1.A ([[Media:Array.1.A.pdf |pdf]]) * Type.1.A ([[Media:Type.1.A.pdf |pdf]]) * Structure.1.A ([[Media:Structure.1.A.pdf |pdf]]) go to [ [[C programming in plain view]] ] [[Category:C programming language]] </br> kbpgnc6g0jsw239nrppr8v9wcnorv73 2823654 2823652 2026-08-20T14:21:44Z Young1lim 21186 /* Applications */ 2823654 wikitext text/x-wiki === Introduction === * Overview ([[Media:C01.Intro1.Overview.1.A.20170925.pdf |A.pdf]], [[Media:C01.Intro1.Overview.1.B.20170901.pdf |B.pdf]], [[Media:C01.Intro1.Overview.1.C.20170904.pdf |C.pdf]]) * Number System ([[Media:C01.Intro2.Number.1.A.20171023.pdf |A.pdf]], [[Media:C01.Intro2.Number.1.B.20170909.pdf |B.pdf]], [[Media:C01.Intro2.Number.1.C.20170914.pdf |C.pdf]]) * Memory System ([[Media:C01.Intro2.Memory.1.A.20170907.pdf |A.pdf]], [[Media:C01.Intro3.Memory.1.B.20170909.pdf |B.pdf]], [[Media:C01.Intro3.Memory.1.C.20170914.pdf |C.pdf]]) === Handling Repetition === * Control ([[Media:C02.Repeat1.Control.1.A.20170925.pdf |A.pdf]], [[Media:C02.Repeat1.Control.1.B.20170918.pdf |B.pdf]], [[Media:C02.Repeat1.Control.1.C.20170926.pdf |C.pdf]]) * Loop ([[Media:C02.Repeat2.Loop.1.A.20170925.pdf |A.pdf]], [[Media:C02.Repeat2.Loop.1.B.20170918.pdf |B.pdf]]) === Handling a Big Work === * Function Overview ([[Media:C03.Func1.Overview.1.A.20171030.pdf |A.pdf]], [[Media:C03.Func1.Oerview.1.B.20161022.pdf |B.pdf]]) * Functions & Variables ([[Media:C03.Func2.Variable.1.A.20161222.pdf |A.pdf]], [[Media:C03.Func2.Variable.1.B.20161222.pdf |B.pdf]]) * Functions & Pointers ([[Media:C03.Func3.Pointer.1.A.20161122.pdf |A.pdf]], [[Media:C03.Func3.Pointer.1.B.20161122.pdf |B.pdf]]) * Functions & Recursions ([[Media:C03.Func4.Recursion.1.A.20161214.pdf |A.pdf]], [[Media:C03.Func4.Recursion.1.B.20161214.pdf |B.pdf]]) === Handling Series of Data === ==== Background ==== * Background ([[Media:C04.Series0.Background.1.A.20180727.pdf |A.pdf]]) ==== Basics ==== * Pointers ([[Media:C04.S1.Pointer.1A.20240524.pdf |A.pdf]], [[Media:C04.Series2.Pointer.1.B.20161115.pdf |B.pdf]]) * Arrays ([[Media:C04.S2.Array.1A.20240514.pdf |A.pdf]], [[Media:C04.Series1.Array.1.B.20161115.pdf |B.pdf]]) * Array Pointers ([[Media:C04.S3.ArrayPointer.1A.20240208.pdf |A.pdf]], [[Media:C04.Series3.ArrayPointer.1.B.20181203.pdf |B.pdf]]) * Multi-dimensional Arrays ([[Media:C04.Series4.MultiDim.1.A.20221130.pdf |A.pdf]], [[Media:C04.Series4.MultiDim.1.B.1111.pdf |B.pdf]]) * Array Access Methods ([[Media:C04.Series4.ArrayAccess.1.A.20190511.pdf |A.pdf]], [[Media:C04.Series3.ArrayPointer.1.B.20181203.pdf |B.pdf]]) * Structures ([[Media:C04.Series3.Structure.1.A.20171204.pdf |A.pdf]], [[Media:C04.Series2.Structure.1.B.20161130.pdf |B.pdf]]) ==== Examples ==== * Spreadsheet Example Programs :: Example 1 ([[Media:C04.Series7.Example.1.A.20171213.pdf |A.pdf]], [[Media:C04.Series7.Example.1.C.20171213.pdf |C.pdf]]) :: Example 2 ([[Media:C04.Series7.Example.2.A.20171213.pdf |A.pdf]], [[Media:C04.Series7.Example.2.C.20171213.pdf |C.pdf]]) :: Example 3 ([[Media:C04.Series7.Example.3.A.20171213.pdf |A.pdf]], [[Media:C04.Series7.Example.3.C.20171213.pdf |C.pdf]]) :: Bubble Sort ([[Media:C04.Series7.BubbleSort.1.A.20171211.pdf |A.pdf]]) ==== Applications ==== * Address-of and de-reference operators ([[Media:C04.SA0.PtrOperator.1A.20260820.pdf |A.pdf]]) * Applications of Pointers ([[Media:C04.SA1.AppPointer.1A.20241121.pdf |A.pdf]]) * Applications of Arrays ([[Media:C04.SA2.AppArray.1A.20240715.pdf |A.pdf]]) * Applications of Array Pointers ([[Media:C04.SA3.AppArrayPointer.1A.20240210.pdf |A.pdf]]) * Applications of Multi-dimensional Arrays ([[Media:C04.Series4App.MultiDim.1.A.20210719.pdf |A.pdf]]) * Applications of Array Access Methods ([[Media:C04.Series9.AppArrAcess.1.A.20190511.pdf |A.pdf]]) * Applications of Structures ([[Media:C04.Series6.AppStruct.1.A.20190423.pdf |A.pdf]]) === Handling Various Kinds of Data === * Types ([[Media:C05.Data1.Type.1.A.20180217.pdf |A.pdf]], [[Media:C05.Data1.Type.1.B.20161212.pdf |B.pdf]]) * Typecasts ([[Media:C05.Data2.TypeCast.1.A.20180217.pdf |A.pdf]], [[Media:C05.Data2.TypeCast.1.B.20161216.pdf |A.pdf]]) * Operators ([[Media:C05.Data3.Operators.1.A.20161219.pdf |A.pdf]], [[Media:C05.Data3.Operators.1.B.20161216.pdf |B.pdf]]) * Files ([[Media:C05.Data4.File.1.A.20161124.pdf |A.pdf]], [[Media:C05.Data4.File.1.B.20161212.pdf |B.pdf]]) === Handling Low Level Operations === * Bitwise Operations ([[Media:BitOp.1.B.20161214.pdf |A.pdf]], [[Media:BitOp.1.B.20161203.pdf |B.pdf]]) * Bit Field ([[Media:BitField.1.A.20161214.pdf |A.pdf]], [[Media:BitField.1.B.20161202.pdf |B.pdf]]) * Union ([[Media:Union.1.A.20161221.pdf |A.pdf]], [[Media:Union.1.B.20161111.pdf |B.pdf]]) * Accessing IO Registers ([[Media:IO.1.A.20141215.pdf |A.pdf]], [[Media:IO.1.B.20161217.pdf |B.pdf]]) === Declarations === * Type Specifiers and Qualifiers ([[Media:C07.Spec1.Type.1.A.20171004.pdf |pdf]]) * Storage Class Specifiers ([[Media:C07.Spec2.Storage.1.A.20171009.pdf |pdf]]) * Scope === Class Notes === * TOC ([[Media:TOC.20171007.pdf |TOC.pdf]]) * Day01 ([[Media:Day01.A.20171007.pdf |A.pdf]], [[Media:Day01.B.20171209.pdf |B.pdf]], [[Media:Day01.C.20171211.pdf |C.pdf]]) ...... Introduction (1) Standard Library * Day02 ([[Media:Day02.A.20171007.pdf |A.pdf]], [[Media:Day02.B.20171209.pdf |B.pdf]], [[Media:Day02.C.20171209.pdf |C.pdf]]) ...... Introduction (2) Basic Elements * Day03 ([[Media:Day03.A.20171007.pdf |A.pdf]], [[Media:Day03.B.20170908.pdf |B.pdf]], [[Media:Day03.C.20171209.pdf |C.pdf]]) ...... Introduction (3) Numbers * Day04 ([[Media:Day04.A.20171007.pdf |A.pdf]], [[Media:Day04.B.20170915.pdf |B.pdf]], [[Media:Day04.C.20171209.pdf |C.pdf]]) ...... Structured Programming (1) Flowcharts * Day05 ([[Media:Day05.A.20171007.pdf |A.pdf]], [[Media:Day05.B.20170915.pdf |B.pdf]], [[Media:Day05.C.20171209.pdf |C.pdf]]) ...... Structured Programming (2) Conditions and Loops * Day06 ([[Media:Day06.A.20171007.pdf |A.pdf]], [[Media:Day06.B.20170923.pdf |B.pdf]], [[Media:Day06.C.20171209.pdf |C.pdf]]) ...... Program Control * Day07 ([[Media:Day07.A.20171007.pdf |A.pdf]], [[Media:Day07.B.20170926.pdf |B.pdf]], [[Media:Day07.C.20171209.pdf |C.pdf]]) ...... Function (1) Definitions * Day08 ([[Media:Day08.A.20171028.pdf |A.pdf]], [[Media:Day08.B.20171016.pdf |B.pdf]], [[Media:Day08.C.20171209.pdf |C.pdf]]) ...... Function (2) Storage Class and Scope * Day09 ([[Media:Day09.A.20171007.pdf |A.pdf]], [[Media:Day09.B.20171017.pdf |B.pdf]], [[Media:Day09.C.20171209.pdf |C.pdf]]) ...... Function (3) Recursion * Day10 ([[Media:Day10.A.20171209.pdf |A.pdf]], [[Media:Day10.B.20171017.pdf |B.pdf]], [[Media:Day10.C.20171209.pdf |C.pdf]]) ...... Arrays (1) Definitions * Day11 ([[Media:Day11.A.20171024.pdf |A.pdf]], [[Media:Day11.B.20171017.pdf |B.pdf]], [[Media:Day11.C.20171212.pdf |C.pdf]]) ...... Arrays (2) Applications * Day12 ([[Media:Day12.A.20171024.pdf |A.pdf]], [[Media:Day12.B.20171020.pdf |B.pdf]], [[Media:Day12.C.20171209.pdf |C.pdf]]) ...... Pointers (1) Definitions * Day13 ([[Media:Day13.A.20171025.pdf |A.pdf]], [[Media:Day13.B.20171024.pdf |B.pdf]], [[Media:Day13.C.20171209.pdf |C.pdf]]) ...... Pointers (2) Applications * Day14 ([[Media:Day14.A.20171226.pdf |A.pdf]], [[Media:Day14.B.20171101.pdf |B.pdf]], [[Media:Day14.C.20171209.pdf |C.pdf]]) ...... C String (1) * Day15 ([[Media:Day15.A.20171209.pdf |A.pdf]], [[Media:Day15.B.20171124.pdf |B.pdf]], [[Media:Day15.C.20171209.pdf |C.pdf]]) ...... C String (2) * Day16 ([[Media:Day16.A.20171208.pdf |A.pdf]], [[Media:Day16.B.20171114.pdf |B.pdf]], [[Media:Day16.C.20171209.pdf |C.pdf]]) ...... C Formatted IO * Day17 ([[Media:Day17.A.20171031.pdf |A.pdf]], [[Media:Day17.B.20171111.pdf |B.pdf]], [[Media:Day17.C.20171209.pdf |C.pdf]]) ...... Structure (1) Definitions * Day18 ([[Media:Day18.A.20171206.pdf |A.pdf]], [[Media:Day18.B.20171128.pdf |B.pdf]], [[Media:Day18.C.20171212.pdf |C.pdf]]) ...... Structure (2) Applications * Day19 ([[Media:Day19.A.20171205.pdf |A.pdf]], [[Media:Day19.B.20171121.pdf |B.pdf]], [[Media:Day19.C.20171209.pdf |C.pdf]]) ...... Union, Bitwise Operators, Enum * Day20 ([[Media:Day20.A.20171205.pdf |A.pdf]], [[Media:Day20.B.20171201.pdf |B.pdf]], [[Media:Day20.C.20171212.pdf |C.pdf]]) ...... Linked List * Day21 ([[Media:Day21.A.20171206.pdf |A.pdf]], [[Media:Day21.B.20171208.pdf |B.pdf]], [[Media:Day21.C.20171212.pdf |C.pdf]]) ...... File Processing * Day22 ([[Media:Day22.A.20171212.pdf |A.pdf]], [[Media:Day22.B.20171213.pdf |B.pdf]], [[Media:Day22.C.20171212.pdf |C.pdf]]) ...... Preprocessing <!----------------------------------------------------------------------> </br> See also https://cprogramex.wordpress.com/ == '''Old Materials '''== until 201201 * Intro.Overview.1.A ([[Media:C.Intro.Overview.1.A.20120107.pdf |pdf]]) * Intro.Memory.1.A ([[Media:C.Intro.Memory.1.A.20120107.pdf |pdf]]) * Intro.Number.1.A ([[Media:C.Intro.Number.1.A.20120107.pdf |pdf]]) * Repeat.Control.1.A ([[Media:C.Repeat.Control.1.A.20120109.pdf |pdf]]) * Repeat.Loop.1.A ([[Media:C.Repeat.Loop.1.A.20120113.pdf |pdf]]) * Work.Function.1.A ([[Media:C.Work.Function.1.A.20120117.pdf |pdf]]) * Work.Scope.1.A ([[Media:C.Work.Scope.1.A.20120117.pdf |pdf]]) * Series.Array.1.A ([[Media:Series.Array.1.A.20110718.pdf |pdf]]) * Series.Pointer.1.A ([[Media:Series.Pointer.1.A.20110719.pdf |pdf]]) * Series.Structure.1.A ([[Media:Series.Structure.1.A.20110805.pdf |pdf]]) * Data.Type.1.A ([[Media:C05.Data2.TypeCast.1.A.20130813.pdf |pdf]]) * Data.TypeCast.1.A ([[Media:Data.TypeCast.1.A.pdf |pdf]]) * Data.Operators.1.A ([[Media:Data.Operators.1.A.20110712.pdf |pdf]]) <br> until 201107 * Intro.1.A ([[Media:Intro.1.A.pdf |pdf]]) * Control.1.A ([[Media:Control.1.A.20110706.pdf |pdf]]) * Iteration.1.A ([[Media:Iteration.1.A.pdf |pdf]]) * Function.1.A ([[Media:Function.1.A.20110705.pdf |pdf]]) * Variable.1.A ([[Media:Variable.1.A.20110708.pdf |pdf]]) * Operators.1.A ([[Media:Operators.1.A.20110712.pdf |pdf]]) * Pointer.1.A ([[Media:Pointer.1.A.pdf |pdf]]) * Pointer.2.A ([[Media:Pointer.2.A.pdf |pdf]]) * Array.1.A ([[Media:Array.1.A.pdf |pdf]]) * Type.1.A ([[Media:Type.1.A.pdf |pdf]]) * Structure.1.A ([[Media:Structure.1.A.pdf |pdf]]) go to [ [[C programming in plain view]] ] [[Category:C programming language]] </br> d0edqr5l9bsdk2l29r8jdqy64gfer3t 2 289273 2823701 2822627 2026-08-20T20:35:05Z Dc.samizdat 2856930 /* Special relativity describes Euclidean 4-space */ 2823701 wikitext text/x-wiki = Real Euclidean four-dimensional space R⁴ = {{align|center|David Brooks Christie}} {{align|center|dc@samizdat.org}} {{align|center|Draft in progress}} {{align|center|June 2023 - August 2026}} <blockquote>'''Abstract:''' The physical universe is properly visualized as a Euclidean space of four orthogonal spatial dimensions. Space itself has a fourth orthogonal dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and our planet are only 3-dimensional objects, but nonetheless we can see in four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.</blockquote> == Summary == We observe that physical space has four perpendicular dimensions, not just three; atoms are [[W:4-polytope|4-polytopes]]; the sun is a 4-ball that is round in four dimensions; everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space; and our entire 3-space manifold is translating through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions. == A theory of the Euclidean cosmos == The physical universe is properly visualized as a [[w:Four-dimensional_space|Euclidean space of four orthogonal spatial dimensions]]. Space itself has a fourth orthogonal dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planets, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. All objects with mass move inertially through Euclidean 4-space at velocity <math>c</math> as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity <math>c</math> is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space. A typical spiral galaxy such as ours is a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our galaxy appear from our viewpoint to be distributed in a cloud of elliptical spirals occupying a flattened ellipsoid region of 3-dimensional space, but they are not so confined: they are distributed within a spherical region of 4-dimensional space. The galaxy's actual shape is spherical, not a flattened ellipsoid, but it is rounder than round can be in our ordinary experience: it occupies a hyperspherical region of space. The concentric spirals of stars that we observe lie on concentric [[W:3-sphere|3-sphere]]s (4-dimensional spheres), not on concentric 2-ellipsoids (3-dimensional elliptical spirals). Our sun and solar system lies on one of those concentric 3-spheres. More generally, orbits are circular in 4-space, and elliptical in the 3-space of their elliptic hyperplane. [[File:Hypersphere.png|thumb|Rotating illustration of the 4-ball galaxy showimg its spirals of star clouds on the surface of concentric 3-spheres, obtained by reverse sterographic projection from 3D images of the galaxy.]] The galaxy as a whole, or more properly its orbital center point, is translating through 4-space at velocity <math>c</math>, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity <math>c</math> in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity <math>c</math>. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the cylinder; their trajectories are screw-displacements, the compound of a simple rotation and a linear translation. The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around a barycentric axis. It is the tremendous inertial force of stars in motion at velocity <math>c</math> that holds the cylinder of motion together. The observed universe as a whole appears to be a 3-sphere expanding radially from a central origin point at velocity <math>c</math>, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. For all observers, the conjectured origin point of the universe corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space (the same point in the same Euclidean 4-space for all observers). The big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured separately, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity <math>c</math>. All objects in our solar system except the sun itself lie within this thinest three-dimensional manifold. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. The enclosing surface of a spherical region of 4-space is itself a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. We live within such a 3-space, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience, and it contains the earth, all the planets and the 3-dimensional space between them. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our particular 3-sphere is one of the galaxy's concentric 3-spheres of spiral star-clouds. The solar system occupies a tiny patch of this filmy 4-dimensional soap-bubble of galactic size, that is thicker-skinned than the diameter of an atom only in the interior of stars and supermassive objects. Our entire 3-sphere manifold, as a 3-spherical shell within the moving 4-ball galaxy, is translating through 4-space at velocity <math>c</math> with the galaxy, in a distinct direction that is orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the galaxy's translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of rotating objects through Euclidean space by screw translation. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity <math>c</math>, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. Any moving 3-dimensional manifold that is such an evolving surface boundary is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. Every object which we find occurring naturally in the solar system other than the sun itself, even the largest of 3-dimensional objects a planet, is a three-dimensional smear of atoms no thicker than one atom in its fourth dimension, which is the direction of its linear translation through 4-space at velocity <math>c</math>. The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be "heaped up" into larger 4-dimensional objects that form a lump in its moving surface. We have little understanding of such 4-dimensional lumps thicker than one atom, since they occur naturally in our vicinity only in the interior of the sun. In fact the sun is the only such lump occurring naturally in our solar system. We refer to 4-dimensional lumps of matter as plasma, and have little experimental knowledge of their geometry or internal structure. We know that such a lump as the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know nothing about its interior 4-ball. Every such moving 3-dimensional surface boundary of matter in the observed universe is evolving in four dimensions at velocity <math>c</math>. Its current location in 4-space corresponds to the present moment in the proper time of its inertial reference frame. Its direction of movement at velocity <math>c</math> corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from atoms to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, two orthogonal inertial motions each at the constant universal rate of transformation <math>c</math>. Every object moves relative to universal 4-coordinate space on its own distinct geodesic spiral, a screw translation trajectory that is the compound of two orthogonal inertial motions, a rotation and a translation. Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity <math>c</math> in all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is <math>c^\prime = 2c</math>, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity <math>c</math>. For example, we can look across the center of our mostly-empty 4-ball galaxy and see stars in the opposite sides of its concentric 3-sphere surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math> in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper space. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space. == Symmetries == It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel & Goodman-Strauss|2008}} As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. [[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}} <blockquote>Let <small><math>\mathrm{Q}</math></small> denote a rotation, <small><math>\mathrm{R}</math></small> a reflection, <small><math>\mathrm{T}</math></small> a translation, and let <small><math>\mathrm{Q}^q \mathrm{R}^r\mathrm{T}</math></small> denote a product of several such transformations, all commutative with one another. Then <small><math>\mathrm{RT}</math></small> is a glide-reflection (in two or three dimensions), <small><math>\mathrm{QR}</math></small> is a rotary-reflection, <small><math>\mathrm{QT}</math></small> is a screw-displacement, and <small><math>\mathrm{Q^2}</math></small> is a double rotation (in four dimensions).<br> Every orthogonal transformation is expressible as:<br> :<small><math>\mathrm{Q}^q \mathrm{R}^r</math></small><br> where <small><math>(2^q + r \le n)</math></small>, the number of dimensions.<br> Transformations involving a translation are expressible as:<br> :<small><math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}</math></small><br> where <small><math>(2^q + r + 1 \le n)</math></small>.<br> For <small><math>(n = 4)</math></small> in particular, every displacement is either a double rotation <small><math>\mathrm{Q}^2</math></small>, or a screw-displacement <small><math>\mathrm{QT}</math></small> [where the rotation component <small><math>\mathrm{Q}</math></small> is a simple rotation, but the <small><math>\mathrm{QT}</math></small> is chiral like a <small><math>\mathrm{Q^2}</math></small>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <small><math>\mathrm{QRT}</math></small>.</blockquote> If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a <small><math>\mathrm{Q^2}</math></small> or a <small><math>\mathrm{QT}</math></small>, because we can view any <small><math>\mathrm{QT}</math></small> as a <small><math>\mathrm{Q^2}</math></small> in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a <small><math>\mathrm{Q^2}</math></small>. By the same principle, we can view any <small><math>\mathrm{QT}</math></small> or <small><math>\mathrm{Q^2}</math></small> as an isoclinic (equi-angled) <small><math>\mathrm{Q^2}</math></small> by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (<small><math>\mathrm{T}</math></small>) for ''one'' of the two rotations (<small><math>\mathrm{Q}</math></small>). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (<small><math>\mathrm{Q}</math></small>) up to uncertainty, and can always distinguish the direction of their own proper time translation (<small><math>\mathrm{T}</math></small>). As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebra), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group <small><math>SO(4)</math></small> [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic <small><math>SO(4)</math></small> rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, stationary atoms exhibit the <small><math>SO(4)</math></small> symmetries of the discrete isoclinic (equi-angled) double rotations (<small><math>\mathrm{Q^2}</math></small>) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]]. == Special relativity describes Euclidean 4-space == <blockquote>Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.<ref>{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}</ref></blockquote> Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional "space" because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign to the three space coordinates so spacetime is hyperbolic, not a flat Euclidean 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was first described by Einstein himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction. Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity ''c'', in some 4-space direction. This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always ''c'', as measured by all observers from any inertial reference frame. This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source. But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity ''c''. In physics as it has been universally understood, observers are not supposed to be able to move at velocity ''c''. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four. In the Euclidean relativity alternative view, however, every observer is always moving at velocity ''c'' through the universe, which is real Euclidean 4-dimensional space <small><math>\mathbb{R^4}</math></small>. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity ''c''. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and proper space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity ''c'', in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space <small><math>\mathbb{R^4}</math></small>.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity ''c'' relative to universal 4-coordinate space, so the maximum relative velocity between two observers is 2''c'' when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to ''c'', it is the same measurement in different units. Special relativity measures all velocities in a 3-space of Minkowski spacetime. Euclidean relativity measures all velocities in Euclidean 4-space.}} So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity ''c'' in Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the "speed of light" ''c'', although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity ''c'', but in at least slightly different directions. In Einstein's relativity, the invariant ''c'' is the speed of light through 3-space. In Euclidean relativity, the invariant ''c'' is the speed of matter through 4-space! The speed of light through 3-space is also perceived as ''c'' by all observers, because they are each living in a moving 3-manifold that is moving through 4-space at velocity ''c''. Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same predictions about how observers in different reference frames will perceive each other's motions in time and space, and we shall see that they also agree on the predictions of general relativity. They both describe the same geometric relations of space and time, but they describe that geometry as embedded in two very different universal host spaces: Minkowski spacetime versus Euclidean 4-space. ...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity <math>c</math> through space and proper time ...cite Yamashita{{Sfn|Yamashita|2023}} on the equivalence of special relativity and Euclidean 4-space relativity ...cite Kappraff & Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff & Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff & Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords. Euclidean relativity is not even a fringe theory; no physicists have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could "catch up" with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at ''c'' (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than ''c''. Euclidean relativity is a revolutionary theory indeed, in which ''c'' cannot possibly be the speed of light! We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for it to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be <math>c^\prime = 2c</math>, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate linearly along the edge of a unit 4-hypercube. This is conceivable in 4-space (and in no other Euclidean space of any dimensionality) because the diagonal of the unit 4-hypercube is the natural number <small><math>\sqrt{4}</math></small>. == An object's motion in space is the product of its discrete self-reflections == Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a small number of discrete self-reflections. Any action of a geometric object that transforms its position and orientation in space may be measured as a distinct group of self-reflections of the object in its own surfaces. Any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete set of local self-reflections. Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which touch (intersect each other). When a object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality. Coxeter's laws of motion are a geometric counterpart to Newton's laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures. But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. For example, they give us geometric pictures of all the possible motions of objects in four dimensional Euclidean space: <blockquote>Every orthogonal transformation in 4-space is expressible as:<br> :<small><math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t</math></small><br> where <small><math>(2^q + r + t \le 4)</math></small>. Every displacement is either a double rotation <small><math>\mathrm{Q}^2</math></small>, or a screw-displacement <small><math>\mathrm{QT}</math></small> [where the rotation component <small><math>\mathrm{Q}</math></small> is a simple rotation, but the <small><math>\mathrm{QT}</math></small> is chiral like a <small><math>\mathrm{Q^2}</math></small>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <small><math>\mathrm{QRT}</math></small>.</blockquote> While this description should be understood as simple geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (<small><math>\mathrm{Q}</math></small>), reflection (<small><math>\mathrm{R}</math></small>) and translation (<small><math>\mathrm{T}</math></small>) are just what they are in three-dimensional space, but double rotation (<small><math>\mathrm{Q}^2</math></small>) is something new and unprecedented in our physical experience, because double rotations cannot occur until you have four or more dimensions of space to rotate in. ...to readers who have not studied Coxeter (almost all readers including TAC), the blockquote above is "just math", not visualizable geometry...but I could describe Coxeter's congruent transformations in 4-space here geometrically: I could say clearly what they mean in spatial terms, in language anyone can understand, because they don't require any math to be understood; the "math" here is really just simple pictures (reflections and rotations); even double rotations can be visualized by dimensional analogy, as compounds of simple rotations...since even most physicists are unacquainted with Coxeter geometry, it might be useful to do this here... == Light propagates through 4-space at twice its apparent velocity ''c''== Coxeter's geometric laws of motion apply to all objects with mass in 4-dimensional Euclidean space, but we find there is an additional kind of displacement which applies only to massless particles such as photons. Light quanta (photons) translate through 4-space by 4-dimensional reflection <small><math>\mathrm{R}^4</math></small>, which may be termed a double translation <small><math>\mathrm{T}^2</math></small>, a pure translation via two pairs of parallel reflections, without any rotation component <small><math>\mathrm{Q}</math></small>. Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by <small><math>\mathrm{QT}</math></small>, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic <small><math>\mathrm{Q^2}</math></small>, an isoclinically rotating object such as an atom. A simple rotation <small><math>\mathrm{Q}</math></small> or simple translation <small><math>\mathrm{T}</math></small> is a double reflection <small><math>\mathrm{R^2}</math></small>, so a <small><math>\mathrm{QT}</math></small> or <small><math>\mathrm{Q^2}</math></small> is also an <small><math>\mathrm{R^4}</math></small>, but not with the same group of reflection angles as a light signal <small><math>\mathrm{R^4}</math></small>. A translation <small><math>\mathrm{T = R^2}</math></small> is a double reflection in two parallel planes, and a rotation <small><math>\mathrm{Q = R^2}</math></small> is a double reflection in two intersecting planes, as in a <small><math>\mathrm{QT = R^4}</math></small> which is both at once. A double translation <small><math>\mathrm{T^2 = R^4}</math></small> is two double reflections in pairs of parallel planes at once, a reflection in four or more non-intersecting parallel planes; it is all translation and no rotation. In a <small><math>\mathrm{T^2}</math></small> all the motion goes to translation, so the translation goes twice as far as the simple translation <small><math>\mathrm{T}</math></small> in a <small><math>\mathrm{QT}</math></small>. A double translation <small><math>\mathrm{T^2 = R^4}</math></small> is the opposite of a double rotation <small><math>\mathrm{Q^2 = R^4}</math></small>, which is stationary but rotates twice as fast as the simple rotation <small><math>\mathrm{Q}</math></small> in a <small><math>\mathrm{QT}</math></small>. The product of the two translations in a <small><math>\mathrm{T^2}</math></small> is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple <small><math>\mathrm{T}</math></small> over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double-the-distance translation, but without any rotation component, so it cannot carry any mass with it. A <small><math>\mathrm{T^2}</math></small> cannot reposition a 4-polytope the way a <small><math>\mathrm{QT}</math></small> does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter. ...lensing of double translations <small><math>\mathrm{T^2 = R^4}</math></small> in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet... == The Kepler problem is framed in Euclidean 4-space == The [[W:Kepler problem|Kepler problem]] is named for [[W:Johannes Kepler|Johannes Kepler]], arguably the greatest geometer since the ancients up to [[w:Ludwig Schläfli|Ludwig Schläfli]], who proposed [[W:Kepler's laws of planetary motion|Kepler's laws of planetary motion]] which solved the problem of the orbits of the planets, and investigated the types of forces that would result in orbits obeying those laws. Those forces were later identified by [[W:Isaac Newton|Isaac Newton]] in his[[W:Philosophiæ Naturalis Principia Mathematica| Principia]], where he proves what today might be called the "inverse Kepler problem": the orbit characteristics require the force to depend on the inverse square of the distance.<ref>{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton & Company|isbn=978-0393039184}}</ref> The inverse square law behind the Kepler problem is the [[W:Central force|central force]] law which governs not only [[W:Newtonian gravity|Newtonian gravity]] and celestial orbits, but also the motion of two charged particles in [[W:Coulomb’s law|Coulomb’s law]] of [[W:Electrostatics|electrostatics]]; it applies to attractive or repulsive forces. Problems in which two bodies interact by a central force that varies as the [[W:Inverse square law|inverse square]] of the distance between them are called Kepler problems. Thus the [[W:Hydrogen atom|hydrogen atom]] is a Kepler problem, since it comprises two charged particles interacting by Coulomb's law, another inverse-square central force. Using classical mechanics, the solution to a Kepler problem can be expressed as a [[W:Kepler orbit|Kepler orbit]] using six kinematical variables or [[W:Orbital elements|orbital elements]]. The solution conserves an orbital element called the [[W:Laplace–Runge–Lenz vector|Laplace–Runge–Lenz (LRL) vector]], a [[W:Constant of motion|constant of motion]], meaning that it is the same no matter where it is calculated on the orbit. The LRL vector was essential in the first quantum mechanical derivation of the [[W:Atomic emission spectrum|spectrum]] of the hydrogen atom, but this approach has rarely been used since the development of the [[W:Schrödinger equation|Schrödinger equation]]. The conservation of the LRL vector corresponds to the <small><math>SO(4)</math></small> symmetry, by Nother's theorem. The LRL vector lies orthogonal to both the orbital plane and the angular momentum vector of the Kepler orbit; we observe that it lies in a fourth orthogonal dimension. Fock in 1935<ref>V. Fock, Zur Theorie des Wasserstoffatoms, Zeitschrift für Physik. 98 (3-4) (1935), 145–154.</ref> and Moser in 1970<ref>J. Moser, Regularization of Kepler’s problem and the averaging method on a manifold, Commun. Pure Appl. 23 (1970), 609–636</ref> observed that the Kepler problem is mathematically equivalent to non-affine geodesic motion (a particle moving freely) on the surface of a 3-sphere, so that the whole problem is symmetric under certain rotations of the four-dimensional space. This higher-dimensional symmetry results in two well-known properties of the Kepler problem: the momentum vector always moves in a perfect circle and, for a given total energy, all such velocity circles intersect each other in the same two points. ... Relativity establishes that an orbit in space is viewed in a different way in each distinct inertial reference frame. Depending on the choice of reference frame, the same Kepler system may be seen to be performing any one of a sequence of relativistically equivalent rotations in 4-space, on a continuum from an isoclinic rotation (Q²) in the orbit's proper reference frame, to a screw transfer (QT) with a simple rotation component (Q) and a translation component (T) at velocity <math>c</math>, in the universal reference frame of 4-coordinate space wherein every object is seen to be translating at velocity <math>c</math>. In reference frames between these two limit cases, the orbit is seen to be performing a double rotation (Q²) at two unequal, completely orthogonal angular rates of rotation: an elliptical double rotation. These include the reference frames of most typical observers, who are moving slowly relative to the observed orbital system's reference frame (their relative motion is a small fraction of the speed of light). ...this is probably misplaced here and should not interrupt the discussion at this point: ...These typical observations agree closely with the predictions of special relativity, because the non-isoclinic elliptical (Q²) resembles a (QT), since one of its two completely orthogonal rotations (Q) has such a long period that it is almost indistinguishable from a straight translation (T). All orbits in 4-space are isoclinic in their own reference frame. Orbiting objects in their own proper Kepler systems follow circular geodesic isoclines through 4-space. Orbits in 4-space are perfectly circular in their own reference frame, as Copernicus assumed the orbits of planets to be. It is the orbit's path through the 3-space of its elliptic hyperplane that is an ellipse, as Kepler found it to be. ...cite Jesper Goransson's very concise paper The geodesic circle that an orbiting object follows through 4-space in the proper reference frame of its own Kepler system is not a simple great circle which turns in two orthogonal dimensions. It is a helical great circle that turns in four orthogonal dimensions at once.{{Efn|Geodesic orbits in 4-space are not simple 2-dimensional great circles; they are helical 4-dimensional great circles that curve in all four dimensions at once. Their circular trajectories are helixes which we call ''isoclines'', since they are the paths taken by points on a rigid object undergoing isoclinic rotation.}} Such circles lie outside our physical experience, since our local space has only three orthogonal dimensions. Nonetheless we can visualize them in imagination, because their helical, circular shape is perfectly well defined by the kinematical variables of the Kepler orbit. The real physical correlates of abstract orthogonal planes and rotation angles are already familiar to us viscerally in our body-language of physical experience, since we are endowed biologically with highly evolved visual signal processing engines. These enable us to see and understand spatial relations and motions, including rotations, without even thinking about angles and orthogonal planes. This physical endowment is an inborn capacity for dimensional analogy which our biologic evolution has provided. All our instinctive spatial reasoning is by dimensional analogy from flat 2-dimensional retinal images to 3-dimensional scenes, using our powerful inborn visualization capacities of reverse stereographic projection and pattern recognition. We humans are thus very well equipped with everything we need to see in four-dimensional space, except experience. ... Recently Anco and Moghadam found that through Noether’s theorem in reverse, the LRL vector gives rise to a corresponding infinitesimal dynamical symmetry on the kinematical variables, which they show to be the semi-direct product of <small><math>SO(3)</math></small> and <small><math>\mathbb{R^3}</math></small>, in contrast to the <small><math>SO(4)</math></small> symmetry group generated by the LRL symmetries and the rotations.{{Sfn|Anco|Moghadam|2026|ps=; The physically relevant part of the LRL vector is its direction ... since its magnitude is just a function of energy and angular momentum.}} This remarkable symmetry breaking is expressive of the ''dimensional relativity'' between ordinary 3-space <small><math>\mathbb{R^3}</math></small>, spherical space <small><math>S^3</math></small> and Euclidean space <small><math>\mathbb{R^4}</math></small>. Consider a hydrogen atom in a Kepler orbit: for example, a hydrogen atom moving freely in space in an orbit around the sun. It is a ''double'' Kepler problem: an electrostatic Kepler problem within itself, and a gravitational Kepler problem in its environment. The ''single'' electrostatic Kepler problem of a hydrogen atom moving freely in space beyond any gravitational influence is a problem in special relativity. In our Euclidean 4-space model, this atom viewed as stationary in its own proper reference frame exhibits an <small><math>SO(4)</math></small> rotation symmetry corresponding to an isoclinic double rotation (<small><math>\mathrm{Q^2}</math></small>). The fourth dimension in this reference frame is the atom's proper time vector; it has constant velocity <math>c</math> and constant direction. From the point of view of our universal 4-coordinate space (which cannot be the proper inertial reference frame of any physical observer, all of whom are moving relative to it at velocity ''c''), the entire Kepler system (the atom) is translating through 4-space via a screw translation (<small><math>\mathrm{QT}</math></small>) at constant velocity <math>c</math>. From this viewpoint the atom has only a simple <small><math>SO(3)</math></small> rotation component (<small><math>\mathrm{Q}</math></small>), breaking its stationary <small><math>SO(4)</math></small> isoclinic rotation symmetry (<small><math>\mathrm{Q^2}</math></small>). Because each discrete part of the rotating atom moves along a helical trajectory through 4-space, the atom is in orbit around a barycentric axis (like a star in a galaxy), but only in a tiny orbit within its own radius, which is its inertial domain of rotation. The straight 4-dimensional cylinder it progresses along at velocity <math>c</math> is very narrow: only the diameter of the rotating atom itself. The gravitational Kepler problem of a hydrogen atom in a Kepler orbit around the sun is a problem in general relativity. In our 4-space model, this atom viewed in its own proper reference frame exhibits the same <small><math>SO(4)</math></small> rotation symmetry as it did in the electrostatic Kepler problem where the atom was translating linearly through space. The Kepler system in this case is not just the atom; it is the entire solar system. The LRL vector of this Kepler system is the proper time vector of the atom's inertial reference frame; once again it has constant velocity ''and constant direction''. Although the momentum vector moves in a perfect circle as the atom orbits the sun, the 4-space LRL vector does not move at all: it is a constant of motion, of linear motion (<small><math>\mathrm{T}</math></small>) of the Kepler system (the entire solar system in this case) in a constant 4-space direction, the proper time direction of the system. The direction of the system's proper time vector would vary under some kinds of acceleration of the atom, but it is constant under this kind of orbital acceleration. It continues to point in the same direction, like a 4-space compass needle, as the atom winds its way along its spiral path around the axis of the sun's straight-line translation through 4-space at velocity <math>c</math>. This compass needle always points in the direction the sun is moving, not the direction the atom is moving at any instant. ...Its Kepler orbit around the sun is its <small><math>SO(3)</math></small> rotation component (<small><math>\mathrm{Q}</math></small>). Although the atom is moving on a geodesic circle in the second problem, by the [[equivalence principle]] the difference in the state of the atomic systems in these two problems cannot be observed by examining the atoms alone. Even from another inertial reference frame, where the atom in the second problem is seen to be translating through 4-space via a wide screw translation (<small><math>\mathrm{QT}</math></small>) around the sun's axis of motion, there is still no difference between the two problems which can be detected by examining only the atoms within their own proper reference frames (even over time), because the LRL vector (<small><math>\mathrm{T}</math></small>) is a constant of motion of the entire system in both cases. ...Anco and Maghadam found that <small><math>SO(4)</math></small>) breaks to ... <small><math>S^3</math></small>)... if the energy in the Kepler orbit is negative (an elliptical orbit), and to ... <small><math>H^3</math></small>) ... Minkowski spacetime if the energy is positive (a hyperbolic orbit). ... Finally we consider a third problem in which a hydrogen atom enters the solar system as a comet, loops around the sun and exits the solar system again. This atom... ... As Hamilton found when he discovered the quaternions, we see that it is necessary to admit a fourth dimension to the system in order to properly model the problem: in Hamilton's case the general problem of ..., and in our case the Kepler problem. These are instances of the same problem in 4-dimensional Euclidean geometry, and indeed a solution to the Kepler problem in quaternions (the four Cartesian coordinates of Euclidean 4-space) is a solution to it in our model of the 4-coordinate Euclidean cosmos. == Distribution of stars in our galaxy == The stars in our own galaxy appear to us to be a rotating spiral cluster in 3-dimensional space. By assuming that light from them reaches us on straight lines through space, by assuming that we can measure their distance from us by its red shift, and by assuming that they are distributed in three dimensions of space, we have plotted their locations in 3-space. If we abandon the last of those three assumptions, we can just as easily reinterpret that dataset to plot their distribution around us in 4-dimensional space, and see how they actually lie. When we perform this experiment on the data for the stars in our galaxy, do we indeed find that they are distributed non-uniformly in various concentric spirals, but the spirals lie on the surface of various 3-spheres, rather than in elliptical orbits as we saw them in 3-space? That would be an expected consequence of the special rotational symmetry group of 4-space <small><math>SO(4)</math></small>, in which circular (isoclinic) orbits are the geodesics (shortest rotational paths) rather than elliptical (non-equi-angled double rotation) orbits. ...have to perform this experiment somehow, at least as a conclusive thought experiment, before I publish this paper... == Rotations == The [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotations]] of the convex [[W:regular 4-polytope|regular 4-polytope]]s are usually described as discrete rotations of a rigid object. For example, the rigid [[24-cell]] can rotate in a [[24-cell#Great hexagons|hexagonal]] (6-vertex) central [[24-cell#Planes of rotation|plane of rotation]]. A 4-dimensional [[24-cell#Isoclinic rotations|''isoclinic'' rotation]] (as distinct from a [[24-cell#Simple rotations|''simple'' rotation]] like the ones that occur in 3-dimensional space) is a ''diagonal'' rotation in multiple [[W:Clifford parallel|Clifford parallel]] [[24-cell#Geodesics|central planes]] of rotation at once. It is diagonal because it is a [[W:SO(4)#Double rotations|double rotation]]: in addition to rotating in parallel (like wheels), the multiple planes of rotation also tilt sideways in the completely orthogonal plane of rotation (like coins flipping) into each other's planes. Consequently, the path taken by each vertex is a [[24-cell#Helical hexagrams and their isoclines|twisted helical circle]], rather than the ordinary flat great circle a vertex follows in a simple rotation. In a rigid 4-polytope rotating isoclinically, ''all'' the vertices lie in one of the parallel planes of rotation, so all the vertices move in parallel along Clifford parallel twisting circular paths. [[24-cell#Clifford parallel polytopes|Clifford parallel planes]] are not parallel in the normal sense of parallel planes in three dimensions; the vertices are all moving in different directions around the [[W:3-sphere|3-sphere]]. In one complete 360° isoclinic revolution, a rigid 4-polytope turns itself inside out. This is sufficiently different from the simple rotations of rigid bodies in our 3-dimensional experience that a [[24-cell#Rotations|detailed description]] enabling the reader to properly visualize its counter-intuitive consequences runs to many pages and illustrations, with many accompanying pages of explanatory notes on surprising phenomena that arise in 4-dimensional space: [[24-cell#Great squares|completely orthogonal planes]], [[24-cell#Clifford parallel polytopes|Clifford parallelism]]{{Efn|name=Clifford parallels}} and [[W:Hopf fibration|Hopf fiber bundles]], [[24-cell#Isoclinic rotations|isoclinic geodesic paths]], and [[24-cell#Double rotations|chiral (mirror image) pairs of rotations]], among other complexities. Moreover, the characteristic rotations of the various regular 4-polytopes are all different; each is a unique surprise. [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|The 6 regular convex 4-polytopes]] have different numbers of vertices (5, 8, 16, 24, 120 and 600 respectively) and those with fewer vertices occur inscribed in those with more vertices (with one exception), with the result that the more complex 4-polytopes subsume the kinds of rotations characteristic of their less complex predecessors, as well as each having a characteristic kind of rotation not found in their predecessors. None of these symmetries is to be found in 3-dimensional space, although their simpler 3-dimensional analogues are all present there. [[W:Euclidean geometry#Higher dimensions|Four dimensional Euclidean space]] is more complicated (and more interesting) than three dimensional space because there is more room in it, in which unprecedented things can happen. It subsumes 3-dimensional space, with all of the symmetries we are accustomed to, and adds astonishing new surprises. These are hard for us to visualize, because the only way we can experience them is in our imagination; we have no body of sensory experience in 4-dimensional space to draw upon, other than our evolution in time. For that reason (our difficulty in visualizing them), descriptions of isoclinic rotations usually begin and end with rigid rotations: [[24-cell#Isoclinic rotations|for example]], all 24 vertices of a single rigid 24-cell rotating in unison, with 6 vertices evenly spaced around each of 4 Clifford parallel twisted circles.{{Efn|name=360 degree geodesic path visiting 3 hexagonal planes}} But that is only the simplest case, which is easiest for us to understand. Compound and [[W:Kinematics|kinematic]] 24-cells (with moving parts) are even more interesting (and more complicated) than the rotation of a single rigid 24-cell. To begin with, when we examine the individual parts of a single rigid 24-cell that are moving in an isoclinic rotation, such as the orbits of individual vertices, we can imagine a case where fewer than 24 point-objects are orbiting on those twisted circular paths at once. [[24-cell#Reflections|For example]], if we imagine just 8 point-objects, evenly spaced around the 24-cell at [[24-cell#Reciprocal constructions from 8-cell and 16-cell|the 8 vertices that lie on the 4 coordinate axes]], and rotate them isoclinically along exactly the same orbits they would take in the above-mentioned rotation of a rigid 24-cell, then in the course of a single 360° rotation the 8 point-objects will trace out the whole 24-cell, with just one point-object reaching each of the 24 vertex positions just once, and no point-object colliding with (or even crossing the path of) any other at any time. This is an example of a discrete Hopf fibration. But it is still an example of a rigid object in a discrete isoclinic rotation: a rigid 8-vertex object (called the 4-[[W:orthoplex|orthoplex]] or [[16-cell]]) performing one half of the characteristic rotation of the 24-cell. We can also imagine ''combining'' distinct isoclinic rotations. What happens when multiple point-objects are orbiting at once, but do ''not'' all follow the Clifford parallel paths characteristic of the ''same'' distinct rigid rotation? What happens when we combine orbits from distinct rotations characteristic of different 4-polytopes, for example when different rigid 4-polytopes are concentric and rotating simultaneously in their characteristic ways? What kinds of such hybrid rotations are possible in the same 3-sphere shell without collisions? In adjacent concentric shells without asymmetric imbalance? What sort of [[Kinematics of the cuboctahedron|kinematic polytopes]] do they trace out, and how do their [[24-cell#Clifford parallel polytopes|component parts]] relate to each other as they move? Is there (sometimes) some kind of mutual stability amid their lack of combined rigidity? Visualizing isoclinic rotations (rigid and otherwise) allows us to explore such questions of [[W:kinematics|kinematics]], and where dynamic stabilities arise, of [[wikipedia:kinetics (physics)|kinetics]]. In four dimensions, we discover that space has more room in it than we have experienced, which permits previously unimagined motions. Even 3-space is more commodious than we thought; when it is curved and lies embedded in a higher-dimensional space, it permits previously impossible symmetric packings. Sadoc studied double-twisted 3-dimensional molecules, and imagined them embedded in 4-dimensional space as the Hopf fibrations of regular 4-polytopes. He found that these molecules would close-pack on the 3-sphere perfectly without exhibiting any torsion, although their packing in ordinary flat 3-space is imperfect, "frustrated" by their twisted geometry. <blockquote>The frustration, which arises when the molecular orientation is transported along the two [spiral] AB paths of figure 1 [double twist helix], is imposed by the very topological nature of the Euclidean space R³. It would not occur if the molecules were embedded in the non-Euclidean space of the [[W:3-sphere|3-sphere]] S³, or hypersphere. This space with a homogeneous positive curvature can indeed be described by equidistant and uniformly twisted fibers, along which the molecules can be aligned without any conflict between compactness and [[W:torsion of a curve|torsion]].... The fibres of this [[W:Hopf fibration|Hopf fibration]] are great circles of S³, the whole family of which is also called the [[W:Clifford parallel|Clifford parallel]]s.{{Efn|name=Clifford parallels}} Two of these fibers are C_∞ symmetry axes for the whole fibration; each fibre makes one turn around each axis and regularly rotates when moving from one axis to another.{{Efn|name=helical geodesic}} These fibers build a double twist configuration while staying parallel, i.e. without any frustration, in the whole volume of S³.{{Efn|name=Petrie polygon of a honeycomb}} They can therefore be used as models to study the condensation of long molecules in the presence of a double twist constraint.{{Sfn|Sadoc & Charvolin|2009|loc=§1.2 The curved space approach|ps=; studies the helical orientation of molecules in crystal structures and their imperfect packings ("frustrations") in 3-dimensional space.}}</blockquote> Of course we do not find molecules condensing to close-pack the 3-sphere in our experience, and Sadoc does not say that we do. We find 3-spheres in the atomic realm (if atoms are 4-polytopes), and in the cosmic realm (as the surface boundaries of stars, and the concentric surfaces of galaxies). But in between, in the realm of ordinary experience which includes the molecular realm, ourselves and all the objects we can materially handle or observe up close including the planets, we are confined together by gravity as inertia within a curved 3-dimensional space that is no more than one atom thick in the fourth spatial dimension. That is why in the molecular realm we find only objects that occupy 3-spaces which, though infinitesimally curved in the fourth dimension, are tiny patches on whole 3-spheres of galactic size. So Sadoc's exercise is a thought experiment, like Einstein's gedankenexperiments about railroad embankments and trains moving at nearly the speed of light. It is no less illuminating, despite the symmetry it reveals not having a realization as an actual 3-sphere of actual molecules. And might not something very like it have an actual realization in the atomic realm? We know that atoms have their own complex internal structure, which we are unable to model geometrically in ordinary 3-dimensional space. Suppose such a model is impossible because an atom is actually a 4-polytope occupying a tiny spherical region of 4-dimensional space, and so we only find its constituent particles in close-packed helical orbits on the 3-sphere, in the manner of Sadoc's imaginary twisted molecules, but as real 4-dimensional helices of atomic scale. We would expect to find the atomic orbit of a fundamental particle in some discrete Hopf fibration characteristic of a symmetry group, that is, on the maximally symmetric isoclines of a discrete isoclinic rotation characteristic of some regular 4-polytope and the particle. == A theory of the Euclidean atom == <blockquote>Because quantum physics could be tested without being understood, it allowed humans to see how the universe worked without knowing why.<ref>Sebastian Junger, In My Time of Dying</ref></blockquote> ... == Light and Mass are Reflection and Rotation == The phenomena of light and mass are expressions of reflection symmetries and rotation symmetries, respectively. ... Atoms are 4-polytopes, elementary objects with SO(4) rotational symmetry. Light is .... Motion in space is the propagation of the elementary objects of light and matter in Coxeter congruent transformations by kaleidoscopic self-reflections, like the motion of self-reproducing cellular automata in [[Conway's Game of Life|Conway's game of life]]. ... Light is discrete reflections. Mass is discrete rotations. Both are group actions, expressions of intrinsic symmetries. That is all of physics. === Atoms are 4-polytopes === ... == Relativity in real space of four or more orthogonal dimensions == Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions. General relativity is Galilean relativity in a general space of four or more orthogonal dimensions, e.g. in Euclidean 4-space <math>R^4</math>, spherical 4-space <math>S^4</math>, and any orthogonal 4-manifold. Light is a consequence of symmetry group reflections at quantum scale. Gravity and the other fundamental forces are consequences of rotations, which are consequences of quantum reflections. Light is discrete reflections. Gravity and all forces are discrete rotations. Both are group actions, expressions of intrinsic symmetries. That is all of physics. Every observer may properly see themself as stationary and the universe as an ''n''-sphere with themself at the center. The curvature of these spheres is a function of the rate at which causality evolves, and can be measured by the observer as the speed of light. === Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions === ...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here... Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in three spatial dimensions. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (In general relativity, discussed below, the actual rate of physical processes varies from place to place, and those differences are neither reciprocal nor illusory.) None of these Lorentz effects are beyond geometric explanation or paradoxical. The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, successive Euclidean spaces are dimensionally analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature, is an exact expression of intrinsic symmetries: that is Nother's great discovery. === General relativity is Galilean relativity in a general space of four orthogonal dimensions === ... == Dimensional relativity == Coxeter's kinetic law of <math>n</math>-dimensional congruent Euclidean transformations may be called ''dimensional relativity'', since it captures the theories of special and general relativity entire, and has its roots in dimensional analogy. Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessable by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated. By analogy to the surface of the earth, the bounding surface of a spherical region of <math>n</math>-dimensional Euclidean space is an <math>(n-1)</math>-sphere, a spherical space of one fewer dimensions than the <math>n</math>-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean <math>n</math>-spaces of increasing <math>n</math>, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating <math>n</math>-spaces. By the degree of dimensional analogy of which they are capable, some observers see deeper into <math>n</math>-dimensional space than others. == Polycentric spherical relativity == An intelligent observer equipped with the principle of relativity may perceive the universe from any inertial reference frame, not only from their own proper perspective. We see that every observer may properly view themself as stationary and the universe as an ''n''-sphere with themself at the center observing it, perceptually equidistant from all points on its surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything. This ''polycentric model'' of the universe is a further restatement of the principle of relativity. It is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. It should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849: "The universe is a sphere whose center is wherever there is intelligence."{{Sfn|Thoreau|1849|p=349|ps=; "The universe is a sphere whose center is wherever there is intelligence." [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}} == Revolutions == The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity ''c'', with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may, or may not, all have the same origin in space and time. As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment we dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed us that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a sense related to time, at least, it must be 4-dimensional. In this work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space. Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we now observe them, any more than they lie in the three dimensional hyperplane of local space in which we find everything residing in our solar system. When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us only by virtue of how long it takes their light to reach us. We can measure their distribution around us in 4-space, but that is simply how we choose to measure them, not a finding of how they are actually distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean ''n''-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity <math>c</math>, on more or less divergent paths from each other. But only much closer observation will reveal evidence of whether everything we see lies in the same 4-space, or if it is distributed in five or more dimensions, and how it is moving there. To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity <math>c</math>, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw displacements), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw displacement has ''two'' [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity <math>c</math> in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that each galaxy's own distinct 3-sphere is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to lightspeed long ago, in whatever big bang our atoms emerged from, and have never slowed down since. == Origins of the theory == Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of the geometry of Euclidean 4-space relativity, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] contains the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and did not describe our ordinary 3-space embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.<ref>{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}</ref> He invited us to imagine "A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions", but he was careful to disclaim parenthetically that "The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice." Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal of that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.'' The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified spacetime of four dimensions. Anco and Maghadam found that <small><math>SO(4)</math></small> breaks to ... <small><math>S^3</math></small>... if the energy in the Kepler orbit is negative (an elliptical orbit), and to ... <small><math>H^3</math></small> ... Minkowski spacetime if the energy is positive (a hyperbolic orbit). Because the planets orbit on ellipses in our 3-space, Euclidean 4-space is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the truer model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position of centrality as our exclusive conception of our place in space. ...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others. The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; "Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions."}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.<ref>{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}</ref>}} == Boundaries == <blockquote>Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.<ref>{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}</ref></blockquote> Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? ''What is the nature of the boundary which confines us to just three dimensions?'' We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell. Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined motions and objects. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. A boundary is an explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force. <blockquote>The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three .... In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it. We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed "Dimensional Analogy."<ref>{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}</ref></blockquote> I believe, but I cannot prove, that we live in real space, which is Schläfli's and Coxeter's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover in imagination and then explore physically, each an astonishing new enlightenment.<ref>{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}<blockquote> :We shall not cease from exploration :And the end of all our exploring :Will be to arrive where we started :And know the place for the first time. :Through the unknown, remembered gate :When the last of earth left to discover :Is that which was the beginning; :At the source of the longest river :The voice of the hidden waterfall :And the children in the apple-tree :Not known, because not looked for :But heard, half-heard, in the stillness :Between two waves of the sea. </blockquote></ref> Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. This project is forever beginning anew. Coxeter showed us that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether showed us all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions, in which all objects with mass move ceaselessly at the constant velocity <math>c</math>, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages. <blockquote> ::::::BEECH :Where my imaginary line :Bends square in woods, an iron spine :And pile of real rocks have been founded. :And off this corner in the wild, :Where these are driven in and piled, :One tree, by being deeply wounded, :Has been impressed as Witness Tree :And made commit to memory :My proof of being not unbounded. :Thus truth's established and borne out, :Though circumstanced with dark and doubt— :Though by a world of doubt surrounded. :::::::—''The Moodie Forester''<ref>{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}</ref> </blockquote> == Appendix: Sequence of regular 4-polytopes == {{Regular convex 4-polytopes|wiki=W:|columns=7}} == ... == {{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}} {{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}} {{Efn|The long radius (center to vertex) of the 24-cell is equal to its edge length; thus its long diameter (vertex to opposite vertex) is 2 edge lengths. Only a few uniform polytopes have this property, including the four-dimensional 24-cell and [[W:Tesseract#Radial equilateral symmetry|tesseract]], the three-dimensional [[W:Cuboctahedron#Radial equilateral symmetry|cuboctahedron]], and the two-dimensional [[W:Hexagon#Regular hexagon|hexagon]]. (The cuboctahedron is the equatorial cross section of the 24-cell, and the hexagon is the equatorial cross section of the cuboctahedron.) '''Radially equilateral''' polytopes are those which can be constructed, with their long radii, from equilateral triangles which meet at the center of the polytope, each contributing two radii and an edge.|name=radially equilateral|group=}} {{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as "the convex hull of the neighbouring vertices of a given vertex".{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its "radius" equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}} {{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example: {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0) {{indent|5}}({{spaces|2}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>){{spaces|3}}({{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>) {{indent|5}}(–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>){{spaces|3}}(–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>) {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)<br> is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}} {{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60° rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the "left" is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}} {{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}} {{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; "In mathematics, the path that the (1, 1) knot on the torus traces is also known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two intersecting circles that are the cross-section of a torus by a well-chosen plane cutting it. Picking one such circle and rotating it around the torus axis, the resulting family of circles can be used to rule the torus. By nesting tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the (1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles]."}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}} {{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}} {{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}} {{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}} {{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}} {{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}} {{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}} {{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}} {{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}} {{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90^o bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60^o bend, or as a straight line with one 60^o bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}} {{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; "In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)"}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}} {{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}} {{Efn|Departing from any vertex V₀ in the original great hexagon plane of isoclinic rotation P₀, the first vertex reached V₁ is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P₁. P₁ is inclined to P₀ at a 60° angle.{{Efn|P₀ and P₁ lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V₂ is 120 degrees beyond V₁ along a second {{radic|3}} chord lying in another hexagonal plane P₂ that is Clifford parallel to P₀.{{Efn|P₀ and P₂ are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V₀ and V₂ are ''two'' {{radic|3}} chords apart{{Efn|V₀ and V₂ are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V₀ and V₂ are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P₀ and P₂ are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V₁ lies in both intersecting planes P₁ and P₂, as V₀ lies in both P₀ and P₁. But P₀ and P₂ have ''no'' vertices in common; they do not intersect.) The third vertex reached V₃ is 120 degrees beyond V₂ along a third {{radic|3}} chord lying in another hexagonal plane P₃ that is Clifford parallel to P₁. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V₀ to V₃ is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}} {{Sfn|Mamone, Pileio & Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹₄.}} ==Notes== {{Regular convex 4-polytopes Notelist|wiki=W:}} ==Citations== {{Regular convex 4-polytopes Reflist|wiki=W:}} ==References== {{Refbegin}} * {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}} * {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1}} * {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}} === [[Polyscheme|Polyschemes]] === {{Regular convex 4-polytopes Refs|wiki=W:}} {{Refend}} adquo2q5pnmig3vqtjhfevwqgqrt87t 2823706 2823701 2026-08-20T20:45:16Z Dc.samizdat 2856930 /* Special relativity describes Euclidean 4-space */ 2823706 wikitext text/x-wiki = Real Euclidean four-dimensional space R⁴ = {{align|center|David Brooks Christie}} {{align|center|dc@samizdat.org}} {{align|center|Draft in progress}} {{align|center|June 2023 - August 2026}} <blockquote>'''Abstract:''' The physical universe is properly visualized as a Euclidean space of four orthogonal spatial dimensions. Space itself has a fourth orthogonal dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and our planet are only 3-dimensional objects, but nonetheless we can see in four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.</blockquote> == Summary == We observe that physical space has four perpendicular dimensions, not just three; atoms are [[W:4-polytope|4-polytopes]]; the sun is a 4-ball that is round in four dimensions; everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space; and our entire 3-space manifold is translating through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions. == A theory of the Euclidean cosmos == The physical universe is properly visualized as a [[w:Four-dimensional_space|Euclidean space of four orthogonal spatial dimensions]]. Space itself has a fourth orthogonal dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planets, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. All objects with mass move inertially through Euclidean 4-space at velocity <math>c</math> as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity <math>c</math> is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space. A typical spiral galaxy such as ours is a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our galaxy appear from our viewpoint to be distributed in a cloud of elliptical spirals occupying a flattened ellipsoid region of 3-dimensional space, but they are not so confined: they are distributed within a spherical region of 4-dimensional space. The galaxy's actual shape is spherical, not a flattened ellipsoid, but it is rounder than round can be in our ordinary experience: it occupies a hyperspherical region of space. The concentric spirals of stars that we observe lie on concentric [[W:3-sphere|3-sphere]]s (4-dimensional spheres), not on concentric 2-ellipsoids (3-dimensional elliptical spirals). Our sun and solar system lies on one of those concentric 3-spheres. More generally, orbits are circular in 4-space, and elliptical in the 3-space of their elliptic hyperplane. [[File:Hypersphere.png|thumb|Rotating illustration of the 4-ball galaxy showimg its spirals of star clouds on the surface of concentric 3-spheres, obtained by reverse sterographic projection from 3D images of the galaxy.]] The galaxy as a whole, or more properly its orbital center point, is translating through 4-space at velocity <math>c</math>, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity <math>c</math> in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity <math>c</math>. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the cylinder; their trajectories are screw-displacements, the compound of a simple rotation and a linear translation. The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around a barycentric axis. It is the tremendous inertial force of stars in motion at velocity <math>c</math> that holds the cylinder of motion together. The observed universe as a whole appears to be a 3-sphere expanding radially from a central origin point at velocity <math>c</math>, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. For all observers, the conjectured origin point of the universe corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space (the same point in the same Euclidean 4-space for all observers). The big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured separately, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity <math>c</math>. All objects in our solar system except the sun itself lie within this thinest three-dimensional manifold. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. The enclosing surface of a spherical region of 4-space is itself a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. We live within such a 3-space, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience, and it contains the earth, all the planets and the 3-dimensional space between them. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our particular 3-sphere is one of the galaxy's concentric 3-spheres of spiral star-clouds. The solar system occupies a tiny patch of this filmy 4-dimensional soap-bubble of galactic size, that is thicker-skinned than the diameter of an atom only in the interior of stars and supermassive objects. Our entire 3-sphere manifold, as a 3-spherical shell within the moving 4-ball galaxy, is translating through 4-space at velocity <math>c</math> with the galaxy, in a distinct direction that is orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the galaxy's translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of rotating objects through Euclidean space by screw translation. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity <math>c</math>, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. Any moving 3-dimensional manifold that is such an evolving surface boundary is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. Every object which we find occurring naturally in the solar system other than the sun itself, even the largest of 3-dimensional objects a planet, is a three-dimensional smear of atoms no thicker than one atom in its fourth dimension, which is the direction of its linear translation through 4-space at velocity <math>c</math>. The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be "heaped up" into larger 4-dimensional objects that form a lump in its moving surface. We have little understanding of such 4-dimensional lumps thicker than one atom, since they occur naturally in our vicinity only in the interior of the sun. In fact the sun is the only such lump occurring naturally in our solar system. We refer to 4-dimensional lumps of matter as plasma, and have little experimental knowledge of their geometry or internal structure. We know that such a lump as the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know nothing about its interior 4-ball. Every such moving 3-dimensional surface boundary of matter in the observed universe is evolving in four dimensions at velocity <math>c</math>. Its current location in 4-space corresponds to the present moment in the proper time of its inertial reference frame. Its direction of movement at velocity <math>c</math> corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from atoms to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, two orthogonal inertial motions each at the constant universal rate of transformation <math>c</math>. Every object moves relative to universal 4-coordinate space on its own distinct geodesic spiral, a screw translation trajectory that is the compound of two orthogonal inertial motions, a rotation and a translation. Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity <math>c</math> in all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is <math>c^\prime = 2c</math>, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity <math>c</math>. For example, we can look across the center of our mostly-empty 4-ball galaxy and see stars in the opposite sides of its concentric 3-sphere surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math> in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper space. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space. == Symmetries == It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel & Goodman-Strauss|2008}} As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. [[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}} <blockquote>Let <small><math>\mathrm{Q}</math></small> denote a rotation, <small><math>\mathrm{R}</math></small> a reflection, <small><math>\mathrm{T}</math></small> a translation, and let <small><math>\mathrm{Q}^q \mathrm{R}^r\mathrm{T}</math></small> denote a product of several such transformations, all commutative with one another. Then <small><math>\mathrm{RT}</math></small> is a glide-reflection (in two or three dimensions), <small><math>\mathrm{QR}</math></small> is a rotary-reflection, <small><math>\mathrm{QT}</math></small> is a screw-displacement, and <small><math>\mathrm{Q^2}</math></small> is a double rotation (in four dimensions).<br> Every orthogonal transformation is expressible as:<br> :<small><math>\mathrm{Q}^q \mathrm{R}^r</math></small><br> where <small><math>(2^q + r \le n)</math></small>, the number of dimensions.<br> Transformations involving a translation are expressible as:<br> :<small><math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}</math></small><br> where <small><math>(2^q + r + 1 \le n)</math></small>.<br> For <small><math>(n = 4)</math></small> in particular, every displacement is either a double rotation <small><math>\mathrm{Q}^2</math></small>, or a screw-displacement <small><math>\mathrm{QT}</math></small> [where the rotation component <small><math>\mathrm{Q}</math></small> is a simple rotation, but the <small><math>\mathrm{QT}</math></small> is chiral like a <small><math>\mathrm{Q^2}</math></small>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <small><math>\mathrm{QRT}</math></small>.</blockquote> If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a <small><math>\mathrm{Q^2}</math></small> or a <small><math>\mathrm{QT}</math></small>, because we can view any <small><math>\mathrm{QT}</math></small> as a <small><math>\mathrm{Q^2}</math></small> in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a <small><math>\mathrm{Q^2}</math></small>. By the same principle, we can view any <small><math>\mathrm{QT}</math></small> or <small><math>\mathrm{Q^2}</math></small> as an isoclinic (equi-angled) <small><math>\mathrm{Q^2}</math></small> by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (<small><math>\mathrm{T}</math></small>) for ''one'' of the two rotations (<small><math>\mathrm{Q}</math></small>). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (<small><math>\mathrm{Q}</math></small>) up to uncertainty, and can always distinguish the direction of their own proper time translation (<small><math>\mathrm{T}</math></small>). As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebra), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group <small><math>SO(4)</math></small> [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic <small><math>SO(4)</math></small> rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, stationary atoms exhibit the <small><math>SO(4)</math></small> symmetries of the discrete isoclinic (equi-angled) double rotations (<small><math>\mathrm{Q^2}</math></small>) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]]. == Special relativity describes Euclidean 4-space == <blockquote>Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.<ref>{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}</ref></blockquote> Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional "space" because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign to the three space coordinates so spacetime is hyperbolic, not a flat Euclidean 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was first described by Einstein himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction. Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity ''c'', in some 4-space direction. This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always ''c'', as measured by all observers from any inertial reference frame. This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source. But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity ''c''. In physics as it has been universally understood, observers are not supposed to be able to move at velocity ''c''. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four. In the Euclidean relativity alternative view, however, every observer is always moving at velocity ''c'' through the universe, which is real Euclidean 4-dimensional space <small><math>\mathbb{R^4}</math></small>. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity ''c''. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and proper space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity ''c'', in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space <small><math>\mathbb{R^4}</math></small>.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity ''c'' relative to universal 4-coordinate space, so the maximum relative velocity between two observers is 2''c'' when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to ''c'', it is the same measurement in different units. Special relativity measures all velocities in a 3-space of Minkowski spacetime. Euclidean relativity measures all velocities in Euclidean 4-space.}} So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity ''c'' in Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the "speed of light" ''c'', although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity ''c'', but in at least slightly different directions. In Einstein's relativity, the invariant ''c'' is the speed of light through 3-space. In Euclidean relativity, the invariant ''c'' is the speed of matter through 4-space! The speed of light through 3-space is also perceived as ''c'' by all observers, because they are each living in a moving 3-manifold that is moving through 4-space at velocity ''c''. Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same predictions about how observers in different reference frames will perceive each other's motions in time and space, and we shall see that they also agree on the predictions of general relativity. They both describe the same geometric relations of space and time, but they describe that geometry as embedded in two very different universal host spaces: Minkowski spacetime versus Euclidean 4-space. ...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity <math>c</math> through space and proper time ...cite Yamashita{{Sfn|Yamashita|2023}} on the equivalence of special relativity and Euclidean 4-space relativity ...cite Kappraff & Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff & Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff & Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords. Euclidean relativity is not even a fringe theory; no physicists have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could "catch up" with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at ''c'' (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than ''c''. Euclidean relativity is a revolutionary theory indeed, in which ''c'' cannot possibly be the speed of light! We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for <math>\mathbb{R^4}</math>\mathbb{R^4} to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be <math>c^\prime = 2c</math>, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate linearly along the edge of a unit 4-hypercube. This is conceivable in 4-space (and in no other Euclidean space of any dimensionality) because the diagonal of the unit 4-hypercube is the natural number <small><math>\sqrt{4}</math></small>. == An object's motion in space is the product of its discrete self-reflections == Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a small number of discrete self-reflections. Any action of a geometric object that transforms its position and orientation in space may be measured as a distinct group of self-reflections of the object in its own surfaces. Any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete set of local self-reflections. Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which touch (intersect each other). When a object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality. Coxeter's laws of motion are a geometric counterpart to Newton's laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures. But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. For example, they give us geometric pictures of all the possible motions of objects in four dimensional Euclidean space: <blockquote>Every orthogonal transformation in 4-space is expressible as:<br> :<small><math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t</math></small><br> where <small><math>(2^q + r + t \le 4)</math></small>. Every displacement is either a double rotation <small><math>\mathrm{Q}^2</math></small>, or a screw-displacement <small><math>\mathrm{QT}</math></small> [where the rotation component <small><math>\mathrm{Q}</math></small> is a simple rotation, but the <small><math>\mathrm{QT}</math></small> is chiral like a <small><math>\mathrm{Q^2}</math></small>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <small><math>\mathrm{QRT}</math></small>.</blockquote> While this description should be understood as simple geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (<small><math>\mathrm{Q}</math></small>), reflection (<small><math>\mathrm{R}</math></small>) and translation (<small><math>\mathrm{T}</math></small>) are just what they are in three-dimensional space, but double rotation (<small><math>\mathrm{Q}^2</math></small>) is something new and unprecedented in our physical experience, because double rotations cannot occur until you have four or more dimensions of space to rotate in. ...to readers who have not studied Coxeter (almost all readers including TAC), the blockquote above is "just math", not visualizable geometry...but I could describe Coxeter's congruent transformations in 4-space here geometrically: I could say clearly what they mean in spatial terms, in language anyone can understand, because they don't require any math to be understood; the "math" here is really just simple pictures (reflections and rotations); even double rotations can be visualized by dimensional analogy, as compounds of simple rotations...since even most physicists are unacquainted with Coxeter geometry, it might be useful to do this here... == Light propagates through 4-space at twice its apparent velocity ''c''== Coxeter's geometric laws of motion apply to all objects with mass in 4-dimensional Euclidean space, but we find there is an additional kind of displacement which applies only to massless particles such as photons. Light quanta (photons) translate through 4-space by 4-dimensional reflection <small><math>\mathrm{R}^4</math></small>, which may be termed a double translation <small><math>\mathrm{T}^2</math></small>, a pure translation via two pairs of parallel reflections, without any rotation component <small><math>\mathrm{Q}</math></small>. Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by <small><math>\mathrm{QT}</math></small>, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic <small><math>\mathrm{Q^2}</math></small>, an isoclinically rotating object such as an atom. A simple rotation <small><math>\mathrm{Q}</math></small> or simple translation <small><math>\mathrm{T}</math></small> is a double reflection <small><math>\mathrm{R^2}</math></small>, so a <small><math>\mathrm{QT}</math></small> or <small><math>\mathrm{Q^2}</math></small> is also an <small><math>\mathrm{R^4}</math></small>, but not with the same group of reflection angles as a light signal <small><math>\mathrm{R^4}</math></small>. A translation <small><math>\mathrm{T = R^2}</math></small> is a double reflection in two parallel planes, and a rotation <small><math>\mathrm{Q = R^2}</math></small> is a double reflection in two intersecting planes, as in a <small><math>\mathrm{QT = R^4}</math></small> which is both at once. A double translation <small><math>\mathrm{T^2 = R^4}</math></small> is two double reflections in pairs of parallel planes at once, a reflection in four or more non-intersecting parallel planes; it is all translation and no rotation. In a <small><math>\mathrm{T^2}</math></small> all the motion goes to translation, so the translation goes twice as far as the simple translation <small><math>\mathrm{T}</math></small> in a <small><math>\mathrm{QT}</math></small>. A double translation <small><math>\mathrm{T^2 = R^4}</math></small> is the opposite of a double rotation <small><math>\mathrm{Q^2 = R^4}</math></small>, which is stationary but rotates twice as fast as the simple rotation <small><math>\mathrm{Q}</math></small> in a <small><math>\mathrm{QT}</math></small>. The product of the two translations in a <small><math>\mathrm{T^2}</math></small> is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple <small><math>\mathrm{T}</math></small> over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double-the-distance translation, but without any rotation component, so it cannot carry any mass with it. A <small><math>\mathrm{T^2}</math></small> cannot reposition a 4-polytope the way a <small><math>\mathrm{QT}</math></small> does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter. ...lensing of double translations <small><math>\mathrm{T^2 = R^4}</math></small> in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet... == The Kepler problem is framed in Euclidean 4-space == The [[W:Kepler problem|Kepler problem]] is named for [[W:Johannes Kepler|Johannes Kepler]], arguably the greatest geometer since the ancients up to [[w:Ludwig Schläfli|Ludwig Schläfli]], who proposed [[W:Kepler's laws of planetary motion|Kepler's laws of planetary motion]] which solved the problem of the orbits of the planets, and investigated the types of forces that would result in orbits obeying those laws. Those forces were later identified by [[W:Isaac Newton|Isaac Newton]] in his[[W:Philosophiæ Naturalis Principia Mathematica| Principia]], where he proves what today might be called the "inverse Kepler problem": the orbit characteristics require the force to depend on the inverse square of the distance.<ref>{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton & Company|isbn=978-0393039184}}</ref> The inverse square law behind the Kepler problem is the [[W:Central force|central force]] law which governs not only [[W:Newtonian gravity|Newtonian gravity]] and celestial orbits, but also the motion of two charged particles in [[W:Coulomb’s law|Coulomb’s law]] of [[W:Electrostatics|electrostatics]]; it applies to attractive or repulsive forces. Problems in which two bodies interact by a central force that varies as the [[W:Inverse square law|inverse square]] of the distance between them are called Kepler problems. Thus the [[W:Hydrogen atom|hydrogen atom]] is a Kepler problem, since it comprises two charged particles interacting by Coulomb's law, another inverse-square central force. Using classical mechanics, the solution to a Kepler problem can be expressed as a [[W:Kepler orbit|Kepler orbit]] using six kinematical variables or [[W:Orbital elements|orbital elements]]. The solution conserves an orbital element called the [[W:Laplace–Runge–Lenz vector|Laplace–Runge–Lenz (LRL) vector]], a [[W:Constant of motion|constant of motion]], meaning that it is the same no matter where it is calculated on the orbit. The LRL vector was essential in the first quantum mechanical derivation of the [[W:Atomic emission spectrum|spectrum]] of the hydrogen atom, but this approach has rarely been used since the development of the [[W:Schrödinger equation|Schrödinger equation]]. The conservation of the LRL vector corresponds to the <small><math>SO(4)</math></small> symmetry, by Nother's theorem. The LRL vector lies orthogonal to both the orbital plane and the angular momentum vector of the Kepler orbit; we observe that it lies in a fourth orthogonal dimension. Fock in 1935<ref>V. Fock, Zur Theorie des Wasserstoffatoms, Zeitschrift für Physik. 98 (3-4) (1935), 145–154.</ref> and Moser in 1970<ref>J. Moser, Regularization of Kepler’s problem and the averaging method on a manifold, Commun. Pure Appl. 23 (1970), 609–636</ref> observed that the Kepler problem is mathematically equivalent to non-affine geodesic motion (a particle moving freely) on the surface of a 3-sphere, so that the whole problem is symmetric under certain rotations of the four-dimensional space. This higher-dimensional symmetry results in two well-known properties of the Kepler problem: the momentum vector always moves in a perfect circle and, for a given total energy, all such velocity circles intersect each other in the same two points. ... Relativity establishes that an orbit in space is viewed in a different way in each distinct inertial reference frame. Depending on the choice of reference frame, the same Kepler system may be seen to be performing any one of a sequence of relativistically equivalent rotations in 4-space, on a continuum from an isoclinic rotation (Q²) in the orbit's proper reference frame, to a screw transfer (QT) with a simple rotation component (Q) and a translation component (T) at velocity <math>c</math>, in the universal reference frame of 4-coordinate space wherein every object is seen to be translating at velocity <math>c</math>. In reference frames between these two limit cases, the orbit is seen to be performing a double rotation (Q²) at two unequal, completely orthogonal angular rates of rotation: an elliptical double rotation. These include the reference frames of most typical observers, who are moving slowly relative to the observed orbital system's reference frame (their relative motion is a small fraction of the speed of light). ...this is probably misplaced here and should not interrupt the discussion at this point: ...These typical observations agree closely with the predictions of special relativity, because the non-isoclinic elliptical (Q²) resembles a (QT), since one of its two completely orthogonal rotations (Q) has such a long period that it is almost indistinguishable from a straight translation (T). All orbits in 4-space are isoclinic in their own reference frame. Orbiting objects in their own proper Kepler systems follow circular geodesic isoclines through 4-space. Orbits in 4-space are perfectly circular in their own reference frame, as Copernicus assumed the orbits of planets to be. It is the orbit's path through the 3-space of its elliptic hyperplane that is an ellipse, as Kepler found it to be. ...cite Jesper Goransson's very concise paper The geodesic circle that an orbiting object follows through 4-space in the proper reference frame of its own Kepler system is not a simple great circle which turns in two orthogonal dimensions. It is a helical great circle that turns in four orthogonal dimensions at once.{{Efn|Geodesic orbits in 4-space are not simple 2-dimensional great circles; they are helical 4-dimensional great circles that curve in all four dimensions at once. Their circular trajectories are helixes which we call ''isoclines'', since they are the paths taken by points on a rigid object undergoing isoclinic rotation.}} Such circles lie outside our physical experience, since our local space has only three orthogonal dimensions. Nonetheless we can visualize them in imagination, because their helical, circular shape is perfectly well defined by the kinematical variables of the Kepler orbit. The real physical correlates of abstract orthogonal planes and rotation angles are already familiar to us viscerally in our body-language of physical experience, since we are endowed biologically with highly evolved visual signal processing engines. These enable us to see and understand spatial relations and motions, including rotations, without even thinking about angles and orthogonal planes. This physical endowment is an inborn capacity for dimensional analogy which our biologic evolution has provided. All our instinctive spatial reasoning is by dimensional analogy from flat 2-dimensional retinal images to 3-dimensional scenes, using our powerful inborn visualization capacities of reverse stereographic projection and pattern recognition. We humans are thus very well equipped with everything we need to see in four-dimensional space, except experience. ... Recently Anco and Moghadam found that through Noether’s theorem in reverse, the LRL vector gives rise to a corresponding infinitesimal dynamical symmetry on the kinematical variables, which they show to be the semi-direct product of <small><math>SO(3)</math></small> and <small><math>\mathbb{R^3}</math></small>, in contrast to the <small><math>SO(4)</math></small> symmetry group generated by the LRL symmetries and the rotations.{{Sfn|Anco|Moghadam|2026|ps=; The physically relevant part of the LRL vector is its direction ... since its magnitude is just a function of energy and angular momentum.}} This remarkable symmetry breaking is expressive of the ''dimensional relativity'' between ordinary 3-space <small><math>\mathbb{R^3}</math></small>, spherical space <small><math>S^3</math></small> and Euclidean space <small><math>\mathbb{R^4}</math></small>. Consider a hydrogen atom in a Kepler orbit: for example, a hydrogen atom moving freely in space in an orbit around the sun. It is a ''double'' Kepler problem: an electrostatic Kepler problem within itself, and a gravitational Kepler problem in its environment. The ''single'' electrostatic Kepler problem of a hydrogen atom moving freely in space beyond any gravitational influence is a problem in special relativity. In our Euclidean 4-space model, this atom viewed as stationary in its own proper reference frame exhibits an <small><math>SO(4)</math></small> rotation symmetry corresponding to an isoclinic double rotation (<small><math>\mathrm{Q^2}</math></small>). The fourth dimension in this reference frame is the atom's proper time vector; it has constant velocity <math>c</math> and constant direction. From the point of view of our universal 4-coordinate space (which cannot be the proper inertial reference frame of any physical observer, all of whom are moving relative to it at velocity ''c''), the entire Kepler system (the atom) is translating through 4-space via a screw translation (<small><math>\mathrm{QT}</math></small>) at constant velocity <math>c</math>. From this viewpoint the atom has only a simple <small><math>SO(3)</math></small> rotation component (<small><math>\mathrm{Q}</math></small>), breaking its stationary <small><math>SO(4)</math></small> isoclinic rotation symmetry (<small><math>\mathrm{Q^2}</math></small>). Because each discrete part of the rotating atom moves along a helical trajectory through 4-space, the atom is in orbit around a barycentric axis (like a star in a galaxy), but only in a tiny orbit within its own radius, which is its inertial domain of rotation. The straight 4-dimensional cylinder it progresses along at velocity <math>c</math> is very narrow: only the diameter of the rotating atom itself. The gravitational Kepler problem of a hydrogen atom in a Kepler orbit around the sun is a problem in general relativity. In our 4-space model, this atom viewed in its own proper reference frame exhibits the same <small><math>SO(4)</math></small> rotation symmetry as it did in the electrostatic Kepler problem where the atom was translating linearly through space. The Kepler system in this case is not just the atom; it is the entire solar system. The LRL vector of this Kepler system is the proper time vector of the atom's inertial reference frame; once again it has constant velocity ''and constant direction''. Although the momentum vector moves in a perfect circle as the atom orbits the sun, the 4-space LRL vector does not move at all: it is a constant of motion, of linear motion (<small><math>\mathrm{T}</math></small>) of the Kepler system (the entire solar system in this case) in a constant 4-space direction, the proper time direction of the system. The direction of the system's proper time vector would vary under some kinds of acceleration of the atom, but it is constant under this kind of orbital acceleration. It continues to point in the same direction, like a 4-space compass needle, as the atom winds its way along its spiral path around the axis of the sun's straight-line translation through 4-space at velocity <math>c</math>. This compass needle always points in the direction the sun is moving, not the direction the atom is moving at any instant. ...Its Kepler orbit around the sun is its <small><math>SO(3)</math></small> rotation component (<small><math>\mathrm{Q}</math></small>). Although the atom is moving on a geodesic circle in the second problem, by the [[equivalence principle]] the difference in the state of the atomic systems in these two problems cannot be observed by examining the atoms alone. Even from another inertial reference frame, where the atom in the second problem is seen to be translating through 4-space via a wide screw translation (<small><math>\mathrm{QT}</math></small>) around the sun's axis of motion, there is still no difference between the two problems which can be detected by examining only the atoms within their own proper reference frames (even over time), because the LRL vector (<small><math>\mathrm{T}</math></small>) is a constant of motion of the entire system in both cases. ...Anco and Maghadam found that <small><math>SO(4)</math></small>) breaks to ... <small><math>S^3</math></small>)... if the energy in the Kepler orbit is negative (an elliptical orbit), and to ... <small><math>H^3</math></small>) ... Minkowski spacetime if the energy is positive (a hyperbolic orbit). ... Finally we consider a third problem in which a hydrogen atom enters the solar system as a comet, loops around the sun and exits the solar system again. This atom... ... As Hamilton found when he discovered the quaternions, we see that it is necessary to admit a fourth dimension to the system in order to properly model the problem: in Hamilton's case the general problem of ..., and in our case the Kepler problem. These are instances of the same problem in 4-dimensional Euclidean geometry, and indeed a solution to the Kepler problem in quaternions (the four Cartesian coordinates of Euclidean 4-space) is a solution to it in our model of the 4-coordinate Euclidean cosmos. == Distribution of stars in our galaxy == The stars in our own galaxy appear to us to be a rotating spiral cluster in 3-dimensional space. By assuming that light from them reaches us on straight lines through space, by assuming that we can measure their distance from us by its red shift, and by assuming that they are distributed in three dimensions of space, we have plotted their locations in 3-space. If we abandon the last of those three assumptions, we can just as easily reinterpret that dataset to plot their distribution around us in 4-dimensional space, and see how they actually lie. When we perform this experiment on the data for the stars in our galaxy, do we indeed find that they are distributed non-uniformly in various concentric spirals, but the spirals lie on the surface of various 3-spheres, rather than in elliptical orbits as we saw them in 3-space? That would be an expected consequence of the special rotational symmetry group of 4-space <small><math>SO(4)</math></small>, in which circular (isoclinic) orbits are the geodesics (shortest rotational paths) rather than elliptical (non-equi-angled double rotation) orbits. ...have to perform this experiment somehow, at least as a conclusive thought experiment, before I publish this paper... == Rotations == The [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotations]] of the convex [[W:regular 4-polytope|regular 4-polytope]]s are usually described as discrete rotations of a rigid object. For example, the rigid [[24-cell]] can rotate in a [[24-cell#Great hexagons|hexagonal]] (6-vertex) central [[24-cell#Planes of rotation|plane of rotation]]. A 4-dimensional [[24-cell#Isoclinic rotations|''isoclinic'' rotation]] (as distinct from a [[24-cell#Simple rotations|''simple'' rotation]] like the ones that occur in 3-dimensional space) is a ''diagonal'' rotation in multiple [[W:Clifford parallel|Clifford parallel]] [[24-cell#Geodesics|central planes]] of rotation at once. It is diagonal because it is a [[W:SO(4)#Double rotations|double rotation]]: in addition to rotating in parallel (like wheels), the multiple planes of rotation also tilt sideways in the completely orthogonal plane of rotation (like coins flipping) into each other's planes. Consequently, the path taken by each vertex is a [[24-cell#Helical hexagrams and their isoclines|twisted helical circle]], rather than the ordinary flat great circle a vertex follows in a simple rotation. In a rigid 4-polytope rotating isoclinically, ''all'' the vertices lie in one of the parallel planes of rotation, so all the vertices move in parallel along Clifford parallel twisting circular paths. [[24-cell#Clifford parallel polytopes|Clifford parallel planes]] are not parallel in the normal sense of parallel planes in three dimensions; the vertices are all moving in different directions around the [[W:3-sphere|3-sphere]]. In one complete 360° isoclinic revolution, a rigid 4-polytope turns itself inside out. This is sufficiently different from the simple rotations of rigid bodies in our 3-dimensional experience that a [[24-cell#Rotations|detailed description]] enabling the reader to properly visualize its counter-intuitive consequences runs to many pages and illustrations, with many accompanying pages of explanatory notes on surprising phenomena that arise in 4-dimensional space: [[24-cell#Great squares|completely orthogonal planes]], [[24-cell#Clifford parallel polytopes|Clifford parallelism]]{{Efn|name=Clifford parallels}} and [[W:Hopf fibration|Hopf fiber bundles]], [[24-cell#Isoclinic rotations|isoclinic geodesic paths]], and [[24-cell#Double rotations|chiral (mirror image) pairs of rotations]], among other complexities. Moreover, the characteristic rotations of the various regular 4-polytopes are all different; each is a unique surprise. [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|The 6 regular convex 4-polytopes]] have different numbers of vertices (5, 8, 16, 24, 120 and 600 respectively) and those with fewer vertices occur inscribed in those with more vertices (with one exception), with the result that the more complex 4-polytopes subsume the kinds of rotations characteristic of their less complex predecessors, as well as each having a characteristic kind of rotation not found in their predecessors. None of these symmetries is to be found in 3-dimensional space, although their simpler 3-dimensional analogues are all present there. [[W:Euclidean geometry#Higher dimensions|Four dimensional Euclidean space]] is more complicated (and more interesting) than three dimensional space because there is more room in it, in which unprecedented things can happen. It subsumes 3-dimensional space, with all of the symmetries we are accustomed to, and adds astonishing new surprises. These are hard for us to visualize, because the only way we can experience them is in our imagination; we have no body of sensory experience in 4-dimensional space to draw upon, other than our evolution in time. For that reason (our difficulty in visualizing them), descriptions of isoclinic rotations usually begin and end with rigid rotations: [[24-cell#Isoclinic rotations|for example]], all 24 vertices of a single rigid 24-cell rotating in unison, with 6 vertices evenly spaced around each of 4 Clifford parallel twisted circles.{{Efn|name=360 degree geodesic path visiting 3 hexagonal planes}} But that is only the simplest case, which is easiest for us to understand. Compound and [[W:Kinematics|kinematic]] 24-cells (with moving parts) are even more interesting (and more complicated) than the rotation of a single rigid 24-cell. To begin with, when we examine the individual parts of a single rigid 24-cell that are moving in an isoclinic rotation, such as the orbits of individual vertices, we can imagine a case where fewer than 24 point-objects are orbiting on those twisted circular paths at once. [[24-cell#Reflections|For example]], if we imagine just 8 point-objects, evenly spaced around the 24-cell at [[24-cell#Reciprocal constructions from 8-cell and 16-cell|the 8 vertices that lie on the 4 coordinate axes]], and rotate them isoclinically along exactly the same orbits they would take in the above-mentioned rotation of a rigid 24-cell, then in the course of a single 360° rotation the 8 point-objects will trace out the whole 24-cell, with just one point-object reaching each of the 24 vertex positions just once, and no point-object colliding with (or even crossing the path of) any other at any time. This is an example of a discrete Hopf fibration. But it is still an example of a rigid object in a discrete isoclinic rotation: a rigid 8-vertex object (called the 4-[[W:orthoplex|orthoplex]] or [[16-cell]]) performing one half of the characteristic rotation of the 24-cell. We can also imagine ''combining'' distinct isoclinic rotations. What happens when multiple point-objects are orbiting at once, but do ''not'' all follow the Clifford parallel paths characteristic of the ''same'' distinct rigid rotation? What happens when we combine orbits from distinct rotations characteristic of different 4-polytopes, for example when different rigid 4-polytopes are concentric and rotating simultaneously in their characteristic ways? What kinds of such hybrid rotations are possible in the same 3-sphere shell without collisions? In adjacent concentric shells without asymmetric imbalance? What sort of [[Kinematics of the cuboctahedron|kinematic polytopes]] do they trace out, and how do their [[24-cell#Clifford parallel polytopes|component parts]] relate to each other as they move? Is there (sometimes) some kind of mutual stability amid their lack of combined rigidity? Visualizing isoclinic rotations (rigid and otherwise) allows us to explore such questions of [[W:kinematics|kinematics]], and where dynamic stabilities arise, of [[wikipedia:kinetics (physics)|kinetics]]. In four dimensions, we discover that space has more room in it than we have experienced, which permits previously unimagined motions. Even 3-space is more commodious than we thought; when it is curved and lies embedded in a higher-dimensional space, it permits previously impossible symmetric packings. Sadoc studied double-twisted 3-dimensional molecules, and imagined them embedded in 4-dimensional space as the Hopf fibrations of regular 4-polytopes. He found that these molecules would close-pack on the 3-sphere perfectly without exhibiting any torsion, although their packing in ordinary flat 3-space is imperfect, "frustrated" by their twisted geometry. <blockquote>The frustration, which arises when the molecular orientation is transported along the two [spiral] AB paths of figure 1 [double twist helix], is imposed by the very topological nature of the Euclidean space R³. It would not occur if the molecules were embedded in the non-Euclidean space of the [[W:3-sphere|3-sphere]] S³, or hypersphere. This space with a homogeneous positive curvature can indeed be described by equidistant and uniformly twisted fibers, along which the molecules can be aligned without any conflict between compactness and [[W:torsion of a curve|torsion]].... The fibres of this [[W:Hopf fibration|Hopf fibration]] are great circles of S³, the whole family of which is also called the [[W:Clifford parallel|Clifford parallel]]s.{{Efn|name=Clifford parallels}} Two of these fibers are C_∞ symmetry axes for the whole fibration; each fibre makes one turn around each axis and regularly rotates when moving from one axis to another.{{Efn|name=helical geodesic}} These fibers build a double twist configuration while staying parallel, i.e. without any frustration, in the whole volume of S³.{{Efn|name=Petrie polygon of a honeycomb}} They can therefore be used as models to study the condensation of long molecules in the presence of a double twist constraint.{{Sfn|Sadoc & Charvolin|2009|loc=§1.2 The curved space approach|ps=; studies the helical orientation of molecules in crystal structures and their imperfect packings ("frustrations") in 3-dimensional space.}}</blockquote> Of course we do not find molecules condensing to close-pack the 3-sphere in our experience, and Sadoc does not say that we do. We find 3-spheres in the atomic realm (if atoms are 4-polytopes), and in the cosmic realm (as the surface boundaries of stars, and the concentric surfaces of galaxies). But in between, in the realm of ordinary experience which includes the molecular realm, ourselves and all the objects we can materially handle or observe up close including the planets, we are confined together by gravity as inertia within a curved 3-dimensional space that is no more than one atom thick in the fourth spatial dimension. That is why in the molecular realm we find only objects that occupy 3-spaces which, though infinitesimally curved in the fourth dimension, are tiny patches on whole 3-spheres of galactic size. So Sadoc's exercise is a thought experiment, like Einstein's gedankenexperiments about railroad embankments and trains moving at nearly the speed of light. It is no less illuminating, despite the symmetry it reveals not having a realization as an actual 3-sphere of actual molecules. And might not something very like it have an actual realization in the atomic realm? We know that atoms have their own complex internal structure, which we are unable to model geometrically in ordinary 3-dimensional space. Suppose such a model is impossible because an atom is actually a 4-polytope occupying a tiny spherical region of 4-dimensional space, and so we only find its constituent particles in close-packed helical orbits on the 3-sphere, in the manner of Sadoc's imaginary twisted molecules, but as real 4-dimensional helices of atomic scale. We would expect to find the atomic orbit of a fundamental particle in some discrete Hopf fibration characteristic of a symmetry group, that is, on the maximally symmetric isoclines of a discrete isoclinic rotation characteristic of some regular 4-polytope and the particle. == A theory of the Euclidean atom == <blockquote>Because quantum physics could be tested without being understood, it allowed humans to see how the universe worked without knowing why.<ref>Sebastian Junger, In My Time of Dying</ref></blockquote> ... == Light and Mass are Reflection and Rotation == The phenomena of light and mass are expressions of reflection symmetries and rotation symmetries, respectively. ... Atoms are 4-polytopes, elementary objects with SO(4) rotational symmetry. Light is .... Motion in space is the propagation of the elementary objects of light and matter in Coxeter congruent transformations by kaleidoscopic self-reflections, like the motion of self-reproducing cellular automata in [[Conway's Game of Life|Conway's game of life]]. ... Light is discrete reflections. Mass is discrete rotations. Both are group actions, expressions of intrinsic symmetries. That is all of physics. === Atoms are 4-polytopes === ... == Relativity in real space of four or more orthogonal dimensions == Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions. General relativity is Galilean relativity in a general space of four or more orthogonal dimensions, e.g. in Euclidean 4-space <math>R^4</math>, spherical 4-space <math>S^4</math>, and any orthogonal 4-manifold. Light is a consequence of symmetry group reflections at quantum scale. Gravity and the other fundamental forces are consequences of rotations, which are consequences of quantum reflections. Light is discrete reflections. Gravity and all forces are discrete rotations. Both are group actions, expressions of intrinsic symmetries. That is all of physics. Every observer may properly see themself as stationary and the universe as an ''n''-sphere with themself at the center. The curvature of these spheres is a function of the rate at which causality evolves, and can be measured by the observer as the speed of light. === Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions === ...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here... Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in three spatial dimensions. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (In general relativity, discussed below, the actual rate of physical processes varies from place to place, and those differences are neither reciprocal nor illusory.) None of these Lorentz effects are beyond geometric explanation or paradoxical. The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, successive Euclidean spaces are dimensionally analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature, is an exact expression of intrinsic symmetries: that is Nother's great discovery. === General relativity is Galilean relativity in a general space of four orthogonal dimensions === ... == Dimensional relativity == Coxeter's kinetic law of <math>n</math>-dimensional congruent Euclidean transformations may be called ''dimensional relativity'', since it captures the theories of special and general relativity entire, and has its roots in dimensional analogy. Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessable by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated. By analogy to the surface of the earth, the bounding surface of a spherical region of <math>n</math>-dimensional Euclidean space is an <math>(n-1)</math>-sphere, a spherical space of one fewer dimensions than the <math>n</math>-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean <math>n</math>-spaces of increasing <math>n</math>, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating <math>n</math>-spaces. By the degree of dimensional analogy of which they are capable, some observers see deeper into <math>n</math>-dimensional space than others. == Polycentric spherical relativity == An intelligent observer equipped with the principle of relativity may perceive the universe from any inertial reference frame, not only from their own proper perspective. We see that every observer may properly view themself as stationary and the universe as an ''n''-sphere with themself at the center observing it, perceptually equidistant from all points on its surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything. This ''polycentric model'' of the universe is a further restatement of the principle of relativity. It is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. It should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849: "The universe is a sphere whose center is wherever there is intelligence."{{Sfn|Thoreau|1849|p=349|ps=; "The universe is a sphere whose center is wherever there is intelligence." [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}} == Revolutions == The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity ''c'', with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may, or may not, all have the same origin in space and time. As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment we dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed us that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a sense related to time, at least, it must be 4-dimensional. In this work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space. Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we now observe them, any more than they lie in the three dimensional hyperplane of local space in which we find everything residing in our solar system. When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us only by virtue of how long it takes their light to reach us. We can measure their distribution around us in 4-space, but that is simply how we choose to measure them, not a finding of how they are actually distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean ''n''-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity <math>c</math>, on more or less divergent paths from each other. But only much closer observation will reveal evidence of whether everything we see lies in the same 4-space, or if it is distributed in five or more dimensions, and how it is moving there. To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity <math>c</math>, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw displacements), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw displacement has ''two'' [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity <math>c</math> in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that each galaxy's own distinct 3-sphere is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to lightspeed long ago, in whatever big bang our atoms emerged from, and have never slowed down since. == Origins of the theory == Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of the geometry of Euclidean 4-space relativity, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] contains the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and did not describe our ordinary 3-space embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.<ref>{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}</ref> He invited us to imagine "A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions", but he was careful to disclaim parenthetically that "The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice." Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal of that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.'' The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified spacetime of four dimensions. Anco and Maghadam found that <small><math>SO(4)</math></small> breaks to ... <small><math>S^3</math></small>... if the energy in the Kepler orbit is negative (an elliptical orbit), and to ... <small><math>H^3</math></small> ... Minkowski spacetime if the energy is positive (a hyperbolic orbit). Because the planets orbit on ellipses in our 3-space, Euclidean 4-space is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the truer model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position of centrality as our exclusive conception of our place in space. ...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others. The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; "Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions."}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.<ref>{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}</ref>}} == Boundaries == <blockquote>Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.<ref>{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}</ref></blockquote> Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? ''What is the nature of the boundary which confines us to just three dimensions?'' We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell. Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined motions and objects. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. A boundary is an explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force. <blockquote>The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three .... In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it. We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed "Dimensional Analogy."<ref>{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}</ref></blockquote> I believe, but I cannot prove, that we live in real space, which is Schläfli's and Coxeter's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover in imagination and then explore physically, each an astonishing new enlightenment.<ref>{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}<blockquote> :We shall not cease from exploration :And the end of all our exploring :Will be to arrive where we started :And know the place for the first time. :Through the unknown, remembered gate :When the last of earth left to discover :Is that which was the beginning; :At the source of the longest river :The voice of the hidden waterfall :And the children in the apple-tree :Not known, because not looked for :But heard, half-heard, in the stillness :Between two waves of the sea. </blockquote></ref> Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. This project is forever beginning anew. Coxeter showed us that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether showed us all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions, in which all objects with mass move ceaselessly at the constant velocity <math>c</math>, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages. <blockquote> ::::::BEECH :Where my imaginary line :Bends square in woods, an iron spine :And pile of real rocks have been founded. :And off this corner in the wild, :Where these are driven in and piled, :One tree, by being deeply wounded, :Has been impressed as Witness Tree :And made commit to memory :My proof of being not unbounded. :Thus truth's established and borne out, :Though circumstanced with dark and doubt— :Though by a world of doubt surrounded. :::::::—''The Moodie Forester''<ref>{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}</ref> </blockquote> == Appendix: Sequence of regular 4-polytopes == {{Regular convex 4-polytopes|wiki=W:|columns=7}} == ... == {{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}} {{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}} {{Efn|The long radius (center to vertex) of the 24-cell is equal to its edge length; thus its long diameter (vertex to opposite vertex) is 2 edge lengths. Only a few uniform polytopes have this property, including the four-dimensional 24-cell and [[W:Tesseract#Radial equilateral symmetry|tesseract]], the three-dimensional [[W:Cuboctahedron#Radial equilateral symmetry|cuboctahedron]], and the two-dimensional [[W:Hexagon#Regular hexagon|hexagon]]. (The cuboctahedron is the equatorial cross section of the 24-cell, and the hexagon is the equatorial cross section of the cuboctahedron.) '''Radially equilateral''' polytopes are those which can be constructed, with their long radii, from equilateral triangles which meet at the center of the polytope, each contributing two radii and an edge.|name=radially equilateral|group=}} {{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as "the convex hull of the neighbouring vertices of a given vertex".{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its "radius" equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}} {{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example: {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0) {{indent|5}}({{spaces|2}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>){{spaces|3}}({{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>) {{indent|5}}(–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>){{spaces|3}}(–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>) {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)<br> is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}} {{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60° rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the "left" is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}} {{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}} {{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; "In mathematics, the path that the (1, 1) knot on the torus traces is also known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two intersecting circles that are the cross-section of a torus by a well-chosen plane cutting it. Picking one such circle and rotating it around the torus axis, the resulting family of circles can be used to rule the torus. By nesting tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the (1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles]."}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}} {{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}} {{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}} {{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}} {{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}} {{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}} {{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}} {{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}} {{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}} {{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90^o bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60^o bend, or as a straight line with one 60^o bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}} {{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; "In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)"}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}} {{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}} {{Efn|Departing from any vertex V₀ in the original great hexagon plane of isoclinic rotation P₀, the first vertex reached V₁ is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P₁. P₁ is inclined to P₀ at a 60° angle.{{Efn|P₀ and P₁ lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V₂ is 120 degrees beyond V₁ along a second {{radic|3}} chord lying in another hexagonal plane P₂ that is Clifford parallel to P₀.{{Efn|P₀ and P₂ are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V₀ and V₂ are ''two'' {{radic|3}} chords apart{{Efn|V₀ and V₂ are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V₀ and V₂ are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P₀ and P₂ are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V₁ lies in both intersecting planes P₁ and P₂, as V₀ lies in both P₀ and P₁. But P₀ and P₂ have ''no'' vertices in common; they do not intersect.) The third vertex reached V₃ is 120 degrees beyond V₂ along a third {{radic|3}} chord lying in another hexagonal plane P₃ that is Clifford parallel to P₁. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V₀ to V₃ is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}} {{Sfn|Mamone, Pileio & Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹₄.}} ==Notes== {{Regular convex 4-polytopes Notelist|wiki=W:}} ==Citations== {{Regular convex 4-polytopes Reflist|wiki=W:}} ==References== {{Refbegin}} * {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}} * {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1}} * {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}} === [[Polyscheme|Polyschemes]] === {{Regular convex 4-polytopes Refs|wiki=W:}} {{Refend}} akcxubbawq8safm2weqs76u9cnmmpr4 2823709 2823706 2026-08-20T20:45:53Z Dc.samizdat 2856930 /* Special relativity describes Euclidean 4-space */ 2823709 wikitext text/x-wiki = Real Euclidean four-dimensional space R⁴ = {{align|center|David Brooks Christie}} {{align|center|dc@samizdat.org}} {{align|center|Draft in progress}} {{align|center|June 2023 - August 2026}} <blockquote>'''Abstract:''' The physical universe is properly visualized as a Euclidean space of four orthogonal spatial dimensions. Space itself has a fourth orthogonal dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and our planet are only 3-dimensional objects, but nonetheless we can see in four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.</blockquote> == Summary == We observe that physical space has four perpendicular dimensions, not just three; atoms are [[W:4-polytope|4-polytopes]]; the sun is a 4-ball that is round in four dimensions; everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space; and our entire 3-space manifold is translating through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions. == A theory of the Euclidean cosmos == The physical universe is properly visualized as a [[w:Four-dimensional_space|Euclidean space of four orthogonal spatial dimensions]]. Space itself has a fourth orthogonal dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planets, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. All objects with mass move inertially through Euclidean 4-space at velocity <math>c</math> as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity <math>c</math> is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space. A typical spiral galaxy such as ours is a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our galaxy appear from our viewpoint to be distributed in a cloud of elliptical spirals occupying a flattened ellipsoid region of 3-dimensional space, but they are not so confined: they are distributed within a spherical region of 4-dimensional space. The galaxy's actual shape is spherical, not a flattened ellipsoid, but it is rounder than round can be in our ordinary experience: it occupies a hyperspherical region of space. The concentric spirals of stars that we observe lie on concentric [[W:3-sphere|3-sphere]]s (4-dimensional spheres), not on concentric 2-ellipsoids (3-dimensional elliptical spirals). Our sun and solar system lies on one of those concentric 3-spheres. More generally, orbits are circular in 4-space, and elliptical in the 3-space of their elliptic hyperplane. [[File:Hypersphere.png|thumb|Rotating illustration of the 4-ball galaxy showimg its spirals of star clouds on the surface of concentric 3-spheres, obtained by reverse sterographic projection from 3D images of the galaxy.]] The galaxy as a whole, or more properly its orbital center point, is translating through 4-space at velocity <math>c</math>, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity <math>c</math> in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity <math>c</math>. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the cylinder; their trajectories are screw-displacements, the compound of a simple rotation and a linear translation. The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around a barycentric axis. It is the tremendous inertial force of stars in motion at velocity <math>c</math> that holds the cylinder of motion together. The observed universe as a whole appears to be a 3-sphere expanding radially from a central origin point at velocity <math>c</math>, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. For all observers, the conjectured origin point of the universe corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space (the same point in the same Euclidean 4-space for all observers). The big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured separately, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity <math>c</math>. All objects in our solar system except the sun itself lie within this thinest three-dimensional manifold. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. The enclosing surface of a spherical region of 4-space is itself a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. We live within such a 3-space, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience, and it contains the earth, all the planets and the 3-dimensional space between them. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our particular 3-sphere is one of the galaxy's concentric 3-spheres of spiral star-clouds. The solar system occupies a tiny patch of this filmy 4-dimensional soap-bubble of galactic size, that is thicker-skinned than the diameter of an atom only in the interior of stars and supermassive objects. Our entire 3-sphere manifold, as a 3-spherical shell within the moving 4-ball galaxy, is translating through 4-space at velocity <math>c</math> with the galaxy, in a distinct direction that is orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the galaxy's translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of rotating objects through Euclidean space by screw translation. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity <math>c</math>, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. Any moving 3-dimensional manifold that is such an evolving surface boundary is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. Every object which we find occurring naturally in the solar system other than the sun itself, even the largest of 3-dimensional objects a planet, is a three-dimensional smear of atoms no thicker than one atom in its fourth dimension, which is the direction of its linear translation through 4-space at velocity <math>c</math>. The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be "heaped up" into larger 4-dimensional objects that form a lump in its moving surface. We have little understanding of such 4-dimensional lumps thicker than one atom, since they occur naturally in our vicinity only in the interior of the sun. In fact the sun is the only such lump occurring naturally in our solar system. We refer to 4-dimensional lumps of matter as plasma, and have little experimental knowledge of their geometry or internal structure. We know that such a lump as the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know nothing about its interior 4-ball. Every such moving 3-dimensional surface boundary of matter in the observed universe is evolving in four dimensions at velocity <math>c</math>. Its current location in 4-space corresponds to the present moment in the proper time of its inertial reference frame. Its direction of movement at velocity <math>c</math> corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from atoms to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, two orthogonal inertial motions each at the constant universal rate of transformation <math>c</math>. Every object moves relative to universal 4-coordinate space on its own distinct geodesic spiral, a screw translation trajectory that is the compound of two orthogonal inertial motions, a rotation and a translation. Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity <math>c</math> in all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is <math>c^\prime = 2c</math>, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity <math>c</math>. For example, we can look across the center of our mostly-empty 4-ball galaxy and see stars in the opposite sides of its concentric 3-sphere surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math> in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper space. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space. == Symmetries == It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel & Goodman-Strauss|2008}} As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. [[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}} <blockquote>Let <small><math>\mathrm{Q}</math></small> denote a rotation, <small><math>\mathrm{R}</math></small> a reflection, <small><math>\mathrm{T}</math></small> a translation, and let <small><math>\mathrm{Q}^q \mathrm{R}^r\mathrm{T}</math></small> denote a product of several such transformations, all commutative with one another. Then <small><math>\mathrm{RT}</math></small> is a glide-reflection (in two or three dimensions), <small><math>\mathrm{QR}</math></small> is a rotary-reflection, <small><math>\mathrm{QT}</math></small> is a screw-displacement, and <small><math>\mathrm{Q^2}</math></small> is a double rotation (in four dimensions).<br> Every orthogonal transformation is expressible as:<br> :<small><math>\mathrm{Q}^q \mathrm{R}^r</math></small><br> where <small><math>(2^q + r \le n)</math></small>, the number of dimensions.<br> Transformations involving a translation are expressible as:<br> :<small><math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}</math></small><br> where <small><math>(2^q + r + 1 \le n)</math></small>.<br> For <small><math>(n = 4)</math></small> in particular, every displacement is either a double rotation <small><math>\mathrm{Q}^2</math></small>, or a screw-displacement <small><math>\mathrm{QT}</math></small> [where the rotation component <small><math>\mathrm{Q}</math></small> is a simple rotation, but the <small><math>\mathrm{QT}</math></small> is chiral like a <small><math>\mathrm{Q^2}</math></small>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <small><math>\mathrm{QRT}</math></small>.</blockquote> If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a <small><math>\mathrm{Q^2}</math></small> or a <small><math>\mathrm{QT}</math></small>, because we can view any <small><math>\mathrm{QT}</math></small> as a <small><math>\mathrm{Q^2}</math></small> in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a <small><math>\mathrm{Q^2}</math></small>. By the same principle, we can view any <small><math>\mathrm{QT}</math></small> or <small><math>\mathrm{Q^2}</math></small> as an isoclinic (equi-angled) <small><math>\mathrm{Q^2}</math></small> by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (<small><math>\mathrm{T}</math></small>) for ''one'' of the two rotations (<small><math>\mathrm{Q}</math></small>). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (<small><math>\mathrm{Q}</math></small>) up to uncertainty, and can always distinguish the direction of their own proper time translation (<small><math>\mathrm{T}</math></small>). As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebra), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group <small><math>SO(4)</math></small> [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic <small><math>SO(4)</math></small> rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, stationary atoms exhibit the <small><math>SO(4)</math></small> symmetries of the discrete isoclinic (equi-angled) double rotations (<small><math>\mathrm{Q^2}</math></small>) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]]. == Special relativity describes Euclidean 4-space == <blockquote>Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.<ref>{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}</ref></blockquote> Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional "space" because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign to the three space coordinates so spacetime is hyperbolic, not a flat Euclidean 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was first described by Einstein himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction. Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity ''c'', in some 4-space direction. This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always ''c'', as measured by all observers from any inertial reference frame. This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source. But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity ''c''. In physics as it has been universally understood, observers are not supposed to be able to move at velocity ''c''. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four. In the Euclidean relativity alternative view, however, every observer is always moving at velocity ''c'' through the universe, which is real Euclidean 4-dimensional space <small><math>\mathbb{R^4}</math></small>. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity ''c''. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and proper space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity ''c'', in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space <small><math>\mathbb{R^4}</math></small>.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity ''c'' relative to universal 4-coordinate space, so the maximum relative velocity between two observers is 2''c'' when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to ''c'', it is the same measurement in different units. Special relativity measures all velocities in a 3-space of Minkowski spacetime. Euclidean relativity measures all velocities in Euclidean 4-space.}} So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity ''c'' in Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the "speed of light" ''c'', although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity ''c'', but in at least slightly different directions. In Einstein's relativity, the invariant ''c'' is the speed of light through 3-space. In Euclidean relativity, the invariant ''c'' is the speed of matter through 4-space! The speed of light through 3-space is also perceived as ''c'' by all observers, because they are each living in a moving 3-manifold that is moving through 4-space at velocity ''c''. Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same predictions about how observers in different reference frames will perceive each other's motions in time and space, and we shall see that they also agree on the predictions of general relativity. They both describe the same geometric relations of space and time, but they describe that geometry as embedded in two very different universal host spaces: Minkowski spacetime versus Euclidean 4-space. ...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity <math>c</math> through space and proper time ...cite Yamashita{{Sfn|Yamashita|2023}} on the equivalence of special relativity and Euclidean 4-space relativity ...cite Kappraff & Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff & Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff & Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords. Euclidean relativity is not even a fringe theory; no physicists have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could "catch up" with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at ''c'' (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than ''c''. Euclidean relativity is a revolutionary theory indeed, in which ''c'' cannot possibly be the speed of light! We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for <math>\mathbb{R^4}</math> to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be <math>c^\prime = 2c</math>, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate linearly along the edge of a unit 4-hypercube. This is conceivable in 4-space (and in no other Euclidean space of any dimensionality) because the diagonal of the unit 4-hypercube is the natural number <small><math>\sqrt{4}</math></small>. == An object's motion in space is the product of its discrete self-reflections == Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a small number of discrete self-reflections. Any action of a geometric object that transforms its position and orientation in space may be measured as a distinct group of self-reflections of the object in its own surfaces. Any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete set of local self-reflections. Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which touch (intersect each other). When a object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality. Coxeter's laws of motion are a geometric counterpart to Newton's laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures. But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. For example, they give us geometric pictures of all the possible motions of objects in four dimensional Euclidean space: <blockquote>Every orthogonal transformation in 4-space is expressible as:<br> :<small><math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t</math></small><br> where <small><math>(2^q + r + t \le 4)</math></small>. Every displacement is either a double rotation <small><math>\mathrm{Q}^2</math></small>, or a screw-displacement <small><math>\mathrm{QT}</math></small> [where the rotation component <small><math>\mathrm{Q}</math></small> is a simple rotation, but the <small><math>\mathrm{QT}</math></small> is chiral like a <small><math>\mathrm{Q^2}</math></small>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <small><math>\mathrm{QRT}</math></small>.</blockquote> While this description should be understood as simple geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (<small><math>\mathrm{Q}</math></small>), reflection (<small><math>\mathrm{R}</math></small>) and translation (<small><math>\mathrm{T}</math></small>) are just what they are in three-dimensional space, but double rotation (<small><math>\mathrm{Q}^2</math></small>) is something new and unprecedented in our physical experience, because double rotations cannot occur until you have four or more dimensions of space to rotate in. ...to readers who have not studied Coxeter (almost all readers including TAC), the blockquote above is "just math", not visualizable geometry...but I could describe Coxeter's congruent transformations in 4-space here geometrically: I could say clearly what they mean in spatial terms, in language anyone can understand, because they don't require any math to be understood; the "math" here is really just simple pictures (reflections and rotations); even double rotations can be visualized by dimensional analogy, as compounds of simple rotations...since even most physicists are unacquainted with Coxeter geometry, it might be useful to do this here... == Light propagates through 4-space at twice its apparent velocity ''c''== Coxeter's geometric laws of motion apply to all objects with mass in 4-dimensional Euclidean space, but we find there is an additional kind of displacement which applies only to massless particles such as photons. Light quanta (photons) translate through 4-space by 4-dimensional reflection <small><math>\mathrm{R}^4</math></small>, which may be termed a double translation <small><math>\mathrm{T}^2</math></small>, a pure translation via two pairs of parallel reflections, without any rotation component <small><math>\mathrm{Q}</math></small>. Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by <small><math>\mathrm{QT}</math></small>, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic <small><math>\mathrm{Q^2}</math></small>, an isoclinically rotating object such as an atom. A simple rotation <small><math>\mathrm{Q}</math></small> or simple translation <small><math>\mathrm{T}</math></small> is a double reflection <small><math>\mathrm{R^2}</math></small>, so a <small><math>\mathrm{QT}</math></small> or <small><math>\mathrm{Q^2}</math></small> is also an <small><math>\mathrm{R^4}</math></small>, but not with the same group of reflection angles as a light signal <small><math>\mathrm{R^4}</math></small>. A translation <small><math>\mathrm{T = R^2}</math></small> is a double reflection in two parallel planes, and a rotation <small><math>\mathrm{Q = R^2}</math></small> is a double reflection in two intersecting planes, as in a <small><math>\mathrm{QT = R^4}</math></small> which is both at once. A double translation <small><math>\mathrm{T^2 = R^4}</math></small> is two double reflections in pairs of parallel planes at once, a reflection in four or more non-intersecting parallel planes; it is all translation and no rotation. In a <small><math>\mathrm{T^2}</math></small> all the motion goes to translation, so the translation goes twice as far as the simple translation <small><math>\mathrm{T}</math></small> in a <small><math>\mathrm{QT}</math></small>. A double translation <small><math>\mathrm{T^2 = R^4}</math></small> is the opposite of a double rotation <small><math>\mathrm{Q^2 = R^4}</math></small>, which is stationary but rotates twice as fast as the simple rotation <small><math>\mathrm{Q}</math></small> in a <small><math>\mathrm{QT}</math></small>. The product of the two translations in a <small><math>\mathrm{T^2}</math></small> is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple <small><math>\mathrm{T}</math></small> over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double-the-distance translation, but without any rotation component, so it cannot carry any mass with it. A <small><math>\mathrm{T^2}</math></small> cannot reposition a 4-polytope the way a <small><math>\mathrm{QT}</math></small> does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter. ...lensing of double translations <small><math>\mathrm{T^2 = R^4}</math></small> in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet... == The Kepler problem is framed in Euclidean 4-space == The [[W:Kepler problem|Kepler problem]] is named for [[W:Johannes Kepler|Johannes Kepler]], arguably the greatest geometer since the ancients up to [[w:Ludwig Schläfli|Ludwig Schläfli]], who proposed [[W:Kepler's laws of planetary motion|Kepler's laws of planetary motion]] which solved the problem of the orbits of the planets, and investigated the types of forces that would result in orbits obeying those laws. Those forces were later identified by [[W:Isaac Newton|Isaac Newton]] in his[[W:Philosophiæ Naturalis Principia Mathematica| Principia]], where he proves what today might be called the "inverse Kepler problem": the orbit characteristics require the force to depend on the inverse square of the distance.<ref>{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton & Company|isbn=978-0393039184}}</ref> The inverse square law behind the Kepler problem is the [[W:Central force|central force]] law which governs not only [[W:Newtonian gravity|Newtonian gravity]] and celestial orbits, but also the motion of two charged particles in [[W:Coulomb’s law|Coulomb’s law]] of [[W:Electrostatics|electrostatics]]; it applies to attractive or repulsive forces. Problems in which two bodies interact by a central force that varies as the [[W:Inverse square law|inverse square]] of the distance between them are called Kepler problems. Thus the [[W:Hydrogen atom|hydrogen atom]] is a Kepler problem, since it comprises two charged particles interacting by Coulomb's law, another inverse-square central force. Using classical mechanics, the solution to a Kepler problem can be expressed as a [[W:Kepler orbit|Kepler orbit]] using six kinematical variables or [[W:Orbital elements|orbital elements]]. The solution conserves an orbital element called the [[W:Laplace–Runge–Lenz vector|Laplace–Runge–Lenz (LRL) vector]], a [[W:Constant of motion|constant of motion]], meaning that it is the same no matter where it is calculated on the orbit. The LRL vector was essential in the first quantum mechanical derivation of the [[W:Atomic emission spectrum|spectrum]] of the hydrogen atom, but this approach has rarely been used since the development of the [[W:Schrödinger equation|Schrödinger equation]]. The conservation of the LRL vector corresponds to the <small><math>SO(4)</math></small> symmetry, by Nother's theorem. The LRL vector lies orthogonal to both the orbital plane and the angular momentum vector of the Kepler orbit; we observe that it lies in a fourth orthogonal dimension. Fock in 1935<ref>V. Fock, Zur Theorie des Wasserstoffatoms, Zeitschrift für Physik. 98 (3-4) (1935), 145–154.</ref> and Moser in 1970<ref>J. Moser, Regularization of Kepler’s problem and the averaging method on a manifold, Commun. Pure Appl. 23 (1970), 609–636</ref> observed that the Kepler problem is mathematically equivalent to non-affine geodesic motion (a particle moving freely) on the surface of a 3-sphere, so that the whole problem is symmetric under certain rotations of the four-dimensional space. This higher-dimensional symmetry results in two well-known properties of the Kepler problem: the momentum vector always moves in a perfect circle and, for a given total energy, all such velocity circles intersect each other in the same two points. ... Relativity establishes that an orbit in space is viewed in a different way in each distinct inertial reference frame. Depending on the choice of reference frame, the same Kepler system may be seen to be performing any one of a sequence of relativistically equivalent rotations in 4-space, on a continuum from an isoclinic rotation (Q²) in the orbit's proper reference frame, to a screw transfer (QT) with a simple rotation component (Q) and a translation component (T) at velocity <math>c</math>, in the universal reference frame of 4-coordinate space wherein every object is seen to be translating at velocity <math>c</math>. In reference frames between these two limit cases, the orbit is seen to be performing a double rotation (Q²) at two unequal, completely orthogonal angular rates of rotation: an elliptical double rotation. These include the reference frames of most typical observers, who are moving slowly relative to the observed orbital system's reference frame (their relative motion is a small fraction of the speed of light). ...this is probably misplaced here and should not interrupt the discussion at this point: ...These typical observations agree closely with the predictions of special relativity, because the non-isoclinic elliptical (Q²) resembles a (QT), since one of its two completely orthogonal rotations (Q) has such a long period that it is almost indistinguishable from a straight translation (T). All orbits in 4-space are isoclinic in their own reference frame. Orbiting objects in their own proper Kepler systems follow circular geodesic isoclines through 4-space. Orbits in 4-space are perfectly circular in their own reference frame, as Copernicus assumed the orbits of planets to be. It is the orbit's path through the 3-space of its elliptic hyperplane that is an ellipse, as Kepler found it to be. ...cite Jesper Goransson's very concise paper The geodesic circle that an orbiting object follows through 4-space in the proper reference frame of its own Kepler system is not a simple great circle which turns in two orthogonal dimensions. It is a helical great circle that turns in four orthogonal dimensions at once.{{Efn|Geodesic orbits in 4-space are not simple 2-dimensional great circles; they are helical 4-dimensional great circles that curve in all four dimensions at once. Their circular trajectories are helixes which we call ''isoclines'', since they are the paths taken by points on a rigid object undergoing isoclinic rotation.}} Such circles lie outside our physical experience, since our local space has only three orthogonal dimensions. Nonetheless we can visualize them in imagination, because their helical, circular shape is perfectly well defined by the kinematical variables of the Kepler orbit. The real physical correlates of abstract orthogonal planes and rotation angles are already familiar to us viscerally in our body-language of physical experience, since we are endowed biologically with highly evolved visual signal processing engines. These enable us to see and understand spatial relations and motions, including rotations, without even thinking about angles and orthogonal planes. This physical endowment is an inborn capacity for dimensional analogy which our biologic evolution has provided. All our instinctive spatial reasoning is by dimensional analogy from flat 2-dimensional retinal images to 3-dimensional scenes, using our powerful inborn visualization capacities of reverse stereographic projection and pattern recognition. We humans are thus very well equipped with everything we need to see in four-dimensional space, except experience. ... Recently Anco and Moghadam found that through Noether’s theorem in reverse, the LRL vector gives rise to a corresponding infinitesimal dynamical symmetry on the kinematical variables, which they show to be the semi-direct product of <small><math>SO(3)</math></small> and <small><math>\mathbb{R^3}</math></small>, in contrast to the <small><math>SO(4)</math></small> symmetry group generated by the LRL symmetries and the rotations.{{Sfn|Anco|Moghadam|2026|ps=; The physically relevant part of the LRL vector is its direction ... since its magnitude is just a function of energy and angular momentum.}} This remarkable symmetry breaking is expressive of the ''dimensional relativity'' between ordinary 3-space <small><math>\mathbb{R^3}</math></small>, spherical space <small><math>S^3</math></small> and Euclidean space <small><math>\mathbb{R^4}</math></small>. Consider a hydrogen atom in a Kepler orbit: for example, a hydrogen atom moving freely in space in an orbit around the sun. It is a ''double'' Kepler problem: an electrostatic Kepler problem within itself, and a gravitational Kepler problem in its environment. The ''single'' electrostatic Kepler problem of a hydrogen atom moving freely in space beyond any gravitational influence is a problem in special relativity. In our Euclidean 4-space model, this atom viewed as stationary in its own proper reference frame exhibits an <small><math>SO(4)</math></small> rotation symmetry corresponding to an isoclinic double rotation (<small><math>\mathrm{Q^2}</math></small>). The fourth dimension in this reference frame is the atom's proper time vector; it has constant velocity <math>c</math> and constant direction. From the point of view of our universal 4-coordinate space (which cannot be the proper inertial reference frame of any physical observer, all of whom are moving relative to it at velocity ''c''), the entire Kepler system (the atom) is translating through 4-space via a screw translation (<small><math>\mathrm{QT}</math></small>) at constant velocity <math>c</math>. From this viewpoint the atom has only a simple <small><math>SO(3)</math></small> rotation component (<small><math>\mathrm{Q}</math></small>), breaking its stationary <small><math>SO(4)</math></small> isoclinic rotation symmetry (<small><math>\mathrm{Q^2}</math></small>). Because each discrete part of the rotating atom moves along a helical trajectory through 4-space, the atom is in orbit around a barycentric axis (like a star in a galaxy), but only in a tiny orbit within its own radius, which is its inertial domain of rotation. The straight 4-dimensional cylinder it progresses along at velocity <math>c</math> is very narrow: only the diameter of the rotating atom itself. The gravitational Kepler problem of a hydrogen atom in a Kepler orbit around the sun is a problem in general relativity. In our 4-space model, this atom viewed in its own proper reference frame exhibits the same <small><math>SO(4)</math></small> rotation symmetry as it did in the electrostatic Kepler problem where the atom was translating linearly through space. The Kepler system in this case is not just the atom; it is the entire solar system. The LRL vector of this Kepler system is the proper time vector of the atom's inertial reference frame; once again it has constant velocity ''and constant direction''. Although the momentum vector moves in a perfect circle as the atom orbits the sun, the 4-space LRL vector does not move at all: it is a constant of motion, of linear motion (<small><math>\mathrm{T}</math></small>) of the Kepler system (the entire solar system in this case) in a constant 4-space direction, the proper time direction of the system. The direction of the system's proper time vector would vary under some kinds of acceleration of the atom, but it is constant under this kind of orbital acceleration. It continues to point in the same direction, like a 4-space compass needle, as the atom winds its way along its spiral path around the axis of the sun's straight-line translation through 4-space at velocity <math>c</math>. This compass needle always points in the direction the sun is moving, not the direction the atom is moving at any instant. ...Its Kepler orbit around the sun is its <small><math>SO(3)</math></small> rotation component (<small><math>\mathrm{Q}</math></small>). Although the atom is moving on a geodesic circle in the second problem, by the [[equivalence principle]] the difference in the state of the atomic systems in these two problems cannot be observed by examining the atoms alone. Even from another inertial reference frame, where the atom in the second problem is seen to be translating through 4-space via a wide screw translation (<small><math>\mathrm{QT}</math></small>) around the sun's axis of motion, there is still no difference between the two problems which can be detected by examining only the atoms within their own proper reference frames (even over time), because the LRL vector (<small><math>\mathrm{T}</math></small>) is a constant of motion of the entire system in both cases. ...Anco and Maghadam found that <small><math>SO(4)</math></small>) breaks to ... <small><math>S^3</math></small>)... if the energy in the Kepler orbit is negative (an elliptical orbit), and to ... <small><math>H^3</math></small>) ... Minkowski spacetime if the energy is positive (a hyperbolic orbit). ... Finally we consider a third problem in which a hydrogen atom enters the solar system as a comet, loops around the sun and exits the solar system again. This atom... ... As Hamilton found when he discovered the quaternions, we see that it is necessary to admit a fourth dimension to the system in order to properly model the problem: in Hamilton's case the general problem of ..., and in our case the Kepler problem. These are instances of the same problem in 4-dimensional Euclidean geometry, and indeed a solution to the Kepler problem in quaternions (the four Cartesian coordinates of Euclidean 4-space) is a solution to it in our model of the 4-coordinate Euclidean cosmos. == Distribution of stars in our galaxy == The stars in our own galaxy appear to us to be a rotating spiral cluster in 3-dimensional space. By assuming that light from them reaches us on straight lines through space, by assuming that we can measure their distance from us by its red shift, and by assuming that they are distributed in three dimensions of space, we have plotted their locations in 3-space. If we abandon the last of those three assumptions, we can just as easily reinterpret that dataset to plot their distribution around us in 4-dimensional space, and see how they actually lie. When we perform this experiment on the data for the stars in our galaxy, do we indeed find that they are distributed non-uniformly in various concentric spirals, but the spirals lie on the surface of various 3-spheres, rather than in elliptical orbits as we saw them in 3-space? That would be an expected consequence of the special rotational symmetry group of 4-space <small><math>SO(4)</math></small>, in which circular (isoclinic) orbits are the geodesics (shortest rotational paths) rather than elliptical (non-equi-angled double rotation) orbits. ...have to perform this experiment somehow, at least as a conclusive thought experiment, before I publish this paper... == Rotations == The [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotations]] of the convex [[W:regular 4-polytope|regular 4-polytope]]s are usually described as discrete rotations of a rigid object. For example, the rigid [[24-cell]] can rotate in a [[24-cell#Great hexagons|hexagonal]] (6-vertex) central [[24-cell#Planes of rotation|plane of rotation]]. A 4-dimensional [[24-cell#Isoclinic rotations|''isoclinic'' rotation]] (as distinct from a [[24-cell#Simple rotations|''simple'' rotation]] like the ones that occur in 3-dimensional space) is a ''diagonal'' rotation in multiple [[W:Clifford parallel|Clifford parallel]] [[24-cell#Geodesics|central planes]] of rotation at once. It is diagonal because it is a [[W:SO(4)#Double rotations|double rotation]]: in addition to rotating in parallel (like wheels), the multiple planes of rotation also tilt sideways in the completely orthogonal plane of rotation (like coins flipping) into each other's planes. Consequently, the path taken by each vertex is a [[24-cell#Helical hexagrams and their isoclines|twisted helical circle]], rather than the ordinary flat great circle a vertex follows in a simple rotation. In a rigid 4-polytope rotating isoclinically, ''all'' the vertices lie in one of the parallel planes of rotation, so all the vertices move in parallel along Clifford parallel twisting circular paths. [[24-cell#Clifford parallel polytopes|Clifford parallel planes]] are not parallel in the normal sense of parallel planes in three dimensions; the vertices are all moving in different directions around the [[W:3-sphere|3-sphere]]. In one complete 360° isoclinic revolution, a rigid 4-polytope turns itself inside out. This is sufficiently different from the simple rotations of rigid bodies in our 3-dimensional experience that a [[24-cell#Rotations|detailed description]] enabling the reader to properly visualize its counter-intuitive consequences runs to many pages and illustrations, with many accompanying pages of explanatory notes on surprising phenomena that arise in 4-dimensional space: [[24-cell#Great squares|completely orthogonal planes]], [[24-cell#Clifford parallel polytopes|Clifford parallelism]]{{Efn|name=Clifford parallels}} and [[W:Hopf fibration|Hopf fiber bundles]], [[24-cell#Isoclinic rotations|isoclinic geodesic paths]], and [[24-cell#Double rotations|chiral (mirror image) pairs of rotations]], among other complexities. Moreover, the characteristic rotations of the various regular 4-polytopes are all different; each is a unique surprise. [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|The 6 regular convex 4-polytopes]] have different numbers of vertices (5, 8, 16, 24, 120 and 600 respectively) and those with fewer vertices occur inscribed in those with more vertices (with one exception), with the result that the more complex 4-polytopes subsume the kinds of rotations characteristic of their less complex predecessors, as well as each having a characteristic kind of rotation not found in their predecessors. None of these symmetries is to be found in 3-dimensional space, although their simpler 3-dimensional analogues are all present there. [[W:Euclidean geometry#Higher dimensions|Four dimensional Euclidean space]] is more complicated (and more interesting) than three dimensional space because there is more room in it, in which unprecedented things can happen. It subsumes 3-dimensional space, with all of the symmetries we are accustomed to, and adds astonishing new surprises. These are hard for us to visualize, because the only way we can experience them is in our imagination; we have no body of sensory experience in 4-dimensional space to draw upon, other than our evolution in time. For that reason (our difficulty in visualizing them), descriptions of isoclinic rotations usually begin and end with rigid rotations: [[24-cell#Isoclinic rotations|for example]], all 24 vertices of a single rigid 24-cell rotating in unison, with 6 vertices evenly spaced around each of 4 Clifford parallel twisted circles.{{Efn|name=360 degree geodesic path visiting 3 hexagonal planes}} But that is only the simplest case, which is easiest for us to understand. Compound and [[W:Kinematics|kinematic]] 24-cells (with moving parts) are even more interesting (and more complicated) than the rotation of a single rigid 24-cell. To begin with, when we examine the individual parts of a single rigid 24-cell that are moving in an isoclinic rotation, such as the orbits of individual vertices, we can imagine a case where fewer than 24 point-objects are orbiting on those twisted circular paths at once. [[24-cell#Reflections|For example]], if we imagine just 8 point-objects, evenly spaced around the 24-cell at [[24-cell#Reciprocal constructions from 8-cell and 16-cell|the 8 vertices that lie on the 4 coordinate axes]], and rotate them isoclinically along exactly the same orbits they would take in the above-mentioned rotation of a rigid 24-cell, then in the course of a single 360° rotation the 8 point-objects will trace out the whole 24-cell, with just one point-object reaching each of the 24 vertex positions just once, and no point-object colliding with (or even crossing the path of) any other at any time. This is an example of a discrete Hopf fibration. But it is still an example of a rigid object in a discrete isoclinic rotation: a rigid 8-vertex object (called the 4-[[W:orthoplex|orthoplex]] or [[16-cell]]) performing one half of the characteristic rotation of the 24-cell. We can also imagine ''combining'' distinct isoclinic rotations. What happens when multiple point-objects are orbiting at once, but do ''not'' all follow the Clifford parallel paths characteristic of the ''same'' distinct rigid rotation? What happens when we combine orbits from distinct rotations characteristic of different 4-polytopes, for example when different rigid 4-polytopes are concentric and rotating simultaneously in their characteristic ways? What kinds of such hybrid rotations are possible in the same 3-sphere shell without collisions? In adjacent concentric shells without asymmetric imbalance? What sort of [[Kinematics of the cuboctahedron|kinematic polytopes]] do they trace out, and how do their [[24-cell#Clifford parallel polytopes|component parts]] relate to each other as they move? Is there (sometimes) some kind of mutual stability amid their lack of combined rigidity? Visualizing isoclinic rotations (rigid and otherwise) allows us to explore such questions of [[W:kinematics|kinematics]], and where dynamic stabilities arise, of [[wikipedia:kinetics (physics)|kinetics]]. In four dimensions, we discover that space has more room in it than we have experienced, which permits previously unimagined motions. Even 3-space is more commodious than we thought; when it is curved and lies embedded in a higher-dimensional space, it permits previously impossible symmetric packings. Sadoc studied double-twisted 3-dimensional molecules, and imagined them embedded in 4-dimensional space as the Hopf fibrations of regular 4-polytopes. He found that these molecules would close-pack on the 3-sphere perfectly without exhibiting any torsion, although their packing in ordinary flat 3-space is imperfect, "frustrated" by their twisted geometry. <blockquote>The frustration, which arises when the molecular orientation is transported along the two [spiral] AB paths of figure 1 [double twist helix], is imposed by the very topological nature of the Euclidean space R³. It would not occur if the molecules were embedded in the non-Euclidean space of the [[W:3-sphere|3-sphere]] S³, or hypersphere. This space with a homogeneous positive curvature can indeed be described by equidistant and uniformly twisted fibers, along which the molecules can be aligned without any conflict between compactness and [[W:torsion of a curve|torsion]].... The fibres of this [[W:Hopf fibration|Hopf fibration]] are great circles of S³, the whole family of which is also called the [[W:Clifford parallel|Clifford parallel]]s.{{Efn|name=Clifford parallels}} Two of these fibers are C_∞ symmetry axes for the whole fibration; each fibre makes one turn around each axis and regularly rotates when moving from one axis to another.{{Efn|name=helical geodesic}} These fibers build a double twist configuration while staying parallel, i.e. without any frustration, in the whole volume of S³.{{Efn|name=Petrie polygon of a honeycomb}} They can therefore be used as models to study the condensation of long molecules in the presence of a double twist constraint.{{Sfn|Sadoc & Charvolin|2009|loc=§1.2 The curved space approach|ps=; studies the helical orientation of molecules in crystal structures and their imperfect packings ("frustrations") in 3-dimensional space.}}</blockquote> Of course we do not find molecules condensing to close-pack the 3-sphere in our experience, and Sadoc does not say that we do. We find 3-spheres in the atomic realm (if atoms are 4-polytopes), and in the cosmic realm (as the surface boundaries of stars, and the concentric surfaces of galaxies). But in between, in the realm of ordinary experience which includes the molecular realm, ourselves and all the objects we can materially handle or observe up close including the planets, we are confined together by gravity as inertia within a curved 3-dimensional space that is no more than one atom thick in the fourth spatial dimension. That is why in the molecular realm we find only objects that occupy 3-spaces which, though infinitesimally curved in the fourth dimension, are tiny patches on whole 3-spheres of galactic size. So Sadoc's exercise is a thought experiment, like Einstein's gedankenexperiments about railroad embankments and trains moving at nearly the speed of light. It is no less illuminating, despite the symmetry it reveals not having a realization as an actual 3-sphere of actual molecules. And might not something very like it have an actual realization in the atomic realm? We know that atoms have their own complex internal structure, which we are unable to model geometrically in ordinary 3-dimensional space. Suppose such a model is impossible because an atom is actually a 4-polytope occupying a tiny spherical region of 4-dimensional space, and so we only find its constituent particles in close-packed helical orbits on the 3-sphere, in the manner of Sadoc's imaginary twisted molecules, but as real 4-dimensional helices of atomic scale. We would expect to find the atomic orbit of a fundamental particle in some discrete Hopf fibration characteristic of a symmetry group, that is, on the maximally symmetric isoclines of a discrete isoclinic rotation characteristic of some regular 4-polytope and the particle. == A theory of the Euclidean atom == <blockquote>Because quantum physics could be tested without being understood, it allowed humans to see how the universe worked without knowing why.<ref>Sebastian Junger, In My Time of Dying</ref></blockquote> ... == Light and Mass are Reflection and Rotation == The phenomena of light and mass are expressions of reflection symmetries and rotation symmetries, respectively. ... Atoms are 4-polytopes, elementary objects with SO(4) rotational symmetry. Light is .... Motion in space is the propagation of the elementary objects of light and matter in Coxeter congruent transformations by kaleidoscopic self-reflections, like the motion of self-reproducing cellular automata in [[Conway's Game of Life|Conway's game of life]]. ... Light is discrete reflections. Mass is discrete rotations. Both are group actions, expressions of intrinsic symmetries. That is all of physics. === Atoms are 4-polytopes === ... == Relativity in real space of four or more orthogonal dimensions == Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions. General relativity is Galilean relativity in a general space of four or more orthogonal dimensions, e.g. in Euclidean 4-space <math>R^4</math>, spherical 4-space <math>S^4</math>, and any orthogonal 4-manifold. Light is a consequence of symmetry group reflections at quantum scale. Gravity and the other fundamental forces are consequences of rotations, which are consequences of quantum reflections. Light is discrete reflections. Gravity and all forces are discrete rotations. Both are group actions, expressions of intrinsic symmetries. That is all of physics. Every observer may properly see themself as stationary and the universe as an ''n''-sphere with themself at the center. The curvature of these spheres is a function of the rate at which causality evolves, and can be measured by the observer as the speed of light. === Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions === ...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here... Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in three spatial dimensions. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (In general relativity, discussed below, the actual rate of physical processes varies from place to place, and those differences are neither reciprocal nor illusory.) None of these Lorentz effects are beyond geometric explanation or paradoxical. The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, successive Euclidean spaces are dimensionally analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature, is an exact expression of intrinsic symmetries: that is Nother's great discovery. === General relativity is Galilean relativity in a general space of four orthogonal dimensions === ... == Dimensional relativity == Coxeter's kinetic law of <math>n</math>-dimensional congruent Euclidean transformations may be called ''dimensional relativity'', since it captures the theories of special and general relativity entire, and has its roots in dimensional analogy. Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessable by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated. By analogy to the surface of the earth, the bounding surface of a spherical region of <math>n</math>-dimensional Euclidean space is an <math>(n-1)</math>-sphere, a spherical space of one fewer dimensions than the <math>n</math>-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean <math>n</math>-spaces of increasing <math>n</math>, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating <math>n</math>-spaces. By the degree of dimensional analogy of which they are capable, some observers see deeper into <math>n</math>-dimensional space than others. == Polycentric spherical relativity == An intelligent observer equipped with the principle of relativity may perceive the universe from any inertial reference frame, not only from their own proper perspective. We see that every observer may properly view themself as stationary and the universe as an ''n''-sphere with themself at the center observing it, perceptually equidistant from all points on its surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything. This ''polycentric model'' of the universe is a further restatement of the principle of relativity. It is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. It should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849: "The universe is a sphere whose center is wherever there is intelligence."{{Sfn|Thoreau|1849|p=349|ps=; "The universe is a sphere whose center is wherever there is intelligence." [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}} == Revolutions == The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity ''c'', with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may, or may not, all have the same origin in space and time. As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment we dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed us that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a sense related to time, at least, it must be 4-dimensional. In this work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space. Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we now observe them, any more than they lie in the three dimensional hyperplane of local space in which we find everything residing in our solar system. When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us only by virtue of how long it takes their light to reach us. We can measure their distribution around us in 4-space, but that is simply how we choose to measure them, not a finding of how they are actually distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean ''n''-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity <math>c</math>, on more or less divergent paths from each other. But only much closer observation will reveal evidence of whether everything we see lies in the same 4-space, or if it is distributed in five or more dimensions, and how it is moving there. To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity <math>c</math>, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw displacements), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw displacement has ''two'' [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity <math>c</math> in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that each galaxy's own distinct 3-sphere is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to lightspeed long ago, in whatever big bang our atoms emerged from, and have never slowed down since. == Origins of the theory == Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of the geometry of Euclidean 4-space relativity, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] contains the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and did not describe our ordinary 3-space embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.<ref>{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}</ref> He invited us to imagine "A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions", but he was careful to disclaim parenthetically that "The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice." Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal of that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.'' The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified spacetime of four dimensions. Anco and Maghadam found that <small><math>SO(4)</math></small> breaks to ... <small><math>S^3</math></small>... if the energy in the Kepler orbit is negative (an elliptical orbit), and to ... <small><math>H^3</math></small> ... Minkowski spacetime if the energy is positive (a hyperbolic orbit). Because the planets orbit on ellipses in our 3-space, Euclidean 4-space is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the truer model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position of centrality as our exclusive conception of our place in space. ...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others. The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; "Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions."}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.<ref>{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}</ref>}} == Boundaries == <blockquote>Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.<ref>{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}</ref></blockquote> Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? ''What is the nature of the boundary which confines us to just three dimensions?'' We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell. Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined motions and objects. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. A boundary is an explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force. <blockquote>The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three .... In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it. We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed "Dimensional Analogy."<ref>{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}</ref></blockquote> I believe, but I cannot prove, that we live in real space, which is Schläfli's and Coxeter's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover in imagination and then explore physically, each an astonishing new enlightenment.<ref>{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}<blockquote> :We shall not cease from exploration :And the end of all our exploring :Will be to arrive where we started :And know the place for the first time. :Through the unknown, remembered gate :When the last of earth left to discover :Is that which was the beginning; :At the source of the longest river :The voice of the hidden waterfall :And the children in the apple-tree :Not known, because not looked for :But heard, half-heard, in the stillness :Between two waves of the sea. </blockquote></ref> Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. This project is forever beginning anew. Coxeter showed us that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether showed us all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions, in which all objects with mass move ceaselessly at the constant velocity <math>c</math>, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages. <blockquote> ::::::BEECH :Where my imaginary line :Bends square in woods, an iron spine :And pile of real rocks have been founded. :And off this corner in the wild, :Where these are driven in and piled, :One tree, by being deeply wounded, :Has been impressed as Witness Tree :And made commit to memory :My proof of being not unbounded. :Thus truth's established and borne out, :Though circumstanced with dark and doubt— :Though by a world of doubt surrounded. :::::::—''The Moodie Forester''<ref>{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}</ref> </blockquote> == Appendix: Sequence of regular 4-polytopes == {{Regular convex 4-polytopes|wiki=W:|columns=7}} == ... == {{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}} {{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}} {{Efn|The long radius (center to vertex) of the 24-cell is equal to its edge length; thus its long diameter (vertex to opposite vertex) is 2 edge lengths. Only a few uniform polytopes have this property, including the four-dimensional 24-cell and [[W:Tesseract#Radial equilateral symmetry|tesseract]], the three-dimensional [[W:Cuboctahedron#Radial equilateral symmetry|cuboctahedron]], and the two-dimensional [[W:Hexagon#Regular hexagon|hexagon]]. (The cuboctahedron is the equatorial cross section of the 24-cell, and the hexagon is the equatorial cross section of the cuboctahedron.) '''Radially equilateral''' polytopes are those which can be constructed, with their long radii, from equilateral triangles which meet at the center of the polytope, each contributing two radii and an edge.|name=radially equilateral|group=}} {{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as "the convex hull of the neighbouring vertices of a given vertex".{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its "radius" equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}} {{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example: {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0) {{indent|5}}({{spaces|2}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>){{spaces|3}}({{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>) {{indent|5}}(–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>){{spaces|3}}(–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>) {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)<br> is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}} {{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60° rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the "left" is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}} {{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}} {{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; "In mathematics, the path that the (1, 1) knot on the torus traces is also known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two intersecting circles that are the cross-section of a torus by a well-chosen plane cutting it. Picking one such circle and rotating it around the torus axis, the resulting family of circles can be used to rule the torus. By nesting tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the (1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles]."}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}} {{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}} {{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}} {{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}} {{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}} {{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}} {{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}} {{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}} {{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}} {{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90^o bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60^o bend, or as a straight line with one 60^o bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}} {{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; "In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)"}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}} {{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}} {{Efn|Departing from any vertex V₀ in the original great hexagon plane of isoclinic rotation P₀, the first vertex reached V₁ is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P₁. P₁ is inclined to P₀ at a 60° angle.{{Efn|P₀ and P₁ lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V₂ is 120 degrees beyond V₁ along a second {{radic|3}} chord lying in another hexagonal plane P₂ that is Clifford parallel to P₀.{{Efn|P₀ and P₂ are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V₀ and V₂ are ''two'' {{radic|3}} chords apart{{Efn|V₀ and V₂ are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V₀ and V₂ are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P₀ and P₂ are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V₁ lies in both intersecting planes P₁ and P₂, as V₀ lies in both P₀ and P₁. But P₀ and P₂ have ''no'' vertices in common; they do not intersect.) The third vertex reached V₃ is 120 degrees beyond V₂ along a third {{radic|3}} chord lying in another hexagonal plane P₃ that is Clifford parallel to P₁. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V₀ to V₃ is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}} {{Sfn|Mamone, Pileio & Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹₄.}} ==Notes== {{Regular convex 4-polytopes Notelist|wiki=W:}} ==Citations== {{Regular convex 4-polytopes Reflist|wiki=W:}} ==References== {{Refbegin}} * {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}} * {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1}} * {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}} === [[Polyscheme|Polyschemes]] === {{Regular convex 4-polytopes Refs|wiki=W:}} {{Refend}} se68v05piral9w9rohhai4urhoecigm 2823711 2823709 2026-08-20T20:46:38Z Dc.samizdat 2856930 /* Special relativity describes Euclidean 4-space */ 2823711 wikitext text/x-wiki = Real Euclidean four-dimensional space R⁴ = {{align|center|David Brooks Christie}} {{align|center|dc@samizdat.org}} {{align|center|Draft in progress}} {{align|center|June 2023 - August 2026}} <blockquote>'''Abstract:''' The physical universe is properly visualized as a Euclidean space of four orthogonal spatial dimensions. Space itself has a fourth orthogonal dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and our planet are only 3-dimensional objects, but nonetheless we can see in four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.</blockquote> == Summary == We observe that physical space has four perpendicular dimensions, not just three; atoms are [[W:4-polytope|4-polytopes]]; the sun is a 4-ball that is round in four dimensions; everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space; and our entire 3-space manifold is translating through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions. == A theory of the Euclidean cosmos == The physical universe is properly visualized as a [[w:Four-dimensional_space|Euclidean space of four orthogonal spatial dimensions]]. Space itself has a fourth orthogonal dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planets, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. All objects with mass move inertially through Euclidean 4-space at velocity <math>c</math> as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity <math>c</math> is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space. A typical spiral galaxy such as ours is a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our galaxy appear from our viewpoint to be distributed in a cloud of elliptical spirals occupying a flattened ellipsoid region of 3-dimensional space, but they are not so confined: they are distributed within a spherical region of 4-dimensional space. The galaxy's actual shape is spherical, not a flattened ellipsoid, but it is rounder than round can be in our ordinary experience: it occupies a hyperspherical region of space. The concentric spirals of stars that we observe lie on concentric [[W:3-sphere|3-sphere]]s (4-dimensional spheres), not on concentric 2-ellipsoids (3-dimensional elliptical spirals). Our sun and solar system lies on one of those concentric 3-spheres. More generally, orbits are circular in 4-space, and elliptical in the 3-space of their elliptic hyperplane. [[File:Hypersphere.png|thumb|Rotating illustration of the 4-ball galaxy showimg its spirals of star clouds on the surface of concentric 3-spheres, obtained by reverse sterographic projection from 3D images of the galaxy.]] The galaxy as a whole, or more properly its orbital center point, is translating through 4-space at velocity <math>c</math>, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity <math>c</math> in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity <math>c</math>. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the cylinder; their trajectories are screw-displacements, the compound of a simple rotation and a linear translation. The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around a barycentric axis. It is the tremendous inertial force of stars in motion at velocity <math>c</math> that holds the cylinder of motion together. The observed universe as a whole appears to be a 3-sphere expanding radially from a central origin point at velocity <math>c</math>, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. For all observers, the conjectured origin point of the universe corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space (the same point in the same Euclidean 4-space for all observers). The big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured separately, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity <math>c</math>. All objects in our solar system except the sun itself lie within this thinest three-dimensional manifold. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. The enclosing surface of a spherical region of 4-space is itself a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. We live within such a 3-space, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience, and it contains the earth, all the planets and the 3-dimensional space between them. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our particular 3-sphere is one of the galaxy's concentric 3-spheres of spiral star-clouds. The solar system occupies a tiny patch of this filmy 4-dimensional soap-bubble of galactic size, that is thicker-skinned than the diameter of an atom only in the interior of stars and supermassive objects. Our entire 3-sphere manifold, as a 3-spherical shell within the moving 4-ball galaxy, is translating through 4-space at velocity <math>c</math> with the galaxy, in a distinct direction that is orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the galaxy's translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of rotating objects through Euclidean space by screw translation. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity <math>c</math>, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. Any moving 3-dimensional manifold that is such an evolving surface boundary is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. Every object which we find occurring naturally in the solar system other than the sun itself, even the largest of 3-dimensional objects a planet, is a three-dimensional smear of atoms no thicker than one atom in its fourth dimension, which is the direction of its linear translation through 4-space at velocity <math>c</math>. The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be "heaped up" into larger 4-dimensional objects that form a lump in its moving surface. We have little understanding of such 4-dimensional lumps thicker than one atom, since they occur naturally in our vicinity only in the interior of the sun. In fact the sun is the only such lump occurring naturally in our solar system. We refer to 4-dimensional lumps of matter as plasma, and have little experimental knowledge of their geometry or internal structure. We know that such a lump as the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know nothing about its interior 4-ball. Every such moving 3-dimensional surface boundary of matter in the observed universe is evolving in four dimensions at velocity <math>c</math>. Its current location in 4-space corresponds to the present moment in the proper time of its inertial reference frame. Its direction of movement at velocity <math>c</math> corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from atoms to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, two orthogonal inertial motions each at the constant universal rate of transformation <math>c</math>. Every object moves relative to universal 4-coordinate space on its own distinct geodesic spiral, a screw translation trajectory that is the compound of two orthogonal inertial motions, a rotation and a translation. Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity <math>c</math> in all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is <math>c^\prime = 2c</math>, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity <math>c</math>. For example, we can look across the center of our mostly-empty 4-ball galaxy and see stars in the opposite sides of its concentric 3-sphere surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math> in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper space. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space. == Symmetries == It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel & Goodman-Strauss|2008}} As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. [[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}} <blockquote>Let <small><math>\mathrm{Q}</math></small> denote a rotation, <small><math>\mathrm{R}</math></small> a reflection, <small><math>\mathrm{T}</math></small> a translation, and let <small><math>\mathrm{Q}^q \mathrm{R}^r\mathrm{T}</math></small> denote a product of several such transformations, all commutative with one another. Then <small><math>\mathrm{RT}</math></small> is a glide-reflection (in two or three dimensions), <small><math>\mathrm{QR}</math></small> is a rotary-reflection, <small><math>\mathrm{QT}</math></small> is a screw-displacement, and <small><math>\mathrm{Q^2}</math></small> is a double rotation (in four dimensions).<br> Every orthogonal transformation is expressible as:<br> :<small><math>\mathrm{Q}^q \mathrm{R}^r</math></small><br> where <small><math>(2^q + r \le n)</math></small>, the number of dimensions.<br> Transformations involving a translation are expressible as:<br> :<small><math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}</math></small><br> where <small><math>(2^q + r + 1 \le n)</math></small>.<br> For <small><math>(n = 4)</math></small> in particular, every displacement is either a double rotation <small><math>\mathrm{Q}^2</math></small>, or a screw-displacement <small><math>\mathrm{QT}</math></small> [where the rotation component <small><math>\mathrm{Q}</math></small> is a simple rotation, but the <small><math>\mathrm{QT}</math></small> is chiral like a <small><math>\mathrm{Q^2}</math></small>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <small><math>\mathrm{QRT}</math></small>.</blockquote> If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a <small><math>\mathrm{Q^2}</math></small> or a <small><math>\mathrm{QT}</math></small>, because we can view any <small><math>\mathrm{QT}</math></small> as a <small><math>\mathrm{Q^2}</math></small> in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a <small><math>\mathrm{Q^2}</math></small>. By the same principle, we can view any <small><math>\mathrm{QT}</math></small> or <small><math>\mathrm{Q^2}</math></small> as an isoclinic (equi-angled) <small><math>\mathrm{Q^2}</math></small> by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (<small><math>\mathrm{T}</math></small>) for ''one'' of the two rotations (<small><math>\mathrm{Q}</math></small>). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (<small><math>\mathrm{Q}</math></small>) up to uncertainty, and can always distinguish the direction of their own proper time translation (<small><math>\mathrm{T}</math></small>). As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebra), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group <small><math>SO(4)</math></small> [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic <small><math>SO(4)</math></small> rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, stationary atoms exhibit the <small><math>SO(4)</math></small> symmetries of the discrete isoclinic (equi-angled) double rotations (<small><math>\mathrm{Q^2}</math></small>) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]]. == Special relativity describes Euclidean 4-space == <blockquote>Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.<ref>{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}</ref></blockquote> Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional "space" because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign to the three space coordinates so spacetime is hyperbolic, not a flat Euclidean 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was first described by Einstein himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction. Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity ''c'', in some 4-space direction. This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always ''c'', as measured by all observers from any inertial reference frame. This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source. But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity ''c''. In physics as it has been universally understood, observers are not supposed to be able to move at velocity ''c''. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four. In the Euclidean relativity alternative view, however, every observer is always moving at velocity ''c'' through the universe, which is real Euclidean 4-dimensional space <small><math>\mathbb{R^4}</math></small>. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity ''c''. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and proper space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity ''c'', in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space <small><math>\mathbb{R^4}</math></small>.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity ''c'' relative to universal 4-coordinate space, so the maximum relative velocity between two observers is 2''c'' when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to ''c'', it is the same measurement in different units. Special relativity measures all velocities in a 3-space of Minkowski spacetime. Euclidean relativity measures all velocities in Euclidean 4-space.}} So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity ''c'' in Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the "speed of light" ''c'', although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity ''c'', but in at least slightly different directions. In Einstein's relativity, the invariant ''c'' is the speed of light through 3-space. In Euclidean relativity, the invariant ''c'' is the speed of matter through 4-space! The speed of light through 3-space is also perceived as ''c'' by all observers, because they are each living in a moving 3-manifold that is moving through 4-space at velocity ''c''. Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same predictions about how observers in different reference frames will perceive each other's motions in time and space, and we shall see that they also agree on the predictions of general relativity. They both describe the same geometric relations of space and time, but they describe that geometry as embedded in two very different universal host spaces: Minkowski spacetime versus Euclidean 4-space. ...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity <math>c</math> through space and proper time ...cite Yamashita{{Sfn|Yamashita|2023}} on the equivalence of special relativity and Euclidean 4-space relativity ...cite Kappraff & Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff & Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff & Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords. Euclidean relativity is not even a fringe theory; no physicists have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could "catch up" with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at ''c'' (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than ''c''. Euclidean relativity is a revolutionary theory indeed, in which ''c'' cannot possibly be the speed of light! We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for <math>\mathbb{R^4}</math> to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be <math>c\prime = 2c</math>, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate linearly along the edge of a unit 4-hypercube. This is conceivable in 4-space (and in no other Euclidean space of any dimensionality) because the diagonal of the unit 4-hypercube is the natural number <small><math>\sqrt{4}</math></small>. == An object's motion in space is the product of its discrete self-reflections == Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a small number of discrete self-reflections. Any action of a geometric object that transforms its position and orientation in space may be measured as a distinct group of self-reflections of the object in its own surfaces. Any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete set of local self-reflections. Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which touch (intersect each other). When a object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality. Coxeter's laws of motion are a geometric counterpart to Newton's laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures. But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. For example, they give us geometric pictures of all the possible motions of objects in four dimensional Euclidean space: <blockquote>Every orthogonal transformation in 4-space is expressible as:<br> :<small><math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t</math></small><br> where <small><math>(2^q + r + t \le 4)</math></small>. Every displacement is either a double rotation <small><math>\mathrm{Q}^2</math></small>, or a screw-displacement <small><math>\mathrm{QT}</math></small> [where the rotation component <small><math>\mathrm{Q}</math></small> is a simple rotation, but the <small><math>\mathrm{QT}</math></small> is chiral like a <small><math>\mathrm{Q^2}</math></small>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <small><math>\mathrm{QRT}</math></small>.</blockquote> While this description should be understood as simple geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (<small><math>\mathrm{Q}</math></small>), reflection (<small><math>\mathrm{R}</math></small>) and translation (<small><math>\mathrm{T}</math></small>) are just what they are in three-dimensional space, but double rotation (<small><math>\mathrm{Q}^2</math></small>) is something new and unprecedented in our physical experience, because double rotations cannot occur until you have four or more dimensions of space to rotate in. ...to readers who have not studied Coxeter (almost all readers including TAC), the blockquote above is "just math", not visualizable geometry...but I could describe Coxeter's congruent transformations in 4-space here geometrically: I could say clearly what they mean in spatial terms, in language anyone can understand, because they don't require any math to be understood; the "math" here is really just simple pictures (reflections and rotations); even double rotations can be visualized by dimensional analogy, as compounds of simple rotations...since even most physicists are unacquainted with Coxeter geometry, it might be useful to do this here... == Light propagates through 4-space at twice its apparent velocity ''c''== Coxeter's geometric laws of motion apply to all objects with mass in 4-dimensional Euclidean space, but we find there is an additional kind of displacement which applies only to massless particles such as photons. Light quanta (photons) translate through 4-space by 4-dimensional reflection <small><math>\mathrm{R}^4</math></small>, which may be termed a double translation <small><math>\mathrm{T}^2</math></small>, a pure translation via two pairs of parallel reflections, without any rotation component <small><math>\mathrm{Q}</math></small>. Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by <small><math>\mathrm{QT}</math></small>, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic <small><math>\mathrm{Q^2}</math></small>, an isoclinically rotating object such as an atom. A simple rotation <small><math>\mathrm{Q}</math></small> or simple translation <small><math>\mathrm{T}</math></small> is a double reflection <small><math>\mathrm{R^2}</math></small>, so a <small><math>\mathrm{QT}</math></small> or <small><math>\mathrm{Q^2}</math></small> is also an <small><math>\mathrm{R^4}</math></small>, but not with the same group of reflection angles as a light signal <small><math>\mathrm{R^4}</math></small>. A translation <small><math>\mathrm{T = R^2}</math></small> is a double reflection in two parallel planes, and a rotation <small><math>\mathrm{Q = R^2}</math></small> is a double reflection in two intersecting planes, as in a <small><math>\mathrm{QT = R^4}</math></small> which is both at once. A double translation <small><math>\mathrm{T^2 = R^4}</math></small> is two double reflections in pairs of parallel planes at once, a reflection in four or more non-intersecting parallel planes; it is all translation and no rotation. In a <small><math>\mathrm{T^2}</math></small> all the motion goes to translation, so the translation goes twice as far as the simple translation <small><math>\mathrm{T}</math></small> in a <small><math>\mathrm{QT}</math></small>. A double translation <small><math>\mathrm{T^2 = R^4}</math></small> is the opposite of a double rotation <small><math>\mathrm{Q^2 = R^4}</math></small>, which is stationary but rotates twice as fast as the simple rotation <small><math>\mathrm{Q}</math></small> in a <small><math>\mathrm{QT}</math></small>. The product of the two translations in a <small><math>\mathrm{T^2}</math></small> is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple <small><math>\mathrm{T}</math></small> over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double-the-distance translation, but without any rotation component, so it cannot carry any mass with it. A <small><math>\mathrm{T^2}</math></small> cannot reposition a 4-polytope the way a <small><math>\mathrm{QT}</math></small> does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter. ...lensing of double translations <small><math>\mathrm{T^2 = R^4}</math></small> in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet... == The Kepler problem is framed in Euclidean 4-space == The [[W:Kepler problem|Kepler problem]] is named for [[W:Johannes Kepler|Johannes Kepler]], arguably the greatest geometer since the ancients up to [[w:Ludwig Schläfli|Ludwig Schläfli]], who proposed [[W:Kepler's laws of planetary motion|Kepler's laws of planetary motion]] which solved the problem of the orbits of the planets, and investigated the types of forces that would result in orbits obeying those laws. Those forces were later identified by [[W:Isaac Newton|Isaac Newton]] in his[[W:Philosophiæ Naturalis Principia Mathematica| Principia]], where he proves what today might be called the "inverse Kepler problem": the orbit characteristics require the force to depend on the inverse square of the distance.<ref>{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton & Company|isbn=978-0393039184}}</ref> The inverse square law behind the Kepler problem is the [[W:Central force|central force]] law which governs not only [[W:Newtonian gravity|Newtonian gravity]] and celestial orbits, but also the motion of two charged particles in [[W:Coulomb’s law|Coulomb’s law]] of [[W:Electrostatics|electrostatics]]; it applies to attractive or repulsive forces. Problems in which two bodies interact by a central force that varies as the [[W:Inverse square law|inverse square]] of the distance between them are called Kepler problems. Thus the [[W:Hydrogen atom|hydrogen atom]] is a Kepler problem, since it comprises two charged particles interacting by Coulomb's law, another inverse-square central force. Using classical mechanics, the solution to a Kepler problem can be expressed as a [[W:Kepler orbit|Kepler orbit]] using six kinematical variables or [[W:Orbital elements|orbital elements]]. The solution conserves an orbital element called the [[W:Laplace–Runge–Lenz vector|Laplace–Runge–Lenz (LRL) vector]], a [[W:Constant of motion|constant of motion]], meaning that it is the same no matter where it is calculated on the orbit. The LRL vector was essential in the first quantum mechanical derivation of the [[W:Atomic emission spectrum|spectrum]] of the hydrogen atom, but this approach has rarely been used since the development of the [[W:Schrödinger equation|Schrödinger equation]]. The conservation of the LRL vector corresponds to the <small><math>SO(4)</math></small> symmetry, by Nother's theorem. The LRL vector lies orthogonal to both the orbital plane and the angular momentum vector of the Kepler orbit; we observe that it lies in a fourth orthogonal dimension. Fock in 1935<ref>V. Fock, Zur Theorie des Wasserstoffatoms, Zeitschrift für Physik. 98 (3-4) (1935), 145–154.</ref> and Moser in 1970<ref>J. Moser, Regularization of Kepler’s problem and the averaging method on a manifold, Commun. Pure Appl. 23 (1970), 609–636</ref> observed that the Kepler problem is mathematically equivalent to non-affine geodesic motion (a particle moving freely) on the surface of a 3-sphere, so that the whole problem is symmetric under certain rotations of the four-dimensional space. This higher-dimensional symmetry results in two well-known properties of the Kepler problem: the momentum vector always moves in a perfect circle and, for a given total energy, all such velocity circles intersect each other in the same two points. ... Relativity establishes that an orbit in space is viewed in a different way in each distinct inertial reference frame. Depending on the choice of reference frame, the same Kepler system may be seen to be performing any one of a sequence of relativistically equivalent rotations in 4-space, on a continuum from an isoclinic rotation (Q²) in the orbit's proper reference frame, to a screw transfer (QT) with a simple rotation component (Q) and a translation component (T) at velocity <math>c</math>, in the universal reference frame of 4-coordinate space wherein every object is seen to be translating at velocity <math>c</math>. In reference frames between these two limit cases, the orbit is seen to be performing a double rotation (Q²) at two unequal, completely orthogonal angular rates of rotation: an elliptical double rotation. These include the reference frames of most typical observers, who are moving slowly relative to the observed orbital system's reference frame (their relative motion is a small fraction of the speed of light). ...this is probably misplaced here and should not interrupt the discussion at this point: ...These typical observations agree closely with the predictions of special relativity, because the non-isoclinic elliptical (Q²) resembles a (QT), since one of its two completely orthogonal rotations (Q) has such a long period that it is almost indistinguishable from a straight translation (T). All orbits in 4-space are isoclinic in their own reference frame. Orbiting objects in their own proper Kepler systems follow circular geodesic isoclines through 4-space. Orbits in 4-space are perfectly circular in their own reference frame, as Copernicus assumed the orbits of planets to be. It is the orbit's path through the 3-space of its elliptic hyperplane that is an ellipse, as Kepler found it to be. ...cite Jesper Goransson's very concise paper The geodesic circle that an orbiting object follows through 4-space in the proper reference frame of its own Kepler system is not a simple great circle which turns in two orthogonal dimensions. It is a helical great circle that turns in four orthogonal dimensions at once.{{Efn|Geodesic orbits in 4-space are not simple 2-dimensional great circles; they are helical 4-dimensional great circles that curve in all four dimensions at once. Their circular trajectories are helixes which we call ''isoclines'', since they are the paths taken by points on a rigid object undergoing isoclinic rotation.}} Such circles lie outside our physical experience, since our local space has only three orthogonal dimensions. Nonetheless we can visualize them in imagination, because their helical, circular shape is perfectly well defined by the kinematical variables of the Kepler orbit. The real physical correlates of abstract orthogonal planes and rotation angles are already familiar to us viscerally in our body-language of physical experience, since we are endowed biologically with highly evolved visual signal processing engines. These enable us to see and understand spatial relations and motions, including rotations, without even thinking about angles and orthogonal planes. This physical endowment is an inborn capacity for dimensional analogy which our biologic evolution has provided. All our instinctive spatial reasoning is by dimensional analogy from flat 2-dimensional retinal images to 3-dimensional scenes, using our powerful inborn visualization capacities of reverse stereographic projection and pattern recognition. We humans are thus very well equipped with everything we need to see in four-dimensional space, except experience. ... Recently Anco and Moghadam found that through Noether’s theorem in reverse, the LRL vector gives rise to a corresponding infinitesimal dynamical symmetry on the kinematical variables, which they show to be the semi-direct product of <small><math>SO(3)</math></small> and <small><math>\mathbb{R^3}</math></small>, in contrast to the <small><math>SO(4)</math></small> symmetry group generated by the LRL symmetries and the rotations.{{Sfn|Anco|Moghadam|2026|ps=; The physically relevant part of the LRL vector is its direction ... since its magnitude is just a function of energy and angular momentum.}} This remarkable symmetry breaking is expressive of the ''dimensional relativity'' between ordinary 3-space <small><math>\mathbb{R^3}</math></small>, spherical space <small><math>S^3</math></small> and Euclidean space <small><math>\mathbb{R^4}</math></small>. Consider a hydrogen atom in a Kepler orbit: for example, a hydrogen atom moving freely in space in an orbit around the sun. It is a ''double'' Kepler problem: an electrostatic Kepler problem within itself, and a gravitational Kepler problem in its environment. The ''single'' electrostatic Kepler problem of a hydrogen atom moving freely in space beyond any gravitational influence is a problem in special relativity. In our Euclidean 4-space model, this atom viewed as stationary in its own proper reference frame exhibits an <small><math>SO(4)</math></small> rotation symmetry corresponding to an isoclinic double rotation (<small><math>\mathrm{Q^2}</math></small>). The fourth dimension in this reference frame is the atom's proper time vector; it has constant velocity <math>c</math> and constant direction. From the point of view of our universal 4-coordinate space (which cannot be the proper inertial reference frame of any physical observer, all of whom are moving relative to it at velocity ''c''), the entire Kepler system (the atom) is translating through 4-space via a screw translation (<small><math>\mathrm{QT}</math></small>) at constant velocity <math>c</math>. From this viewpoint the atom has only a simple <small><math>SO(3)</math></small> rotation component (<small><math>\mathrm{Q}</math></small>), breaking its stationary <small><math>SO(4)</math></small> isoclinic rotation symmetry (<small><math>\mathrm{Q^2}</math></small>). Because each discrete part of the rotating atom moves along a helical trajectory through 4-space, the atom is in orbit around a barycentric axis (like a star in a galaxy), but only in a tiny orbit within its own radius, which is its inertial domain of rotation. The straight 4-dimensional cylinder it progresses along at velocity <math>c</math> is very narrow: only the diameter of the rotating atom itself. The gravitational Kepler problem of a hydrogen atom in a Kepler orbit around the sun is a problem in general relativity. In our 4-space model, this atom viewed in its own proper reference frame exhibits the same <small><math>SO(4)</math></small> rotation symmetry as it did in the electrostatic Kepler problem where the atom was translating linearly through space. The Kepler system in this case is not just the atom; it is the entire solar system. The LRL vector of this Kepler system is the proper time vector of the atom's inertial reference frame; once again it has constant velocity ''and constant direction''. Although the momentum vector moves in a perfect circle as the atom orbits the sun, the 4-space LRL vector does not move at all: it is a constant of motion, of linear motion (<small><math>\mathrm{T}</math></small>) of the Kepler system (the entire solar system in this case) in a constant 4-space direction, the proper time direction of the system. The direction of the system's proper time vector would vary under some kinds of acceleration of the atom, but it is constant under this kind of orbital acceleration. It continues to point in the same direction, like a 4-space compass needle, as the atom winds its way along its spiral path around the axis of the sun's straight-line translation through 4-space at velocity <math>c</math>. This compass needle always points in the direction the sun is moving, not the direction the atom is moving at any instant. ...Its Kepler orbit around the sun is its <small><math>SO(3)</math></small> rotation component (<small><math>\mathrm{Q}</math></small>). Although the atom is moving on a geodesic circle in the second problem, by the [[equivalence principle]] the difference in the state of the atomic systems in these two problems cannot be observed by examining the atoms alone. Even from another inertial reference frame, where the atom in the second problem is seen to be translating through 4-space via a wide screw translation (<small><math>\mathrm{QT}</math></small>) around the sun's axis of motion, there is still no difference between the two problems which can be detected by examining only the atoms within their own proper reference frames (even over time), because the LRL vector (<small><math>\mathrm{T}</math></small>) is a constant of motion of the entire system in both cases. ...Anco and Maghadam found that <small><math>SO(4)</math></small>) breaks to ... <small><math>S^3</math></small>)... if the energy in the Kepler orbit is negative (an elliptical orbit), and to ... <small><math>H^3</math></small>) ... Minkowski spacetime if the energy is positive (a hyperbolic orbit). ... Finally we consider a third problem in which a hydrogen atom enters the solar system as a comet, loops around the sun and exits the solar system again. This atom... ... As Hamilton found when he discovered the quaternions, we see that it is necessary to admit a fourth dimension to the system in order to properly model the problem: in Hamilton's case the general problem of ..., and in our case the Kepler problem. These are instances of the same problem in 4-dimensional Euclidean geometry, and indeed a solution to the Kepler problem in quaternions (the four Cartesian coordinates of Euclidean 4-space) is a solution to it in our model of the 4-coordinate Euclidean cosmos. == Distribution of stars in our galaxy == The stars in our own galaxy appear to us to be a rotating spiral cluster in 3-dimensional space. By assuming that light from them reaches us on straight lines through space, by assuming that we can measure their distance from us by its red shift, and by assuming that they are distributed in three dimensions of space, we have plotted their locations in 3-space. If we abandon the last of those three assumptions, we can just as easily reinterpret that dataset to plot their distribution around us in 4-dimensional space, and see how they actually lie. When we perform this experiment on the data for the stars in our galaxy, do we indeed find that they are distributed non-uniformly in various concentric spirals, but the spirals lie on the surface of various 3-spheres, rather than in elliptical orbits as we saw them in 3-space? That would be an expected consequence of the special rotational symmetry group of 4-space <small><math>SO(4)</math></small>, in which circular (isoclinic) orbits are the geodesics (shortest rotational paths) rather than elliptical (non-equi-angled double rotation) orbits. ...have to perform this experiment somehow, at least as a conclusive thought experiment, before I publish this paper... == Rotations == The [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotations]] of the convex [[W:regular 4-polytope|regular 4-polytope]]s are usually described as discrete rotations of a rigid object. For example, the rigid [[24-cell]] can rotate in a [[24-cell#Great hexagons|hexagonal]] (6-vertex) central [[24-cell#Planes of rotation|plane of rotation]]. A 4-dimensional [[24-cell#Isoclinic rotations|''isoclinic'' rotation]] (as distinct from a [[24-cell#Simple rotations|''simple'' rotation]] like the ones that occur in 3-dimensional space) is a ''diagonal'' rotation in multiple [[W:Clifford parallel|Clifford parallel]] [[24-cell#Geodesics|central planes]] of rotation at once. It is diagonal because it is a [[W:SO(4)#Double rotations|double rotation]]: in addition to rotating in parallel (like wheels), the multiple planes of rotation also tilt sideways in the completely orthogonal plane of rotation (like coins flipping) into each other's planes. Consequently, the path taken by each vertex is a [[24-cell#Helical hexagrams and their isoclines|twisted helical circle]], rather than the ordinary flat great circle a vertex follows in a simple rotation. In a rigid 4-polytope rotating isoclinically, ''all'' the vertices lie in one of the parallel planes of rotation, so all the vertices move in parallel along Clifford parallel twisting circular paths. [[24-cell#Clifford parallel polytopes|Clifford parallel planes]] are not parallel in the normal sense of parallel planes in three dimensions; the vertices are all moving in different directions around the [[W:3-sphere|3-sphere]]. In one complete 360° isoclinic revolution, a rigid 4-polytope turns itself inside out. This is sufficiently different from the simple rotations of rigid bodies in our 3-dimensional experience that a [[24-cell#Rotations|detailed description]] enabling the reader to properly visualize its counter-intuitive consequences runs to many pages and illustrations, with many accompanying pages of explanatory notes on surprising phenomena that arise in 4-dimensional space: [[24-cell#Great squares|completely orthogonal planes]], [[24-cell#Clifford parallel polytopes|Clifford parallelism]]{{Efn|name=Clifford parallels}} and [[W:Hopf fibration|Hopf fiber bundles]], [[24-cell#Isoclinic rotations|isoclinic geodesic paths]], and [[24-cell#Double rotations|chiral (mirror image) pairs of rotations]], among other complexities. Moreover, the characteristic rotations of the various regular 4-polytopes are all different; each is a unique surprise. [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|The 6 regular convex 4-polytopes]] have different numbers of vertices (5, 8, 16, 24, 120 and 600 respectively) and those with fewer vertices occur inscribed in those with more vertices (with one exception), with the result that the more complex 4-polytopes subsume the kinds of rotations characteristic of their less complex predecessors, as well as each having a characteristic kind of rotation not found in their predecessors. None of these symmetries is to be found in 3-dimensional space, although their simpler 3-dimensional analogues are all present there. [[W:Euclidean geometry#Higher dimensions|Four dimensional Euclidean space]] is more complicated (and more interesting) than three dimensional space because there is more room in it, in which unprecedented things can happen. It subsumes 3-dimensional space, with all of the symmetries we are accustomed to, and adds astonishing new surprises. These are hard for us to visualize, because the only way we can experience them is in our imagination; we have no body of sensory experience in 4-dimensional space to draw upon, other than our evolution in time. For that reason (our difficulty in visualizing them), descriptions of isoclinic rotations usually begin and end with rigid rotations: [[24-cell#Isoclinic rotations|for example]], all 24 vertices of a single rigid 24-cell rotating in unison, with 6 vertices evenly spaced around each of 4 Clifford parallel twisted circles.{{Efn|name=360 degree geodesic path visiting 3 hexagonal planes}} But that is only the simplest case, which is easiest for us to understand. Compound and [[W:Kinematics|kinematic]] 24-cells (with moving parts) are even more interesting (and more complicated) than the rotation of a single rigid 24-cell. To begin with, when we examine the individual parts of a single rigid 24-cell that are moving in an isoclinic rotation, such as the orbits of individual vertices, we can imagine a case where fewer than 24 point-objects are orbiting on those twisted circular paths at once. [[24-cell#Reflections|For example]], if we imagine just 8 point-objects, evenly spaced around the 24-cell at [[24-cell#Reciprocal constructions from 8-cell and 16-cell|the 8 vertices that lie on the 4 coordinate axes]], and rotate them isoclinically along exactly the same orbits they would take in the above-mentioned rotation of a rigid 24-cell, then in the course of a single 360° rotation the 8 point-objects will trace out the whole 24-cell, with just one point-object reaching each of the 24 vertex positions just once, and no point-object colliding with (or even crossing the path of) any other at any time. This is an example of a discrete Hopf fibration. But it is still an example of a rigid object in a discrete isoclinic rotation: a rigid 8-vertex object (called the 4-[[W:orthoplex|orthoplex]] or [[16-cell]]) performing one half of the characteristic rotation of the 24-cell. We can also imagine ''combining'' distinct isoclinic rotations. What happens when multiple point-objects are orbiting at once, but do ''not'' all follow the Clifford parallel paths characteristic of the ''same'' distinct rigid rotation? What happens when we combine orbits from distinct rotations characteristic of different 4-polytopes, for example when different rigid 4-polytopes are concentric and rotating simultaneously in their characteristic ways? What kinds of such hybrid rotations are possible in the same 3-sphere shell without collisions? In adjacent concentric shells without asymmetric imbalance? What sort of [[Kinematics of the cuboctahedron|kinematic polytopes]] do they trace out, and how do their [[24-cell#Clifford parallel polytopes|component parts]] relate to each other as they move? Is there (sometimes) some kind of mutual stability amid their lack of combined rigidity? Visualizing isoclinic rotations (rigid and otherwise) allows us to explore such questions of [[W:kinematics|kinematics]], and where dynamic stabilities arise, of [[wikipedia:kinetics (physics)|kinetics]]. In four dimensions, we discover that space has more room in it than we have experienced, which permits previously unimagined motions. Even 3-space is more commodious than we thought; when it is curved and lies embedded in a higher-dimensional space, it permits previously impossible symmetric packings. Sadoc studied double-twisted 3-dimensional molecules, and imagined them embedded in 4-dimensional space as the Hopf fibrations of regular 4-polytopes. He found that these molecules would close-pack on the 3-sphere perfectly without exhibiting any torsion, although their packing in ordinary flat 3-space is imperfect, "frustrated" by their twisted geometry. <blockquote>The frustration, which arises when the molecular orientation is transported along the two [spiral] AB paths of figure 1 [double twist helix], is imposed by the very topological nature of the Euclidean space R³. It would not occur if the molecules were embedded in the non-Euclidean space of the [[W:3-sphere|3-sphere]] S³, or hypersphere. This space with a homogeneous positive curvature can indeed be described by equidistant and uniformly twisted fibers, along which the molecules can be aligned without any conflict between compactness and [[W:torsion of a curve|torsion]].... The fibres of this [[W:Hopf fibration|Hopf fibration]] are great circles of S³, the whole family of which is also called the [[W:Clifford parallel|Clifford parallel]]s.{{Efn|name=Clifford parallels}} Two of these fibers are C_∞ symmetry axes for the whole fibration; each fibre makes one turn around each axis and regularly rotates when moving from one axis to another.{{Efn|name=helical geodesic}} These fibers build a double twist configuration while staying parallel, i.e. without any frustration, in the whole volume of S³.{{Efn|name=Petrie polygon of a honeycomb}} They can therefore be used as models to study the condensation of long molecules in the presence of a double twist constraint.{{Sfn|Sadoc & Charvolin|2009|loc=§1.2 The curved space approach|ps=; studies the helical orientation of molecules in crystal structures and their imperfect packings ("frustrations") in 3-dimensional space.}}</blockquote> Of course we do not find molecules condensing to close-pack the 3-sphere in our experience, and Sadoc does not say that we do. We find 3-spheres in the atomic realm (if atoms are 4-polytopes), and in the cosmic realm (as the surface boundaries of stars, and the concentric surfaces of galaxies). But in between, in the realm of ordinary experience which includes the molecular realm, ourselves and all the objects we can materially handle or observe up close including the planets, we are confined together by gravity as inertia within a curved 3-dimensional space that is no more than one atom thick in the fourth spatial dimension. That is why in the molecular realm we find only objects that occupy 3-spaces which, though infinitesimally curved in the fourth dimension, are tiny patches on whole 3-spheres of galactic size. So Sadoc's exercise is a thought experiment, like Einstein's gedankenexperiments about railroad embankments and trains moving at nearly the speed of light. It is no less illuminating, despite the symmetry it reveals not having a realization as an actual 3-sphere of actual molecules. And might not something very like it have an actual realization in the atomic realm? We know that atoms have their own complex internal structure, which we are unable to model geometrically in ordinary 3-dimensional space. Suppose such a model is impossible because an atom is actually a 4-polytope occupying a tiny spherical region of 4-dimensional space, and so we only find its constituent particles in close-packed helical orbits on the 3-sphere, in the manner of Sadoc's imaginary twisted molecules, but as real 4-dimensional helices of atomic scale. We would expect to find the atomic orbit of a fundamental particle in some discrete Hopf fibration characteristic of a symmetry group, that is, on the maximally symmetric isoclines of a discrete isoclinic rotation characteristic of some regular 4-polytope and the particle. == A theory of the Euclidean atom == <blockquote>Because quantum physics could be tested without being understood, it allowed humans to see how the universe worked without knowing why.<ref>Sebastian Junger, In My Time of Dying</ref></blockquote> ... == Light and Mass are Reflection and Rotation == The phenomena of light and mass are expressions of reflection symmetries and rotation symmetries, respectively. ... Atoms are 4-polytopes, elementary objects with SO(4) rotational symmetry. Light is .... Motion in space is the propagation of the elementary objects of light and matter in Coxeter congruent transformations by kaleidoscopic self-reflections, like the motion of self-reproducing cellular automata in [[Conway's Game of Life|Conway's game of life]]. ... Light is discrete reflections. Mass is discrete rotations. Both are group actions, expressions of intrinsic symmetries. That is all of physics. === Atoms are 4-polytopes === ... == Relativity in real space of four or more orthogonal dimensions == Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions. General relativity is Galilean relativity in a general space of four or more orthogonal dimensions, e.g. in Euclidean 4-space <math>R^4</math>, spherical 4-space <math>S^4</math>, and any orthogonal 4-manifold. Light is a consequence of symmetry group reflections at quantum scale. Gravity and the other fundamental forces are consequences of rotations, which are consequences of quantum reflections. Light is discrete reflections. Gravity and all forces are discrete rotations. Both are group actions, expressions of intrinsic symmetries. That is all of physics. Every observer may properly see themself as stationary and the universe as an ''n''-sphere with themself at the center. The curvature of these spheres is a function of the rate at which causality evolves, and can be measured by the observer as the speed of light. === Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions === ...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here... Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in three spatial dimensions. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (In general relativity, discussed below, the actual rate of physical processes varies from place to place, and those differences are neither reciprocal nor illusory.) None of these Lorentz effects are beyond geometric explanation or paradoxical. The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, successive Euclidean spaces are dimensionally analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature, is an exact expression of intrinsic symmetries: that is Nother's great discovery. === General relativity is Galilean relativity in a general space of four orthogonal dimensions === ... == Dimensional relativity == Coxeter's kinetic law of <math>n</math>-dimensional congruent Euclidean transformations may be called ''dimensional relativity'', since it captures the theories of special and general relativity entire, and has its roots in dimensional analogy. Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessable by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated. By analogy to the surface of the earth, the bounding surface of a spherical region of <math>n</math>-dimensional Euclidean space is an <math>(n-1)</math>-sphere, a spherical space of one fewer dimensions than the <math>n</math>-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean <math>n</math>-spaces of increasing <math>n</math>, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating <math>n</math>-spaces. By the degree of dimensional analogy of which they are capable, some observers see deeper into <math>n</math>-dimensional space than others. == Polycentric spherical relativity == An intelligent observer equipped with the principle of relativity may perceive the universe from any inertial reference frame, not only from their own proper perspective. We see that every observer may properly view themself as stationary and the universe as an ''n''-sphere with themself at the center observing it, perceptually equidistant from all points on its surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything. This ''polycentric model'' of the universe is a further restatement of the principle of relativity. It is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. It should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849: "The universe is a sphere whose center is wherever there is intelligence."{{Sfn|Thoreau|1849|p=349|ps=; "The universe is a sphere whose center is wherever there is intelligence." [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}} == Revolutions == The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity ''c'', with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may, or may not, all have the same origin in space and time. As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment we dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed us that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a sense related to time, at least, it must be 4-dimensional. In this work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space. Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we now observe them, any more than they lie in the three dimensional hyperplane of local space in which we find everything residing in our solar system. When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us only by virtue of how long it takes their light to reach us. We can measure their distribution around us in 4-space, but that is simply how we choose to measure them, not a finding of how they are actually distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean ''n''-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity <math>c</math>, on more or less divergent paths from each other. But only much closer observation will reveal evidence of whether everything we see lies in the same 4-space, or if it is distributed in five or more dimensions, and how it is moving there. To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity <math>c</math>, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw displacements), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw displacement has ''two'' [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity <math>c</math> in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that each galaxy's own distinct 3-sphere is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to lightspeed long ago, in whatever big bang our atoms emerged from, and have never slowed down since. == Origins of the theory == Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of the geometry of Euclidean 4-space relativity, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] contains the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and did not describe our ordinary 3-space embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.<ref>{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}</ref> He invited us to imagine "A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions", but he was careful to disclaim parenthetically that "The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice." Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal of that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.'' The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified spacetime of four dimensions. Anco and Maghadam found that <small><math>SO(4)</math></small> breaks to ... <small><math>S^3</math></small>... if the energy in the Kepler orbit is negative (an elliptical orbit), and to ... <small><math>H^3</math></small> ... Minkowski spacetime if the energy is positive (a hyperbolic orbit). Because the planets orbit on ellipses in our 3-space, Euclidean 4-space is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the truer model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position of centrality as our exclusive conception of our place in space. ...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others. The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; "Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions."}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.<ref>{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}</ref>}} == Boundaries == <blockquote>Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.<ref>{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}</ref></blockquote> Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? ''What is the nature of the boundary which confines us to just three dimensions?'' We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell. Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined motions and objects. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. A boundary is an explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force. <blockquote>The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three .... In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it. We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed "Dimensional Analogy."<ref>{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}</ref></blockquote> I believe, but I cannot prove, that we live in real space, which is Schläfli's and Coxeter's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover in imagination and then explore physically, each an astonishing new enlightenment.<ref>{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}<blockquote> :We shall not cease from exploration :And the end of all our exploring :Will be to arrive where we started :And know the place for the first time. :Through the unknown, remembered gate :When the last of earth left to discover :Is that which was the beginning; :At the source of the longest river :The voice of the hidden waterfall :And the children in the apple-tree :Not known, because not looked for :But heard, half-heard, in the stillness :Between two waves of the sea. </blockquote></ref> Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. This project is forever beginning anew. Coxeter showed us that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether showed us all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions, in which all objects with mass move ceaselessly at the constant velocity <math>c</math>, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages. <blockquote> ::::::BEECH :Where my imaginary line :Bends square in woods, an iron spine :And pile of real rocks have been founded. :And off this corner in the wild, :Where these are driven in and piled, :One tree, by being deeply wounded, :Has been impressed as Witness Tree :And made commit to memory :My proof of being not unbounded. :Thus truth's established and borne out, :Though circumstanced with dark and doubt— :Though by a world of doubt surrounded. :::::::—''The Moodie Forester''<ref>{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}</ref> </blockquote> == Appendix: Sequence of regular 4-polytopes == {{Regular convex 4-polytopes|wiki=W:|columns=7}} == ... == {{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}} {{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}} {{Efn|The long radius (center to vertex) of the 24-cell is equal to its edge length; thus its long diameter (vertex to opposite vertex) is 2 edge lengths. Only a few uniform polytopes have this property, including the four-dimensional 24-cell and [[W:Tesseract#Radial equilateral symmetry|tesseract]], the three-dimensional [[W:Cuboctahedron#Radial equilateral symmetry|cuboctahedron]], and the two-dimensional [[W:Hexagon#Regular hexagon|hexagon]]. (The cuboctahedron is the equatorial cross section of the 24-cell, and the hexagon is the equatorial cross section of the cuboctahedron.) '''Radially equilateral''' polytopes are those which can be constructed, with their long radii, from equilateral triangles which meet at the center of the polytope, each contributing two radii and an edge.|name=radially equilateral|group=}} {{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as "the convex hull of the neighbouring vertices of a given vertex".{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its "radius" equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}} {{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example: {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0) {{indent|5}}({{spaces|2}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>){{spaces|3}}({{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>) {{indent|5}}(–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>){{spaces|3}}(–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>) {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)<br> is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}} {{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60° rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the "left" is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}} {{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}} {{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; "In mathematics, the path that the (1, 1) knot on the torus traces is also known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two intersecting circles that are the cross-section of a torus by a well-chosen plane cutting it. Picking one such circle and rotating it around the torus axis, the resulting family of circles can be used to rule the torus. By nesting tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the (1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles]."}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}} {{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}} {{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}} {{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}} {{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}} {{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}} {{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}} {{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}} {{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}} {{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90^o bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60^o bend, or as a straight line with one 60^o bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}} {{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; "In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)"}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}} {{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}} {{Efn|Departing from any vertex V₀ in the original great hexagon plane of isoclinic rotation P₀, the first vertex reached V₁ is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P₁. P₁ is inclined to P₀ at a 60° angle.{{Efn|P₀ and P₁ lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V₂ is 120 degrees beyond V₁ along a second {{radic|3}} chord lying in another hexagonal plane P₂ that is Clifford parallel to P₀.{{Efn|P₀ and P₂ are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V₀ and V₂ are ''two'' {{radic|3}} chords apart{{Efn|V₀ and V₂ are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V₀ and V₂ are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P₀ and P₂ are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V₁ lies in both intersecting planes P₁ and P₂, as V₀ lies in both P₀ and P₁. But P₀ and P₂ have ''no'' vertices in common; they do not intersect.) The third vertex reached V₃ is 120 degrees beyond V₂ along a third {{radic|3}} chord lying in another hexagonal plane P₃ that is Clifford parallel to P₁. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V₀ to V₃ is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}} {{Sfn|Mamone, Pileio & Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹₄.}} ==Notes== {{Regular convex 4-polytopes Notelist|wiki=W:}} ==Citations== {{Regular convex 4-polytopes Reflist|wiki=W:}} ==References== {{Refbegin}} * {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}} * {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1}} * {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}} === [[Polyscheme|Polyschemes]] === {{Regular convex 4-polytopes Refs|wiki=W:}} {{Refend}} mrwjahbut50i8ffsuaom5xf57fcd1hl 2823712 2823711 2026-08-20T20:47:54Z Dc.samizdat 2856930 2823712 wikitext text/x-wiki = Real Euclidean four-dimensional space R⁴ = {{align|center|David Brooks Christie}} {{align|center|dc@samizdat.org}} {{align|center|Draft in progress}} {{align|center|June 2023 - August 2026}} <blockquote>'''Abstract:''' The physical universe is properly visualized as a Euclidean space of four orthogonal spatial dimensions. Space itself has a fourth orthogonal dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and our planet are only 3-dimensional objects, but nonetheless we can see in four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.</blockquote> == Summary == We observe that physical space has four perpendicular dimensions, not just three; atoms are [[W:4-polytope|4-polytopes]]; the sun is a 4-ball that is round in four dimensions; everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space; and our entire 3-space manifold is translating through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions. == A theory of the Euclidean cosmos == The physical universe is properly visualized as a [[w:Four-dimensional_space|Euclidean space of four orthogonal spatial dimensions]]. Space itself has a fourth orthogonal dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planets, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. All objects with mass move inertially through Euclidean 4-space at velocity <math>c</math> as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity <math>c</math> is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space. A typical spiral galaxy such as ours is a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our galaxy appear from our viewpoint to be distributed in a cloud of elliptical spirals occupying a flattened ellipsoid region of 3-dimensional space, but they are not so confined: they are distributed within a spherical region of 4-dimensional space. The galaxy's actual shape is spherical, not a flattened ellipsoid, but it is rounder than round can be in our ordinary experience: it occupies a hyperspherical region of space. The concentric spirals of stars that we observe lie on concentric [[W:3-sphere|3-sphere]]s (4-dimensional spheres), not on concentric 2-ellipsoids (3-dimensional elliptical spirals). Our sun and solar system lies on one of those concentric 3-spheres. More generally, orbits are circular in 4-space, and elliptical in the 3-space of their elliptic hyperplane. [[File:Hypersphere.png|thumb|Rotating illustration of the 4-ball galaxy showimg its spirals of star clouds on the surface of concentric 3-spheres, obtained by reverse sterographic projection from 3D images of the galaxy.]] The galaxy as a whole, or more properly its orbital center point, is translating through 4-space at velocity <math>c</math>, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity <math>c</math> in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity <math>c</math>. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the cylinder; their trajectories are screw-displacements, the compound of a simple rotation and a linear translation. The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around a barycentric axis. It is the tremendous inertial force of stars in motion at velocity <math>c</math> that holds the cylinder of motion together. The observed universe as a whole appears to be a 3-sphere expanding radially from a central origin point at velocity <math>c</math>, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. For all observers, the conjectured origin point of the universe corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space (the same point in the same Euclidean 4-space for all observers). The big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured separately, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity <math>c</math>. All objects in our solar system except the sun itself lie within this thinest three-dimensional manifold. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. The enclosing surface of a spherical region of 4-space is itself a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. We live within such a 3-space, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience, and it contains the earth, all the planets and the 3-dimensional space between them. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our particular 3-sphere is one of the galaxy's concentric 3-spheres of spiral star-clouds. The solar system occupies a tiny patch of this filmy 4-dimensional soap-bubble of galactic size, that is thicker-skinned than the diameter of an atom only in the interior of stars and supermassive objects. Our entire 3-sphere manifold, as a 3-spherical shell within the moving 4-ball galaxy, is translating through 4-space at velocity <math>c</math> with the galaxy, in a distinct direction that is orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the galaxy's translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of rotating objects through Euclidean space by screw translation. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity <math>c</math>, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. Any moving 3-dimensional manifold that is such an evolving surface boundary is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. Every object which we find occurring naturally in the solar system other than the sun itself, even the largest of 3-dimensional objects a planet, is a three-dimensional smear of atoms no thicker than one atom in its fourth dimension, which is the direction of its linear translation through 4-space at velocity <math>c</math>. The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be "heaped up" into larger 4-dimensional objects that form a lump in its moving surface. We have little understanding of such 4-dimensional lumps thicker than one atom, since they occur naturally in our vicinity only in the interior of the sun. In fact the sun is the only such lump occurring naturally in our solar system. We refer to 4-dimensional lumps of matter as plasma, and have little experimental knowledge of their geometry or internal structure. We know that such a lump as the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know nothing about its interior 4-ball. Every such moving 3-dimensional surface boundary of matter in the observed universe is evolving in four dimensions at velocity <math>c</math>. Its current location in 4-space corr esponds to the present moment in the proper time of its inertial reference frame. Its direction of movement at velocity <math>c</math> corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from atoms to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, two orthogonal inertial motions each at the constant universal rate of transformation <math>c</math>. Every object moves relative to universal 4-coordinate space on its own distinct geodesic spiral, a screw translation trajectory that is the compound of two orthogonal inertial motions, a rotation and a translation. Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity <math>c</math> in all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is <math>c\prime = 2c</math>, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity <math>c</math>. For example, we can look across the center of our mostly-empty 4-ball galaxy and see stars in the opposite sides of its concentric 3-sphere surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math> in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper space. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space. == Symmetries == It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel & Goodman-Strauss|2008}} As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. [[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}} <blockquote>Let <small><math>\mathrm{Q}</math></small> denote a rotation, <small><math>\mathrm{R}</math></small> a reflection, <small><math>\mathrm{T}</math></small> a translation, and let <small><math>\mathrm{Q}^q \mathrm{R}^r\mathrm{T}</math></small> denote a product of several such transformations, all commutative with one another. Then <small><math>\mathrm{RT}</math></small> is a glide-reflection (in two or three dimensions), <small><math>\mathrm{QR}</math></small> is a rotary-reflection, <small><math>\mathrm{QT}</math></small> is a screw-displacement, and <small><math>\mathrm{Q^2}</math></small> is a double rotation (in four dimensions).<br> Every orthogonal transformation is expressible as:<br> :<small><math>\mathrm{Q}^q \mathrm{R}^r</math></small><br> where <small><math>(2^q + r \le n)</math></small>, the number of dimensions.<br> Transformations involving a translation are expressible as:<br> :<small><math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}</math></small><br> where <small><math>(2^q + r + 1 \le n)</math></small>.<br> For <small><math>(n = 4)</math></small> in particular, every displacement is either a double rotation <small><math>\mathrm{Q}^2</math></small>, or a screw-displacement <small><math>\mathrm{QT}</math></small> [where the rotation component <small><math>\mathrm{Q}</math></small> is a simple rotation, but the <small><math>\mathrm{QT}</math></small> is chiral like a <small><math>\mathrm{Q^2}</math></small>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <small><math>\mathrm{QRT}</math></small>.</blockquote> If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a <small><math>\mathrm{Q^2}</math></small> or a <small><math>\mathrm{QT}</math></small>, because we can view any <small><math>\mathrm{QT}</math></small> as a <small><math>\mathrm{Q^2}</math></small> in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a <small><math>\mathrm{Q^2}</math></small>. By the same principle, we can view any <small><math>\mathrm{QT}</math></small> or <small><math>\mathrm{Q^2}</math></small> as an isoclinic (equi-angled) <small><math>\mathrm{Q^2}</math></small> by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (<small><math>\mathrm{T}</math></small>) for ''one'' of the two rotations (<small><math>\mathrm{Q}</math></small>). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (<small><math>\mathrm{Q}</math></small>) up to uncertainty, and can always distinguish the direction of their own proper time translation (<small><math>\mathrm{T}</math></small>). As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebra), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group <small><math>SO(4)</math></small> [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic <small><math>SO(4)</math></small> rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, stationary atoms exhibit the <small><math>SO(4)</math></small> symmetries of the discrete isoclinic (equi-angled) double rotations (<small><math>\mathrm{Q^2}</math></small>) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]]. == Special relativity describes Euclidean 4-space == <blockquote>Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.<ref>{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}</ref></blockquote> Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional "space" because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign to the three space coordinates so spacetime is hyperbolic, not a flat Euclidean 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was first described by Einstein himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction. Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity ''c'', in some 4-space direction. This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always ''c'', as measured by all observers from any inertial reference frame. This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source. But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity ''c''. In physics as it has been universally understood, observers are not supposed to be able to move at velocity ''c''. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four. In the Euclidean relativity alternative view, however, every observer is always moving at velocity ''c'' through the universe, which is real Euclidean 4-dimensional space <small><math>\mathbb{R^4}</math></small>. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity ''c''. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and proper space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity ''c'', in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space <small><math>\mathbb{R^4}</math></small>.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity ''c'' relative to universal 4-coordinate space, so the maximum relative velocity between two observers is 2''c'' when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to ''c'', it is the same measurement in different units. Special relativity measures all velocities in a 3-space of Minkowski spacetime. Euclidean relativity measures all velocities in Euclidean 4-space.}} So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity ''c'' in Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the "speed of light" ''c'', although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity ''c'', but in at least slightly different directions. In Einstein's relativity, the invariant ''c'' is the speed of light through 3-space. In Euclidean relativity, the invariant ''c'' is the speed of matter through 4-space! The speed of light through 3-space is also perceived as ''c'' by all observers, because they are each living in a moving 3-manifold that is moving through 4-space at velocity ''c''. Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same predictions about how observers in different reference frames will perceive each other's motions in time and space, and we shall see that they also agree on the predictions of general relativity. They both describe the same geometric relations of space and time, but they describe that geometry as embedded in two very different universal host spaces: Minkowski spacetime versus Euclidean 4-space. ...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity <math>c</math> through space and proper time ...cite Yamashita{{Sfn|Yamashita|2023}} on the equivalence of special relativity and Euclidean 4-space relativity ...cite Kappraff & Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff & Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff & Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords. Euclidean relativity is not even a fringe theory; no physicists have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could "catch up" with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at ''c'' (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than ''c''. Euclidean relativity is a revolutionary theory indeed, in which ''c'' cannot possibly be the speed of light! We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for <math>\mathbb{R^4}</math> to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be <math>c\prime = 2c</math>, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate linearly along the edge of a unit 4-hypercube. This is conceivable in 4-space (and in no other Euclidean space of any dimensionality) because the diagonal of the unit 4-hypercube is the natural number <small><math>\sqrt{4}</math></small>. == An object's motion in space is the product of its discrete self-reflections == Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a small number of discrete self-reflections. Any action of a geometric object that transforms its position and orientation in space may be measured as a distinct group of self-reflections of the object in its own surfaces. Any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete set of local self-reflections. Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which touch (intersect each other). When a object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality. Coxeter's laws of motion are a geometric counterpart to Newton's laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures. But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. For example, they give us geometric pictures of all the possible motions of objects in four dimensional Euclidean space: <blockquote>Every orthogonal transformation in 4-space is expressible as:<br> :<small><math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t</math></small><br> where <small><math>(2^q + r + t \le 4)</math></small>. Every displacement is either a double rotation <small><math>\mathrm{Q}^2</math></small>, or a screw-displacement <small><math>\mathrm{QT}</math></small> [where the rotation component <small><math>\mathrm{Q}</math></small> is a simple rotation, but the <small><math>\mathrm{QT}</math></small> is chiral like a <small><math>\mathrm{Q^2}</math></small>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <small><math>\mathrm{QRT}</math></small>.</blockquote> While this description should be understood as simple geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (<small><math>\mathrm{Q}</math></small>), reflection (<small><math>\mathrm{R}</math></small>) and translation (<small><math>\mathrm{T}</math></small>) are just what they are in three-dimensional space, but double rotation (<small><math>\mathrm{Q}^2</math></small>) is something new and unprecedented in our physical experience, because double rotations cannot occur until you have four or more dimensions of space to rotate in. ...to readers who have not studied Coxeter (almost all readers including TAC), the blockquote above is "just math", not visualizable geometry...but I could describe Coxeter's congruent transformations in 4-space here geometrically: I could say clearly what they mean in spatial terms, in language anyone can understand, because they don't require any math to be understood; the "math" here is really just simple pictures (reflections and rotations); even double rotations can be visualized by dimensional analogy, as compounds of simple rotations...since even most physicists are unacquainted with Coxeter geometry, it might be useful to do this here... == Light propagates through 4-space at twice its apparent velocity ''c''== Coxeter's geometric laws of motion apply to all objects with mass in 4-dimensional Euclidean space, but we find there is an additional kind of displacement which applies only to massless particles such as photons. Light quanta (photons) translate through 4-space by 4-dimensional reflection <small><math>\mathrm{R}^4</math></small>, which may be termed a double translation <small><math>\mathrm{T}^2</math></small>, a pure translation via two pairs of parallel reflections, without any rotation component <small><math>\mathrm{Q}</math></small>. Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by <small><math>\mathrm{QT}</math></small>, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic <small><math>\mathrm{Q^2}</math></small>, an isoclinically rotating object such as an atom. A simple rotation <small><math>\mathrm{Q}</math></small> or simple translation <small><math>\mathrm{T}</math></small> is a double reflection <small><math>\mathrm{R^2}</math></small>, so a <small><math>\mathrm{QT}</math></small> or <small><math>\mathrm{Q^2}</math></small> is also an <small><math>\mathrm{R^4}</math></small>, but not with the same group of reflection angles as a light signal <small><math>\mathrm{R^4}</math></small>. A translation <small><math>\mathrm{T = R^2}</math></small> is a double reflection in two parallel planes, and a rotation <small><math>\mathrm{Q = R^2}</math></small> is a double reflection in two intersecting planes, as in a <small><math>\mathrm{QT = R^4}</math></small> which is both at once. A double translation <small><math>\mathrm{T^2 = R^4}</math></small> is two double reflections in pairs of parallel planes at once, a reflection in four or more non-intersecting parallel planes; it is all translation and no rotation. In a <small><math>\mathrm{T^2}</math></small> all the motion goes to translation, so the translation goes twice as far as the simple translation <small><math>\mathrm{T}</math></small> in a <small><math>\mathrm{QT}</math></small>. A double translation <small><math>\mathrm{T^2 = R^4}</math></small> is the opposite of a double rotation <small><math>\mathrm{Q^2 = R^4}</math></small>, which is stationary but rotates twice as fast as the simple rotation <small><math>\mathrm{Q}</math></small> in a <small><math>\mathrm{QT}</math></small>. The product of the two translations in a <small><math>\mathrm{T^2}</math></small> is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple <small><math>\mathrm{T}</math></small> over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double-the-distance translation, but without any rotation component, so it cannot carry any mass with it. A <small><math>\mathrm{T^2}</math></small> cannot reposition a 4-polytope the way a <small><math>\mathrm{QT}</math></small> does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter. ...lensing of double translations <small><math>\mathrm{T^2 = R^4}</math></small> in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet... == The Kepler problem is framed in Euclidean 4-space == The [[W:Kepler problem|Kepler problem]] is named for [[W:Johannes Kepler|Johannes Kepler]], arguably the greatest geometer since the ancients up to [[w:Ludwig Schläfli|Ludwig Schläfli]], who proposed [[W:Kepler's laws of planetary motion|Kepler's laws of planetary motion]] which solved the problem of the orbits of the planets, and investigated the types of forces that would result in orbits obeying those laws. Those forces were later identified by [[W:Isaac Newton|Isaac Newton]] in his[[W:Philosophiæ Naturalis Principia Mathematica| Principia]], where he proves what today might be called the "inverse Kepler problem": the orbit characteristics require the force to depend on the inverse square of the distance.<ref>{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton & Company|isbn=978-0393039184}}</ref> The inverse square law behind the Kepler problem is the [[W:Central force|central force]] law which governs not only [[W:Newtonian gravity|Newtonian gravity]] and celestial orbits, but also the motion of two charged particles in [[W:Coulomb’s law|Coulomb’s law]] of [[W:Electrostatics|electrostatics]]; it applies to attractive or repulsive forces. Problems in which two bodies interact by a central force that varies as the [[W:Inverse square law|inverse square]] of the distance between them are called Kepler problems. Thus the [[W:Hydrogen atom|hydrogen atom]] is a Kepler problem, since it comprises two charged particles interacting by Coulomb's law, another inverse-square central force. Using classical mechanics, the solution to a Kepler problem can be expressed as a [[W:Kepler orbit|Kepler orbit]] using six kinematical variables or [[W:Orbital elements|orbital elements]]. The solution conserves an orbital element called the [[W:Laplace–Runge–Lenz vector|Laplace–Runge–Lenz (LRL) vector]], a [[W:Constant of motion|constant of motion]], meaning that it is the same no matter where it is calculated on the orbit. The LRL vector was essential in the first quantum mechanical derivation of the [[W:Atomic emission spectrum|spectrum]] of the hydrogen atom, but this approach has rarely been used since the development of the [[W:Schrödinger equation|Schrödinger equation]]. The conservation of the LRL vector corresponds to the <small><math>SO(4)</math></small> symmetry, by Nother's theorem. The LRL vector lies orthogonal to both the orbital plane and the angular momentum vector of the Kepler orbit; we observe that it lies in a fourth orthogonal dimension. Fock in 1935<ref>V. Fock, Zur Theorie des Wasserstoffatoms, Zeitschrift für Physik. 98 (3-4) (1935), 145–154.</ref> and Moser in 1970<ref>J. Moser, Regularization of Kepler’s problem and the averaging method on a manifold, Commun. Pure Appl. 23 (1970), 609–636</ref> observed that the Kepler problem is mathematically equivalent to non-affine geodesic motion (a particle moving freely) on the surface of a 3-sphere, so that the whole problem is symmetric under certain rotations of the four-dimensional space. This higher-dimensional symmetry results in two well-known properties of the Kepler problem: the momentum vector always moves in a perfect circle and, for a given total energy, all such velocity circles intersect each other in the same two points. ... Relativity establishes that an orbit in space is viewed in a different way in each distinct inertial reference frame. Depending on the choice of reference frame, the same Kepler system may be seen to be performing any one of a sequence of relativistically equivalent rotations in 4-space, on a continuum from an isoclinic rotation (Q²) in the orbit's proper reference frame, to a screw transfer (QT) with a simple rotation component (Q) and a translation component (T) at velocity <math>c</math>, in the universal reference frame of 4-coordinate space wherein every object is seen to be translating at velocity <math>c</math>. In reference frames between these two limit cases, the orbit is seen to be performing a double rotation (Q²) at two unequal, completely orthogonal angular rates of rotation: an elliptical double rotation. These include the reference frames of most typical observers, who are moving slowly relative to the observed orbital system's reference frame (their relative motion is a small fraction of the speed of light). ...this is probably misplaced here and should not interrupt the discussion at this point: ...These typical observations agree closely with the predictions of special relativity, because the non-isoclinic elliptical (Q²) resembles a (QT), since one of its two completely orthogonal rotations (Q) has such a long period that it is almost indistinguishable from a straight translation (T). All orbits in 4-space are isoclinic in their own reference frame. Orbiting objects in their own proper Kepler systems follow circular geodesic isoclines through 4-space. Orbits in 4-space are perfectly circular in their own reference frame, as Copernicus assumed the orbits of planets to be. It is the orbit's path through the 3-space of its elliptic hyperplane that is an ellipse, as Kepler found it to be. ...cite Jesper Goransson's very concise paper The geodesic circle that an orbiting object follows through 4-space in the proper reference frame of its own Kepler system is not a simple great circle which turns in two orthogonal dimensions. It is a helical great circle that turns in four orthogonal dimensions at once.{{Efn|Geodesic orbits in 4-space are not simple 2-dimensional great circles; they are helical 4-dimensional great circles that curve in all four dimensions at once. Their circular trajectories are helixes which we call ''isoclines'', since they are the paths taken by points on a rigid object undergoing isoclinic rotation.}} Such circles lie outside our physical experience, since our local space has only three orthogonal dimensions. Nonetheless we can visualize them in imagination, because their helical, circular shape is perfectly well defined by the kinematical variables of the Kepler orbit. The real physical correlates of abstract orthogonal planes and rotation angles are already familiar to us viscerally in our body-language of physical experience, since we are endowed biologically with highly evolved visual signal processing engines. These enable us to see and understand spatial relations and motions, including rotations, without even thinking about angles and orthogonal planes. This physical endowment is an inborn capacity for dimensional analogy which our biologic evolution has provided. All our instinctive spatial reasoning is by dimensional analogy from flat 2-dimensional retinal images to 3-dimensional scenes, using our powerful inborn visualization capacities of reverse stereographic projection and pattern recognition. We humans are thus very well equipped with everything we need to see in four-dimensional space, except experience. ... Recently Anco and Moghadam found that through Noether’s theorem in reverse, the LRL vector gives rise to a corresponding infinitesimal dynamical symmetry on the kinematical variables, which they show to be the semi-direct product of <small><math>SO(3)</math></small> and <small><math>\mathbb{R^3}</math></small>, in contrast to the <small><math>SO(4)</math></small> symmetry group generated by the LRL symmetries and the rotations.{{Sfn|Anco|Moghadam|2026|ps=; The physically relevant part of the LRL vector is its direction ... since its magnitude is just a function of energy and angular momentum.}} This remarkable symmetry breaking is expressive of the ''dimensional relativity'' between ordinary 3-space <small><math>\mathbb{R^3}</math></small>, spherical space <small><math>S^3</math></small> and Euclidean space <small><math>\mathbb{R^4}</math></small>. Consider a hydrogen atom in a Kepler orbit: for example, a hydrogen atom moving freely in space in an orbit around the sun. It is a ''double'' Kepler problem: an electrostatic Kepler problem within itself, and a gravitational Kepler problem in its environment. The ''single'' electrostatic Kepler problem of a hydrogen atom moving freely in space beyond any gravitational influence is a problem in special relativity. In our Euclidean 4-space model, this atom viewed as stationary in its own proper reference frame exhibits an <small><math>SO(4)</math></small> rotation symmetry corresponding to an isoclinic double rotation (<small><math>\mathrm{Q^2}</math></small>). The fourth dimension in this reference frame is the atom's proper time vector; it has constant velocity <math>c</math> and constant direction. From the point of view of our universal 4-coordinate space (which cannot be the proper inertial reference frame of any physical observer, all of whom are moving relative to it at velocity ''c''), the entire Kepler system (the atom) is translating through 4-space via a screw translation (<small><math>\mathrm{QT}</math></small>) at constant velocity <math>c</math>. From this viewpoint the atom has only a simple <small><math>SO(3)</math></small> rotation component (<small><math>\mathrm{Q}</math></small>), breaking its stationary <small><math>SO(4)</math></small> isoclinic rotation symmetry (<small><math>\mathrm{Q^2}</math></small>). Because each discrete part of the rotating atom moves along a helical trajectory through 4-space, the atom is in orbit around a barycentric axis (like a star in a galaxy), but only in a tiny orbit within its own radius, which is its inertial domain of rotation. The straight 4-dimensional cylinder it progresses along at velocity <math>c</math> is very narrow: only the diameter of the rotating atom itself. The gravitational Kepler problem of a hydrogen atom in a Kepler orbit around the sun is a problem in general relativity. In our 4-space model, this atom viewed in its own proper reference frame exhibits the same <small><math>SO(4)</math></small> rotation symmetry as it did in the electrostatic Kepler problem where the atom was translating linearly through space. The Kepler system in this case is not just the atom; it is the entire solar system. The LRL vector of this Kepler system is the proper time vector of the atom's inertial reference frame; once again it has constant velocity ''and constant direction''. Although the momentum vector moves in a perfect circle as the atom orbits the sun, the 4-space LRL vector does not move at all: it is a constant of motion, of linear motion (<small><math>\mathrm{T}</math></small>) of the Kepler system (the entire solar system in this case) in a constant 4-space direction, the proper time direction of the system. The direction of the system's proper time vector would vary under some kinds of acceleration of the atom, but it is constant under this kind of orbital acceleration. It continues to point in the same direction, like a 4-space compass needle, as the atom winds its way along its spiral path around the axis of the sun's straight-line translation through 4-space at velocity <math>c</math>. This compass needle always points in the direction the sun is moving, not the direction the atom is moving at any instant. ...Its Kepler orbit around the sun is its <small><math>SO(3)</math></small> rotation component (<small><math>\mathrm{Q}</math></small>). Although the atom is moving on a geodesic circle in the second problem, by the [[equivalence principle]] the difference in the state of the atomic systems in these two problems cannot be observed by examining the atoms alone. Even from another inertial reference frame, where the atom in the second problem is seen to be translating through 4-space via a wide screw translation (<small><math>\mathrm{QT}</math></small>) around the sun's axis of motion, there is still no difference between the two problems which can be detected by examining only the atoms within their own proper reference frames (even over time), because the LRL vector (<small><math>\mathrm{T}</math></small>) is a constant of motion of the entire system in both cases. ...Anco and Maghadam found that <small><math>SO(4)</math></small>) breaks to ... <small><math>S^3</math></small>)... if the energy in the Kepler orbit is negative (an elliptical orbit), and to ... <small><math>H^3</math></small>) ... Minkowski spacetime if the energy is positive (a hyperbolic orbit). ... Finally we consider a third problem in which a hydrogen atom enters the solar system as a comet, loops around the sun and exits the solar system again. This atom... ... As Hamilton found when he discovered the quaternions, we see that it is necessary to admit a fourth dimension to the system in order to properly model the problem: in Hamilton's case the general problem of ..., and in our case the Kepler problem. These are instances of the same problem in 4-dimensional Euclidean geometry, and indeed a solution to the Kepler problem in quaternions (the four Cartesian coordinates of Euclidean 4-space) is a solution to it in our model of the 4-coordinate Euclidean cosmos. == Distribution of stars in our galaxy == The stars in our own galaxy appear to us to be a rotating spiral cluster in 3-dimensional space. By assuming that light from them reaches us on straight lines through space, by assuming that we can measure their distance from us by its red shift, and by assuming that they are distributed in three dimensions of space, we have plotted their locations in 3-space. If we abandon the last of those three assumptions, we can just as easily reinterpret that dataset to plot their distribution around us in 4-dimensional space, and see how they actually lie. When we perform this experiment on the data for the stars in our galaxy, do we indeed find that they are distributed non-uniformly in various concentric spirals, but the spirals lie on the surface of various 3-spheres, rather than in elliptical orbits as we saw them in 3-space? That would be an expected consequence of the special rotational symmetry group of 4-space <small><math>SO(4)</math></small>, in which circular (isoclinic) orbits are the geodesics (shortest rotational paths) rather than elliptical (non-equi-angled double rotation) orbits. ...have to perform this experiment somehow, at least as a conclusive thought experiment, before I publish this paper... == Rotations == The [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotations]] of the convex [[W:regular 4-polytope|regular 4-polytope]]s are usually described as discrete rotations of a rigid object. For example, the rigid [[24-cell]] can rotate in a [[24-cell#Great hexagons|hexagonal]] (6-vertex) central [[24-cell#Planes of rotation|plane of rotation]]. A 4-dimensional [[24-cell#Isoclinic rotations|''isoclinic'' rotation]] (as distinct from a [[24-cell#Simple rotations|''simple'' rotation]] like the ones that occur in 3-dimensional space) is a ''diagonal'' rotation in multiple [[W:Clifford parallel|Clifford parallel]] [[24-cell#Geodesics|central planes]] of rotation at once. It is diagonal because it is a [[W:SO(4)#Double rotations|double rotation]]: in addition to rotating in parallel (like wheels), the multiple planes of rotation also tilt sideways in the completely orthogonal plane of rotation (like coins flipping) into each other's planes. Consequently, the path taken by each vertex is a [[24-cell#Helical hexagrams and their isoclines|twisted helical circle]], rather than the ordinary flat great circle a vertex follows in a simple rotation. In a rigid 4-polytope rotating isoclinically, ''all'' the vertices lie in one of the parallel planes of rotation, so all the vertices move in parallel along Clifford parallel twisting circular paths. [[24-cell#Clifford parallel polytopes|Clifford parallel planes]] are not parallel in the normal sense of parallel planes in three dimensions; the vertices are all moving in different directions around the [[W:3-sphere|3-sphere]]. In one complete 360° isoclinic revolution, a rigid 4-polytope turns itself inside out. This is sufficiently different from the simple rotations of rigid bodies in our 3-dimensional experience that a [[24-cell#Rotations|detailed description]] enabling the reader to properly visualize its counter-intuitive consequences runs to many pages and illustrations, with many accompanying pages of explanatory notes on surprising phenomena that arise in 4-dimensional space: [[24-cell#Great squares|completely orthogonal planes]], [[24-cell#Clifford parallel polytopes|Clifford parallelism]]{{Efn|name=Clifford parallels}} and [[W:Hopf fibration|Hopf fiber bundles]], [[24-cell#Isoclinic rotations|isoclinic geodesic paths]], and [[24-cell#Double rotations|chiral (mirror image) pairs of rotations]], among other complexities. Moreover, the characteristic rotations of the various regular 4-polytopes are all different; each is a unique surprise. [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|The 6 regular convex 4-polytopes]] have different numbers of vertices (5, 8, 16, 24, 120 and 600 respectively) and those with fewer vertices occur inscribed in those with more vertices (with one exception), with the result that the more complex 4-polytopes subsume the kinds of rotations characteristic of their less complex predecessors, as well as each having a characteristic kind of rotation not found in their predecessors. None of these symmetries is to be found in 3-dimensional space, although their simpler 3-dimensional analogues are all present there. [[W:Euclidean geometry#Higher dimensions|Four dimensional Euclidean space]] is more complicated (and more interesting) than three dimensional space because there is more room in it, in which unprecedented things can happen. It subsumes 3-dimensional space, with all of the symmetries we are accustomed to, and adds astonishing new surprises. These are hard for us to visualize, because the only way we can experience them is in our imagination; we have no body of sensory experience in 4-dimensional space to draw upon, other than our evolution in time. For that reason (our difficulty in visualizing them), descriptions of isoclinic rotations usually begin and end with rigid rotations: [[24-cell#Isoclinic rotations|for example]], all 24 vertices of a single rigid 24-cell rotating in unison, with 6 vertices evenly spaced around each of 4 Clifford parallel twisted circles.{{Efn|name=360 degree geodesic path visiting 3 hexagonal planes}} But that is only the simplest case, which is easiest for us to understand. Compound and [[W:Kinematics|kinematic]] 24-cells (with moving parts) are even more interesting (and more complicated) than the rotation of a single rigid 24-cell. To begin with, when we examine the individual parts of a single rigid 24-cell that are moving in an isoclinic rotation, such as the orbits of individual vertices, we can imagine a case where fewer than 24 point-objects are orbiting on those twisted circular paths at once. [[24-cell#Reflections|For example]], if we imagine just 8 point-objects, evenly spaced around the 24-cell at [[24-cell#Reciprocal constructions from 8-cell and 16-cell|the 8 vertices that lie on the 4 coordinate axes]], and rotate them isoclinically along exactly the same orbits they would take in the above-mentioned rotation of a rigid 24-cell, then in the course of a single 360° rotation the 8 point-objects will trace out the whole 24-cell, with just one point-object reaching each of the 24 vertex positions just once, and no point-object colliding with (or even crossing the path of) any other at any time. This is an example of a discrete Hopf fibration. But it is still an example of a rigid object in a discrete isoclinic rotation: a rigid 8-vertex object (called the 4-[[W:orthoplex|orthoplex]] or [[16-cell]]) performing one half of the characteristic rotation of the 24-cell. We can also imagine ''combining'' distinct isoclinic rotations. What happens when multiple point-objects are orbiting at once, but do ''not'' all follow the Clifford parallel paths characteristic of the ''same'' distinct rigid rotation? What happens when we combine orbits from distinct rotations characteristic of different 4-polytopes, for example when different rigid 4-polytopes are concentric and rotating simultaneously in their characteristic ways? What kinds of such hybrid rotations are possible in the same 3-sphere shell without collisions? In adjacent concentric shells without asymmetric imbalance? What sort of [[Kinematics of the cuboctahedron|kinematic polytopes]] do they trace out, and how do their [[24-cell#Clifford parallel polytopes|component parts]] relate to each other as they move? Is there (sometimes) some kind of mutual stability amid their lack of combined rigidity? Visualizing isoclinic rotations (rigid and otherwise) allows us to explore such questions of [[W:kinematics|kinematics]], and where dynamic stabilities arise, of [[wikipedia:kinetics (physics)|kinetics]]. In four dimensions, we discover that space has more room in it than we have experienced, which permits previously unimagined motions. Even 3-space is more commodious than we thought; when it is curved and lies embedded in a higher-dimensional space, it permits previously impossible symmetric packings. Sadoc studied double-twisted 3-dimensional molecules, and imagined them embedded in 4-dimensional space as the Hopf fibrations of regular 4-polytopes. He found that these molecules would close-pack on the 3-sphere perfectly without exhibiting any torsion, although their packing in ordinary flat 3-space is imperfect, "frustrated" by their twisted geometry. <blockquote>The frustration, which arises when the molecular orientation is transported along the two [spiral] AB paths of figure 1 [double twist helix], is imposed by the very topological nature of the Euclidean space R³. It would not occur if the molecules were embedded in the non-Euclidean space of the [[W:3-sphere|3-sphere]] S³, or hypersphere. This space with a homogeneous positive curvature can indeed be described by equidistant and uniformly twisted fibers, along which the molecules can be aligned without any conflict between compactness and [[W:torsion of a curve|torsion]].... The fibres of this [[W:Hopf fibration|Hopf fibration]] are great circles of S³, the whole family of which is also called the [[W:Clifford parallel|Clifford parallel]]s.{{Efn|name=Clifford parallels}} Two of these fibers are C_∞ symmetry axes for the whole fibration; each fibre makes one turn around each axis and regularly rotates when moving from one axis to another.{{Efn|name=helical geodesic}} These fibers build a double twist configuration while staying parallel, i.e. without any frustration, in the whole volume of S³.{{Efn|name=Petrie polygon of a honeycomb}} They can therefore be used as models to study the condensation of long molecules in the presence of a double twist constraint.{{Sfn|Sadoc & Charvolin|2009|loc=§1.2 The curved space approach|ps=; studies the helical orientation of molecules in crystal structures and their imperfect packings ("frustrations") in 3-dimensional space.}}</blockquote> Of course we do not find molecules condensing to close-pack the 3-sphere in our experience, and Sadoc does not say that we do. We find 3-spheres in the atomic realm (if atoms are 4-polytopes), and in the cosmic realm (as the surface boundaries of stars, and the concentric surfaces of galaxies). But in between, in the realm of ordinary experience which includes the molecular realm, ourselves and all the objects we can materially handle or observe up close including the planets, we are confined together by gravity as inertia within a curved 3-dimensional space that is no more than one atom thick in the fourth spatial dimension. That is why in the molecular realm we find only objects that occupy 3-spaces which, though infinitesimally curved in the fourth dimension, are tiny patches on whole 3-spheres of galactic size. So Sadoc's exercise is a thought experiment, like Einstein's gedankenexperiments about railroad embankments and trains moving at nearly the speed of light. It is no less illuminating, despite the symmetry it reveals not having a realization as an actual 3-sphere of actual molecules. And might not something very like it have an actual realization in the atomic realm? We know that atoms have their own complex internal structure, which we are unable to model geometrically in ordinary 3-dimensional space. Suppose such a model is impossible because an atom is actually a 4-polytope occupying a tiny spherical region of 4-dimensional space, and so we only find its constituent particles in close-packed helical orbits on the 3-sphere, in the manner of Sadoc's imaginary twisted molecules, but as real 4-dimensional helices of atomic scale. We would expect to find the atomic orbit of a fundamental particle in some discrete Hopf fibration characteristic of a symmetry group, that is, on the maximally symmetric isoclines of a discrete isoclinic rotation characteristic of some regular 4-polytope and the particle. == A theory of the Euclidean atom == <blockquote>Because quantum physics could be tested without being understood, it allowed humans to see how the universe worked without knowing why.<ref>Sebastian Junger, In My Time of Dying</ref></blockquote> ... == Light and Mass are Reflection and Rotation == The phenomena of light and mass are expressions of reflection symmetries and rotation symmetries, respectively. ... Atoms are 4-polytopes, elementary objects with SO(4) rotational symmetry. Light is .... Motion in space is the propagation of the elementary objects of light and matter in Coxeter congruent transformations by kaleidoscopic self-reflections, like the motion of self-reproducing cellular automata in [[Conway's Game of Life|Conway's game of life]]. ... Light is discrete reflections. Mass is discrete rotations. Both are group actions, expressions of intrinsic symmetries. That is all of physics. === Atoms are 4-polytopes === ... == Relativity in real space of four or more orthogonal dimensions == Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions. General relativity is Galilean relativity in a general space of four or more orthogonal dimensions, e.g. in Euclidean 4-space <math>R^4</math>, spherical 4-space <math>S^4</math>, and any orthogonal 4-manifold. Light is a consequence of symmetry group reflections at quantum scale. Gravity and the other fundamental forces are consequences of rotations, which are consequences of quantum reflections. Light is discrete reflections. Gravity and all forces are discrete rotations. Both are group actions, expressions of intrinsic symmetries. That is all of physics. Every observer may properly see themself as stationary and the universe as an ''n''-sphere with themself at the center. The curvature of these spheres is a function of the rate at which causality evolves, and can be measured by the observer as the speed of light. === Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions === ...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here... Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in three spatial dimensions. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (In general relativity, discussed below, the actual rate of physical processes varies from place to place, and those differences are neither reciprocal nor illusory.) None of these Lorentz effects are beyond geometric explanation or paradoxical. The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, successive Euclidean spaces are dimensionally analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature, is an exact expression of intrinsic symmetries: that is Nother's great discovery. === General relativity is Galilean relativity in a general space of four orthogonal dimensions === ... == Dimensional relativity == Coxeter's kinetic law of <math>n</math>-dimensional congruent Euclidean transformations may be called ''dimensional relativity'', since it captures the theories of special and general relativity entire, and has its roots in dimensional analogy. Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessable by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated. By analogy to the surface of the earth, the bounding surface of a spherical region of <math>n</math>-dimensional Euclidean space is an <math>(n-1)</math>-sphere, a spherical space of one fewer dimensions than the <math>n</math>-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean <math>n</math>-spaces of increasing <math>n</math>, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating <math>n</math>-spaces. By the degree of dimensional analogy of which they are capable, some observers see deeper into <math>n</math>-dimensional space than others. == Polycentric spherical relativity == An intelligent observer equipped with the principle of relativity may perceive the universe from any inertial reference frame, not only from their own proper perspective. We see that every observer may properly view themself as stationary and the universe as an ''n''-sphere with themself at the center observing it, perceptually equidistant from all points on its surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything. This ''polycentric model'' of the universe is a further restatement of the principle of relativity. It is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. It should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849: "The universe is a sphere whose center is wherever there is intelligence."{{Sfn|Thoreau|1849|p=349|ps=; "The universe is a sphere whose center is wherever there is intelligence." [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}} == Revolutions == The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity ''c'', with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may, or may not, all have the same origin in space and time. As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment we dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed us that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a sense related to time, at least, it must be 4-dimensional. In this work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space. Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we now observe them, any more than they lie in the three dimensional hyperplane of local space in which we find everything residing in our solar system. When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us only by virtue of how long it takes their light to reach us. We can measure their distribution around us in 4-space, but that is simply how we choose to measure them, not a finding of how they are actually distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean ''n''-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity <math>c</math>, on more or less divergent paths from each other. But only much closer observation will reveal evidence of whether everything we see lies in the same 4-space, or if it is distributed in five or more dimensions, and how it is moving there. To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity <math>c</math>, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw displacements), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw displacement has ''two'' [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity <math>c</math> in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that each galaxy's own distinct 3-sphere is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to lightspeed long ago, in whatever big bang our atoms emerged from, and have never slowed down since. == Origins of the theory == Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of the geometry of Euclidean 4-space relativity, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] contains the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and did not describe our ordinary 3-space embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.<ref>{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}</ref> He invited us to imagine "A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions", but he was careful to disclaim parenthetically that "The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice." Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal of that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.'' The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified spacetime of four dimensions. Anco and Maghadam found that <small><math>SO(4)</math></small> breaks to ... <small><math>S^3</math></small>... if the energy in the Kepler orbit is negative (an elliptical orbit), and to ... <small><math>H^3</math></small> ... Minkowski spacetime if the energy is positive (a hyperbolic orbit). Because the planets orbit on ellipses in our 3-space, Euclidean 4-space is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the truer model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position of centrality as our exclusive conception of our place in space. ...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others. The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; "Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions."}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.<ref>{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}</ref>}} == Boundaries == <blockquote>Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.<ref>{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}</ref></blockquote> Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? ''What is the nature of the boundary which confines us to just three dimensions?'' We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell. Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined motions and objects. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. A boundary is an explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force. <blockquote>The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three .... In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it. We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed "Dimensional Analogy."<ref>{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}</ref></blockquote> I believe, but I cannot prove, that we live in real space, which is Schläfli's and Coxeter's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover in imagination and then explore physically, each an astonishing new enlightenment.<ref>{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}<blockquote> :We shall not cease from exploration :And the end of all our exploring :Will be to arrive where we started :And know the place for the first time. :Through the unknown, remembered gate :When the last of earth left to discover :Is that which was the beginning; :At the source of the longest river :The voice of the hidden waterfall :And the children in the apple-tree :Not known, because not looked for :But heard, half-heard, in the stillness :Between two waves of the sea. </blockquote></ref> Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. This project is forever beginning anew. Coxeter showed us that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether showed us all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions, in which all objects with mass move ceaselessly at the constant velocity <math>c</math>, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages. <blockquote> ::::::BEECH :Where my imaginary line :Bends square in woods, an iron spine :And pile of real rocks have been founded. :And off this corner in the wild, :Where these are driven in and piled, :One tree, by being deeply wounded, :Has been impressed as Witness Tree :And made commit to memory :My proof of being not unbounded. :Thus truth's established and borne out, :Though circumstanced with dark and doubt— :Though by a world of doubt surrounded. :::::::—''The Moodie Forester''<ref>{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}</ref> </blockquote> == Appendix: Sequence of regular 4-polytopes == {{Regular convex 4-polytopes|wiki=W:|columns=7}} == ... == {{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}} {{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}} {{Efn|The long radius (center to vertex) of the 24-cell is equal to its edge length; thus its long diameter (vertex to opposite vertex) is 2 edge lengths. Only a few uniform polytopes have this property, including the four-dimensional 24-cell and [[W:Tesseract#Radial equilateral symmetry|tesseract]], the three-dimensional [[W:Cuboctahedron#Radial equilateral symmetry|cuboctahedron]], and the two-dimensional [[W:Hexagon#Regular hexagon|hexagon]]. (The cuboctahedron is the equatorial cross section of the 24-cell, and the hexagon is the equatorial cross section of the cuboctahedron.) '''Radially equilateral''' polytopes are those which can be constructed, with their long radii, from equilateral triangles which meet at the center of the polytope, each contributing two radii and an edge.|name=radially equilateral|group=}} {{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as "the convex hull of the neighbouring vertices of a given vertex".{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its "radius" equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}} {{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example: {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0) {{indent|5}}({{spaces|2}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>){{spaces|3}}({{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>) {{indent|5}}(–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>){{spaces|3}}(–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>) {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)<br> is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}} {{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60° rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the "left" is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}} {{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}} {{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; "In mathematics, the path that the (1, 1) knot on the torus traces is also known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two intersecting circles that are the cross-section of a torus by a well-chosen plane cutting it. Picking one such circle and rotating it around the torus axis, the resulting family of circles can be used to rule the torus. By nesting tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the (1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles]."}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}} {{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}} {{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}} {{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}} {{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}} {{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}} {{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}} {{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}} {{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}} {{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90^o bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60^o bend, or as a straight line with one 60^o bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}} {{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; "In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)"}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}} {{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}} {{Efn|Departing from any vertex V₀ in the original great hexagon plane of isoclinic rotation P₀, the first vertex reached V₁ is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P₁. P₁ is inclined to P₀ at a 60° angle.{{Efn|P₀ and P₁ lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V₂ is 120 degrees beyond V₁ along a second {{radic|3}} chord lying in another hexagonal plane P₂ that is Clifford parallel to P₀.{{Efn|P₀ and P₂ are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V₀ and V₂ are ''two'' {{radic|3}} chords apart{{Efn|V₀ and V₂ are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V₀ and V₂ are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P₀ and P₂ are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V₁ lies in both intersecting planes P₁ and P₂, as V₀ lies in both P₀ and P₁. But P₀ and P₂ have ''no'' vertices in common; they do not intersect.) The third vertex reached V₃ is 120 degrees beyond V₂ along a third {{radic|3}} chord lying in another hexagonal plane P₃ that is Clifford parallel to P₁. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V₀ to V₃ is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}} {{Sfn|Mamone, Pileio & Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹₄.}} ==Notes== {{Regular convex 4-polytopes Notelist|wiki=W:}} ==Citations== {{Regular convex 4-polytopes Reflist|wiki=W:}} ==References== {{Refbegin}} * {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}} * {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1}} * {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}} === [[Polyscheme|Polyschemes]] === {{Regular convex 4-polytopes Refs|wiki=W:}} {{Refend}} 8zp2wvu0wtpevj7kp894handg3vwuvp 2823715 2823712 2026-08-20T20:50:09Z Dc.samizdat 2856930 2823715 wikitext text/x-wiki = Real Euclidean four-dimensional space R⁴ = {{align|center|David Brooks Christie}} {{align|center|dc@samizdat.org}} {{align|center|Draft in progress}} {{align|center|June 2023 - August 2026}} <blockquote>'''Abstract:''' The physical universe is properly visualized as a Euclidean space of four orthogonal spatial dimensions. Space itself has a fourth orthogonal dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and our planet are only 3-dimensional objects, but nonetheless we can see in four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.</blockquote> == Summary == We observe that physical space has four perpendicular dimensions, not just three; atoms are [[W:4-polytope|4-polytopes]]; the sun is a 4-ball that is round in four dimensions; everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space; and our entire 3-space manifold is translating through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions. == A theory of the Euclidean cosmos == The physical universe is properly visualized as a [[w:Four-dimensional_space|Euclidean space of four orthogonal spatial dimensions]]. Space itself has a fourth orthogonal dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planets, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. All objects with mass move inertially through Euclidean 4-space at velocity <math>c</math> as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity <math>c</math> is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space. A typical spiral galaxy such as ours is a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our galaxy appear from our viewpoint to be distributed in a cloud of elliptical spirals occupying a flattened ellipsoid region of 3-dimensional space, but they are not so confined: they are distributed within a spherical region of 4-dimensional space. The galaxy's actual shape is spherical, not a flattened ellipsoid, but it is rounder than round can be in our ordinary experience: it occupies a hyperspherical region of space. The concentric spirals of stars that we observe lie on concentric [[W:3-sphere|3-sphere]]s (4-dimensional spheres), not on concentric 2-ellipsoids (3-dimensional elliptical spirals). Our sun and solar system lies on one of those concentric 3-spheres. More generally, orbits are circular in 4-space, and elliptical in the 3-space of their elliptic hyperplane. [[File:Hypersphere.png|thumb|Rotating illustration of the 4-ball galaxy showimg its spirals of star clouds on the surface of concentric 3-spheres, obtained by reverse sterographic projection from 3D images of the galaxy.]] The galaxy as a whole, or more properly its orbital center point, is translating through 4-space at velocity <math>c</math>, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity <math>c</math> in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity <math>c</math>. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the cylinder; their trajectories are screw-displacements, the compound of a simple rotation and a linear translation. The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around a barycentric axis. It is the tremendous inertial force of stars in motion at velocity <math>c</math> that holds the cylinder of motion together. The observed universe as a whole appears to be a 3-sphere expanding radially from a central origin point at velocity <math>c</math>, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. For all observers, the conjectured origin point of the universe corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space (the same point in the same Euclidean 4-space for all observers). The big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured separately, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity <math>c</math>. All objects in our solar system except the sun itself lie within this thinest three-dimensional manifold. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. The enclosing surface of a spherical region of 4-space is itself a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. We live within such a 3-space, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience, and it contains the earth, all the planets and the 3-dimensional space between them. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our particular 3-sphere is one of the galaxy's concentric 3-spheres of spiral star-clouds. The solar system occupies a tiny patch of this filmy 4-dimensional soap-bubble of galactic size, that is thicker-skinned than the diameter of an atom only in the interior of stars and supermassive objects. Our entire 3-sphere manifold, as a 3-spherical shell within the moving 4-ball galaxy, is translating through 4-space at velocity <math>c</math> with the galaxy, in a distinct direction that is orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the galaxy's translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of rotating objects through Euclidean space by screw translation. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity <math>c</math>, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. Any moving 3-dimensional manifold that is such an evolving surface boundary is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. Every object which we find occurring naturally in the solar system other than the sun itself, even the largest of 3-dimensional objects a planet, is a three-dimensional smear of atoms no thicker than one atom in its fourth dimension, which is the direction of its linear translation through 4-space at velocity <math>c</math>. The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be "heaped up" into larger 4-dimensional objects that form a lump in its moving surface. We have little understanding of such 4-dimensional lumps thicker than one atom, since they occur naturally in our vicinity only in the interior of the sun. In fact the sun is the only such lump occurring naturally in our solar system. We refer to 4-dimensional lumps of matter as plasma, and have little experimental knowledge of their geometry or internal structure. We know that such a lump as the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know nothing about its interior 4-ball. Every such moving 3-dimensional surface boundary of matter in the observed universe is evolving in four dimensions at velocity <math>c</math>. Its current location in 4-space corr esponds to the present moment in the proper time of its inertial reference frame. Its direction of movement at velocity <math>c</math> corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from atoms to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, two orthogonal inertial motions each at the constant universal rate of transformation <math>c</math>. Every object moves relative to universal 4-coordinate space on its own distinct geodesic spiral, a screw translation trajectory that is the compound of two orthogonal inertial motions, a rotation and a translation. Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity <math>c</math> in all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is <math>c\prime = 2c</math>, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity <math>c</math>. For example, we can look across the center of our mostly-empty 4-ball galaxy and see stars in the opposite sides of its concentric 3-sphere surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math> in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper space. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space. == Symmetries == It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel & Goodman-Strauss|2008}} As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. [[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}} <blockquote>Let <small><math>\mathrm{Q}</math></small> denote a rotation, <small><math>\mathrm{R}</math></small> a reflection, <small><math>\mathrm{T}</math></small> a translation, and let <small><math>\mathrm{Q}^q \mathrm{R}^r\mathrm{T}</math></small> denote a product of several such transformations, all commutative with one another. Then <small><math>\mathrm{RT}</math></small> is a glide-reflection (in two or three dimensions), <small><math>\mathrm{QR}</math></small> is a rotary-reflection, <small><math>\mathrm{QT}</math></small> is a screw-displacement, and <small><math>\mathrm{Q^2}</math></small> is a double rotation (in four dimensions).<br> Every orthogonal transformation is expressible as:<br> :<small><math>\mathrm{Q}^q \mathrm{R}^r</math></small><br> where <small><math>(2^q + r \le n)</math></small>, the number of dimensions.<br> Transformations involving a translation are expressible as:<br> :<small><math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}</math></small><br> where <small><math>(2^q + r + 1 \le n)</math></small>.<br> For <small><math>(n = 4)</math></small> in particular, every displacement is either a double rotation <small><math>\mathrm{Q}^2</math></small>, or a screw-displacement <small><math>\mathrm{QT}</math></small> [where the rotation component <small><math>\mathrm{Q}</math></small> is a simple rotation, but the <small><math>\mathrm{QT}</math></small> is chiral like a <small><math>\mathrm{Q^2}</math></small>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <small><math>\mathrm{QRT}</math></small>.</blockquote> If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a <small><math>\mathrm{Q^2}</math></small> or a <small><math>\mathrm{QT}</math></small>, because we can view any <small><math>\mathrm{QT}</math></small> as a <small><math>\mathrm{Q^2}</math></small> in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a <small><math>\mathrm{Q^2}</math></small>. By the same principle, we can view any <small><math>\mathrm{QT}</math></small> or <small><math>\mathrm{Q^2}</math></small> as an isoclinic (equi-angled) <small><math>\mathrm{Q^2}</math></small> by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (<small><math>\mathrm{T}</math></small>) for ''one'' of the two rotations (<small><math>\mathrm{Q}</math></small>). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (<small><math>\mathrm{Q}</math></small>) up to uncertainty, and can always distinguish the direction of their own proper time translation (<small><math>\mathrm{T}</math></small>). As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebra), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group <small><math>SO(4)</math></small> [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic <small><math>SO(4)</math></small> rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, stationary atoms exhibit the <small><math>SO(4)</math></small> symmetries of the discrete isoclinic (equi-angled) double rotations (<small><math>\mathrm{Q^2}</math></small>) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]]. == Special relativity describes Euclidean 4-space == <blockquote>Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.<ref>{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}</ref></blockquote> Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional "space" because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign to the three space coordinates so spacetime is hyperbolic, not a flat Euclidean 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was first described by Einstein himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction. Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity ''c'', in some 4-space direction. This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always ''c'', as measured by all observers from any inertial reference frame. This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source. But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity ''c''. In physics as it has been universally understood, observers are not supposed to be able to move at velocity ''c''. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four. In the Euclidean relativity alternative view, however, every observer is always moving at velocity ''c'' through the universe, which is real Euclidean 4-dimensional space <small><math>\mathbb{R^4}</math></small>. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity ''c''. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and proper space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity ''c'', in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space <small><math>\mathbb{R^4}</math></small>.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity ''c'' relative to universal 4-coordinate space, so the maximum relative velocity between two observers is 2''c'' when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to ''c'', it is the same measurement in different units. Special relativity measures all velocities in a 3-space of Minkowski spacetime. Euclidean relativity measures all velocities in Euclidean 4-space.}} So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity ''c'' in Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the "speed of light" ''c'', although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity ''c'', but in at least slightly different directions. In Einstein's relativity, the invariant ''c'' is the speed of light through 3-space. In Euclidean relativity, the invariant ''c'' is the speed of matter through 4-space! The speed of light through 3-space is also perceived as ''c'' by all observers, because they are each living in a moving 3-manifold that is moving through 4-space at velocity ''c''. Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same predictions about how observers in different reference frames will perceive each other's motions in time and space, and we shall see that they also agree on the predictions of general relativity. They both describe the same geometric relations of space and time, but they describe that geometry as embedded in two very different universal host spaces: Minkowski spacetime versus Euclidean 4-space. ...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity <math>c</math> through space and proper time ...cite Yamashita{{Sfn|Yamashita|2023}} on the equivalence of special relativity and Euclidean 4-space relativity ...cite Kappraff & Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff & Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff & Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords. Euclidean relativity is not even a fringe theory; no physicists have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could "catch up" with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at ''c'' (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than ''c''. Euclidean relativity is a revolutionary theory indeed, in which ''c'' cannot possibly be the speed of light! We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for <math>\mathbb{R^4}</math> to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be <math>c\prime = 2c</math>, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate linearly along the edge of a unit 4-hypercube. This is conceivable in 4-space (and in no other Euclidean space of any dimensionality) because the diagonal of the unit 4-hypercube is the natural number <small><math>\sqrt{4}</math></small>. == An object's motion in space is the product of its discrete self-reflections == Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a small number of discrete self-reflections. Any action of a geometric object that transforms its position and orientation in space may be measured as a distinct group of self-reflections of the object in its own surfaces. Any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete set of local self-reflections. Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which touch (intersect each other). When a object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality. Coxeter's laws of motion are a geometric counterpart to Newton's laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures. But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. For example, they give us geometric pictures of all the possible motions of objects in four dimensional Euclidean space: <blockquote>Every orthogonal transformation in 4-space is expressible as:<br> :<small><math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t</math></small><br> where <small><math>(2^q + r + t \le 4)</math></small>. Every displacement is either a double rotation <small><math>\mathrm{Q}^2</math></small>, or a screw-displacement <small><math>\mathrm{QT}</math></small> [where the rotation component <small><math>\mathrm{Q}</math></small> is a simple rotation, but the <small><math>\mathrm{QT}</math></small> is chiral like a <small><math>\mathrm{Q^2}</math></small>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <small><math>\mathrm{QRT}</math></small>.</blockquote> While this description should be understood as simple geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (<small><math>\mathrm{Q}</math></small>), reflection (<small><math>\mathrm{R}</math></small>) and translation (<small><math>\mathrm{T}</math></small>) are just what they are in three-dimensional space, but double rotation (<small><math>\mathrm{Q}^2</math></small>) is something new and unprecedented in our physical experience, because double rotations cannot occur until you have four or more dimensions of space to rotate in. ...to readers who have not studied Coxeter (almost all readers including TAC), the blockquote above is "just math", not visualizable geometry...but I could describe Coxeter's congruent transformations in 4-space here geometrically: I could say clearly what they mean in spatial terms, in language anyone can understand, because they don't require any math to be understood; the "math" here is really just simple pictures (reflections and rotations); even double rotations can be visualized by dimensional analogy, as compounds of simple rotations...since even most physicists are unacquainted with Coxeter geometry, it might be useful to do this here... == Light propagates through 4-space at twice its apparent velocity ''c''== Coxeter's geometric laws of motion apply to all objects with mass in 4-dimensional Euclidean space, but we find there is an additional kind of displacement which applies only to massless particles such as photons. Light quanta (photons) translate through 4-space by 4-dimensional reflection <small><math>\mathrm{R}^4</math></small>, which may be termed a double translation <small><math>\mathrm{T}^2</math></small>, a pure translation via two pairs of parallel reflections, without any rotation component <small><math>\mathrm{Q}</math></small>. Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by <small><math>\mathrm{QT}</math></small>, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic <small><math>\mathrm{Q^2}</math></small>, an isoclinically rotating object such as an atom. A simple rotation <small><math>\mathrm{Q}</math></small> or simple translation <small><math>\mathrm{T}</math></small> is a double reflection <small><math>\mathrm{R^2}</math></small>, so a <small><math>\mathrm{QT}</math></small> or <small><math>\mathrm{Q^2}</math></small> is also an <small><math>\mathrm{R^4}</math></small>, but not with the same group of reflection angles as a light signal <small><math>\mathrm{R^4}</math></small>. A translation <small><math>\mathrm{T = R^2}</math></small> is a double reflection in two parallel planes, and a rotation <small><math>\mathrm{Q = R^2}</math></small> is a double reflection in two intersecting planes, as in a <small><math>\mathrm{QT = R^4}</math></small> which is both at once. A double translation <small><math>\mathrm{T^2 = R^4}</math></small> is two double reflections in pairs of parallel planes at once, a reflection in four or more non-intersecting parallel planes; it is all translation and no rotation. In a <small><math>\mathrm{T^2}</math></small> all the motion goes to translation, so the translation goes twice as far as the simple translation <small><math>\mathrm{T}</math></small> in a <small><math>\mathrm{QT}</math></small>. A double translation <small><math>\mathrm{T^2 = R^4}</math></small> is the opposite of a double rotation <small><math>\mathrm{Q^2 = R^4}</math></small>, which is stationary but rotates twice as fast as the simple rotation <small><math>\mathrm{Q}</math></small> in a <small><math>\mathrm{QT}</math></small>. The product of the two translations in a <small><math>\mathrm{T^2}</math></small> is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple <small><math>\mathrm{T}</math></small> over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double-the-distance translation, but without any rotation component, so it cannot carry any mass with it. A <small><math>\mathrm{T^2}</math></small> cannot reposition a 4-polytope the way a <small><math>\mathrm{QT}</math></small> does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter. ...lensing of double translations <small><math>\mathrm{T^2 = R^4}</math></small> in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet... == The Kepler problem is framed in Euclidean 4-space == The [[W:Kepler problem|Kepler problem]] is named for [[W:Johannes Kepler|Johannes Kepler]], arguably the greatest geometer since the ancients up to [[w:Ludwig Schläfli|Ludwig Schläfli]], who proposed [[W:Kepler's laws of planetary motion|Kepler's laws of planetary motion]] which solved the problem of the orbits of the planets, and investigated the types of forces that would result in orbits obeying those laws. Those forces were later identified by [[W:Isaac Newton|Isaac Newton]] in his[[W:Philosophiæ Naturalis Principia Mathematica| Principia]], where he proves what today might be called the "inverse Kepler problem": the orbit characteristics require the force to depend on the inverse square of the distance.<ref>{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton & Company|isbn=978-0393039184}}</ref> The inverse square law behind the Kepler problem is the [[W:Central force|central force]] law which governs not only [[W:Newtonian gravity|Newtonian gravity]] and celestial orbits, but also the motion of two charged particles in [[W:Coulomb’s law|Coulomb’s law]] of [[W:Electrostatics|electrostatics]]; it applies to attractive or repulsive forces. Problems in which two bodies interact by a central force that varies as the [[W:Inverse square law|inverse square]] of the distance between them are called Kepler problems. Thus the [[W:Hydrogen atom|hydrogen atom]] is a Kepler problem, since it comprises two charged particles interacting by Coulomb's law, another inverse-square central force. Using classical mechanics, the solution to a Kepler problem can be expressed as a [[W:Kepler orbit|Kepler orbit]] using six kinematical variables or [[W:Orbital elements|orbital elements]]. The solution conserves an orbital element called the [[W:Laplace–Runge–Lenz vector|Laplace–Runge–Lenz (LRL) vector]], a [[W:Constant of motion|constant of motion]], meaning that it is the same no matter where it is calculated on the orbit. The LRL vector was essential in the first quantum mechanical derivation of the [[W:Atomic emission spectrum|spectrum]] of the hydrogen atom, but this approach has rarely been used since the development of the [[W:Schrödinger equation|Schrödinger equation]]. The conservation of the LRL vector corresponds to the <small><math>SO(4)</math></small> symmetry, by Nother's theorem. The LRL vector lies orthogonal to both the orbital plane and the angular momentum vector of the Kepler orbit; we observe that it lies in a fourth orthogonal dimension. Fock in 1935<ref>V. Fock, Zur Theorie des Wasserstoffatoms, Zeitschrift für Physik. 98 (3-4) (1935), 145–154.</ref> and Moser in 1970<ref>J. Moser, Regularization of Kepler’s problem and the averaging method on a manifold, Commun. Pure Appl. 23 (1970), 609–636</ref> observed that the Kepler problem is mathematically equivalent to non-affine geodesic motion (a particle moving freely) on the surface of a 3-sphere, so that the whole problem is symmetric under certain rotations of the four-dimensional space. This higher-dimensional symmetry results in two well-known properties of the Kepler problem: the momentum vector always moves in a perfect circle and, for a given total energy, all such velocity circles intersect each other in the same two points. ... Relativity establishes that an orbit in space is viewed in a different way in each distinct inertial reference frame. Depending on the choice of reference frame, the same Kepler system may be seen to be performing any one of a sequence of relativistically equivalent rotations in 4-space, on a continuum from an isoclinic rotation (Q²) in the orbit's proper reference frame, to a screw transfer (QT) with a simple rotation component (Q) and a translation component (T) at velocity <math>c</math>, in the universal reference frame of 4-coordinate space wherein every object is seen to be translating at velocity <math>c</math>. In reference frames between these two limit cases, the orbit is seen to be performing a double rotation (Q²) at two unequal, completely orthogonal angular rates of rotation: an elliptical double rotation. These include the reference frames of most typical observers, who are moving slowly relative to the observed orbital system's reference frame (their relative motion is a small fraction of the speed of light). ...this is probably misplaced here and should not interrupt the discussion at this point: ...These typical observations agree closely with the predictions of special relativity, because the non-isoclinic elliptical (Q²) resembles a (QT), since one of its two completely orthogonal rotations (Q) has such a long period that it is almost indistinguishable from a straight translation (T). All orbits in 4-space are isoclinic in their own reference frame. Orbiting objects in their own proper Kepler systems follow circular geodesic isoclines through 4-space. Orbits in 4-space are perfectly circular in their own reference frame, as Copernicus assumed the orbits of planets to be. It is the orbit's path through the 3-space of its elliptic hyperplane that is an ellipse, as Kepler found it to be. ...cite Jesper Goransson's very concise paper The geodesic circle that an orbiting object follows through 4-space in the proper reference frame of its own Kepler system is not a simple great circle which turns in two orthogonal dimensions. It is a helical great circle that turns in four orthogonal dimensions at once.{{Efn|Geodesic orbits in 4-space are not simple 2-dimensional great circles; they are helical 4-dimensional great circles that curve in all four dimensions at once. Their circular trajectories are helixes which we call ''isoclines'', since they are the paths taken by points on a rigid object undergoing isoclinic rotation.}} Such circles lie outside our physical experience, since our local space has only three orthogonal dimensions. Nonetheless we can visualize them in imagination, because their helical, circular shape is perfectly well defined by the kinematical variables of the Kepler orbit. The real physical correlates of abstract orthogonal planes and rotation angles are already familiar to us viscerally in our body-language of physical experience, since we are endowed biologically with highly evolved visual signal processing engines. These enable us to see and understand spatial relations and motions, including rotations, without even thinking about angles and orthogonal planes. This physical endowment is an inborn capacity for dimensional analogy which our biologic evolution has provided. All our instinctive spatial reasoning is by dimensional analogy from flat 2-dimensional retinal images to 3-dimensional scenes, using our powerful inborn visualization capacities of reverse stereographic projection and pattern recognition. We humans are thus very well equipped with everything we need to see in four-dimensional space, except experience. ... Recently Anco and Moghadam found that through Noether’s theorem in reverse, the LRL vector gives rise to a corresponding infinitesimal dynamical symmetry on the kinematical variables, which they show to be the semi-direct product of <small><math>SO(3)</math></small> and <small><math>\mathbb{R^3}</math></small>, in contrast to the <small><math>SO(4)</math></small> symmetry group generated by the LRL symmetries and the rotations.{{Sfn|Anco|Moghadam|2026|ps=; The physically relevant part of the LRL vector is its direction ... since its magnitude is just a function of energy and angular momentum.}} This remarkable symmetry breaking is expressive of the ''dimensional relativity'' between ordinary 3-space <small><math>\mathbb{R^3}</math></small>, spherical space <small><math>S^3</math></small> and Euclidean space <small><math>\mathbb{R^4}</math></small>. Consider a hydrogen atom in a Kepler orbit: for example, a hydrogen atom moving freely in space in an orbit around the sun. It is a ''double'' Kepler problem: an electrostatic Kepler problem within itself, and a gravitational Kepler problem in its environment. The ''single'' electrostatic Kepler problem of a hydrogen atom moving freely in space beyond any gravitational influence is a problem in special relativity. In our Euclidean 4-space model, this atom viewed as stationary in its own proper reference frame exhibits an <small><math>SO(4)</math></small> rotation symmetry corresponding to an isoclinic double rotation (<small><math>\mathrm{Q^2}</math></small>). The fourth dimension in this reference frame is the atom's proper time vector; it has constant velocity <math>c</math> and constant direction. From the point of view of our universal 4-coordinate space (which cannot be the proper inertial reference frame of any physical observer, all of whom are moving relative to it at velocity ''c''), the entire Kepler system (the atom) is translating through 4-space via a screw translation (<small><math>\mathrm{QT}</math></small>) at constant velocity <math>c</math>. From this viewpoint the atom has only a simple <small><math>SO(3)</math></small> rotation component (<small><math>\mathrm{Q}</math></small>), breaking its stationary <small><math>SO(4)</math></small> isoclinic rotation symmetry (<small><math>\mathrm{Q^2}</math></small>). Because each discrete part of the rotating atom moves along a helical trajectory through 4-space, the atom is in orbit around a barycentric axis (like a star in a galaxy), but only in a tiny orbit within its own radius, which is its inertial domain of rotation. The straight 4-dimensional cylinder it progresses along at velocity <math>c</math> is very narrow: only the diameter of the rotating atom itself. The gravitational Kepler problem of a hydrogen atom in a Kepler orbit around the sun is a problem in general relativity. In our 4-space model, this atom viewed in its own proper reference frame exhibits the same <small><math>SO(4)</math></small> rotation symmetry as it did in the electrostatic Kepler problem where the atom was translating linearly through space. The Kepler system in this case is not just the atom; it is the entire solar system. The LRL vector of this Kepler system is the proper time vector of the atom's inertial reference frame; once again it has constant velocity ''and constant direction''. Although the momentum vector moves in a perfect circle as the atom orbits the sun, the 4-space LRL vector does not move at all: it is a constant of motion, of linear motion (<small><math>\mathrm{T}</math></small>) of the Kepler system (the entire solar system in this case) in a constant 4-space direction, the proper time direction of the system. The direction of the system's proper time vector would vary under some kinds of acceleration of the atom, but it is constant under this kind of orbital acceleration. It continues to point in the same direction, like a 4-space compass needle, as the atom winds its way along its spiral path around the axis of the sun's straight-line translation through 4-space at velocity <math>c</math>. This compass needle always points in the direction the sun is moving, not the direction the atom is moving at any instant. ...Its Kepler orbit around the sun is its <small><math>SO(3)</math></small> rotation component (<small><math>\mathrm{Q}</math></small>). Although the atom is moving on a geodesic circle in the second problem, by the [[equivalence principle]] the difference in the state of the atomic systems in these two problems cannot be observed by examining the atoms alone. Even from another inertial reference frame, where the atom in the second problem is seen to be translating through 4-space via a wide screw translation (<small><math>\mathrm{QT}</math></small>) around the sun's axis of motion, there is still no difference between the two problems which can be detected by examining only the atoms within their own proper reference frames (even over time), because the LRL vector (<small><math>\mathrm{T}</math></small>) is a constant of motion of the entire system in both cases. ...Anco and Maghadam found that <small><math>SO(4)</math></small>) breaks to ... <small><math>S^3</math></small>)... if the energy in the Kepler orbit is negative (an elliptical orbit), and to ... <small><math>H^3</math></small>) ... Minkowski spacetime if the energy is positive (a hyperbolic orbit). ... Finally we consider a third problem in which a hydrogen atom enters the solar system as a comet, loops around the sun and exits the solar system again. This atom... ... As Hamilton found when he discovered the quaternions, we see that it is necessary to admit a fourth dimension to the system in order to properly model the problem: in Hamilton's case the general problem of ..., and in our case the Kepler problem. These are instances of the same problem in 4-dimensional Euclidean geometry, and indeed a solution to the Kepler problem in quaternions (the four Cartesian coordinates of Euclidean 4-space) is a solution to it in our model of the 4-coordinate Euclidean cosmos. == Distribution of stars in our galaxy == The stars in our own galaxy appear to us to be a rotating spiral cluster in 3-dimensional space. By assuming that light from them reaches us on straight lines through space, by assuming that we can measure their distance from us by its red shift, and by assuming that they are distributed in three dimensions of space, we have plotted their locations in 3-space. If we abandon the last of those three assumptions, we can just as easily reinterpret that dataset to plot their distribution around us in 4-dimensional space, and see how they actually lie. When we perform this experiment on the data for the stars in our galaxy, do we indeed find that they are distributed non-uniformly in various concentric spirals, but the spirals lie on the surface of various 3-spheres, rather than in elliptical orbits as we saw them in 3-space? That would be an expected consequence of the special rotational symmetry group of 4-space <small><math>SO(4)</math></small>, in which circular (isoclinic) orbits are the geodesics (shortest rotational paths) rather than elliptical (non-equi-angled double rotation) orbits. ...have to perform this experiment somehow, at least as a conclusive thought experiment, before I publish this paper... == Rotations == The [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotations]] of the convex [[W:regular 4-polytope|regular 4-polytope]]s are usually described as discrete rotations of a rigid object. For example, the rigid [[24-cell]] can rotate in a [[24-cell#Great hexagons|hexagonal]] (6-vertex) central [[24-cell#Planes of rotation|plane of rotation]]. A 4-dimensional [[24-cell#Isoclinic rotations|''isoclinic'' rotation]] (as distinct from a [[24-cell#Simple rotations|''simple'' rotation]] like the ones that occur in 3-dimensional space) is a ''diagonal'' rotation in multiple [[W:Clifford parallel|Clifford parallel]] [[24-cell#Geodesics|central planes]] of rotation at once. It is diagonal because it is a [[W:SO(4)#Double rotations|double rotation]]: in addition to rotating in parallel (like wheels), the multiple planes of rotation also tilt sideways in the completely orthogonal plane of rotation (like coins flipping) into each other's planes. Consequently, the path taken by each vertex is a [[24-cell#Helical hexagrams and their isoclines|twisted helical circle]], rather than the ordinary flat great circle a vertex follows in a simple rotation. In a rigid 4-polytope rotating isoclinically, ''all'' the vertices lie in one of the parallel planes of rotation, so all the vertices move in parallel along Clifford parallel twisting circular paths. [[24-cell#Clifford parallel polytopes|Clifford parallel planes]] are not parallel in the normal sense of parallel planes in three dimensions; the vertices are all moving in different directions around the [[W:3-sphere|3-sphere]]. In one complete 360° isoclinic revolution, a rigid 4-polytope turns itself inside out. This is sufficiently different from the simple rotations of rigid bodies in our 3-dimensional experience that a [[24-cell#Rotations|detailed description]] enabling the reader to properly visualize its counter-intuitive consequences runs to many pages and illustrations, with many accompanying pages of explanatory notes on surprising phenomena that arise in 4-dimensional space: [[24-cell#Great squares|completely orthogonal planes]], [[24-cell#Clifford parallel polytopes|Clifford parallelism]]{{Efn|name=Clifford parallels}} and [[W:Hopf fibration|Hopf fiber bundles]], [[24-cell#Isoclinic rotations|isoclinic geodesic paths]], and [[24-cell#Double rotations|chiral (mirror image) pairs of rotations]], among other complexities. Moreover, the characteristic rotations of the various regular 4-polytopes are all different; each is a unique surprise. [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|The 6 regular convex 4-polytopes]] have different numbers of vertices (5, 8, 16, 24, 120 and 600 respectively) and those with fewer vertices occur inscribed in those with more vertices (with one exception), with the result that the more complex 4-polytopes subsume the kinds of rotations characteristic of their less complex predecessors, as well as each having a characteristic kind of rotation not found in their predecessors. None of these symmetries is to be found in 3-dimensional space, although their simpler 3-dimensional analogues are all present there. [[W:Euclidean geometry#Higher dimensions|Four dimensional Euclidean space]] is more complicated (and more interesting) than three dimensional space because there is more room in it, in which unprecedented things can happen. It subsumes 3-dimensional space, with all of the symmetries we are accustomed to, and adds astonishing new surprises. These are hard for us to visualize, because the only way we can experience them is in our imagination; we have no body of sensory experience in 4-dimensional space to draw upon, other than our evolution in time. For that reason (our difficulty in visualizing them), descriptions of isoclinic rotations usually begin and end with rigid rotations: [[24-cell#Isoclinic rotations|for example]], all 24 vertices of a single rigid 24-cell rotating in unison, with 6 vertices evenly spaced around each of 4 Clifford parallel twisted circles.{{Efn|name=360 degree geodesic path visiting 3 hexagonal planes}} But that is only the simplest case, which is easiest for us to understand. Compound and [[W:Kinematics|kinematic]] 24-cells (with moving parts) are even more interesting (and more complicated) than the rotation of a single rigid 24-cell. To begin with, when we examine the individual parts of a single rigid 24-cell that are moving in an isoclinic rotation, such as the orbits of individual vertices, we can imagine a case where fewer than 24 point-objects are orbiting on those twisted circular paths at once. [[24-cell#Reflections|For example]], if we imagine just 8 point-objects, evenly spaced around the 24-cell at [[24-cell#Reciprocal constructions from 8-cell and 16-cell|the 8 vertices that lie on the 4 coordinate axes]], and rotate them isoclinically along exactly the same orbits they would take in the above-mentioned rotation of a rigid 24-cell, then in the course of a single 360° rotation the 8 point-objects will trace out the whole 24-cell, with just one point-object reaching each of the 24 vertex positions just once, and no point-object colliding with (or even crossing the path of) any other at any time. This is an example of a discrete Hopf fibration. But it is still an example of a rigid object in a discrete isoclinic rotation: a rigid 8-vertex object (called the 4-[[W:orthoplex|orthoplex]] or [[16-cell]]) performing one half of the characteristic rotation of the 24-cell. We can also imagine ''combining'' distinct isoclinic rotations. What happens when multiple point-objects are orbiting at once, but do ''not'' all follow the Clifford parallel paths characteristic of the ''same'' distinct rigid rotation? What happens when we combine orbits from distinct rotations characteristic of different 4-polytopes, for example when different rigid 4-polytopes are concentric and rotating simultaneously in their characteristic ways? What kinds of such hybrid rotations are possible in the same 3-sphere shell without collisions? In adjacent concentric shells without asymmetric imbalance? What sort of [[Kinematics of the cuboctahedron|kinematic polytopes]] do they trace out, and how do their [[24-cell#Clifford parallel polytopes|component parts]] relate to each other as they move? Is there (sometimes) some kind of mutual stability amid their lack of combined rigidity? Visualizing isoclinic rotations (rigid and otherwise) allows us to explore such questions of [[W:kinematics|kinematics]], and where dynamic stabilities arise, of [[wikipedia:kinetics (physics)|kinetics]]. In four dimensions, we discover that space has more room in it than we have experienced, which permits previously unimagined motions. Even 3-space is more commodious than we thought; when it is curved and lies embedded in a higher-dimensional space, it permits previously impossible symmetric packings. Sadoc studied double-twisted 3-dimensional molecules, and imagined them embedded in 4-dimensional space as the Hopf fibrations of regular 4-polytopes. He found that these molecules would close-pack on the 3-sphere perfectly without exhibiting any torsion, although their packing in ordinary flat 3-space is imperfect, "frustrated" by their twisted geometry. <blockquote>The frustration, which arises when the molecular orientation is transported along the two [spiral] AB paths of figure 1 [double twist helix], is imposed by the very topological nature of the Euclidean space R³. It would not occur if the molecules were embedded in the non-Euclidean space of the [[W:3-sphere|3-sphere]] S³, or hypersphere. This space with a homogeneous positive curvature can indeed be described by equidistant and uniformly twisted fibers, along which the molecules can be aligned without any conflict between compactness and [[W:torsion of a curve|torsion]].... The fibres of this [[W:Hopf fibration|Hopf fibration]] are great circles of S³, the whole family of which is also called the [[W:Clifford parallel|Clifford parallel]]s.{{Efn|name=Clifford parallels}} Two of these fibers are C_∞ symmetry axes for the whole fibration; each fibre makes one turn around each axis and regularly rotates when moving from one axis to another.{{Efn|name=helical geodesic}} These fibers build a double twist configuration while staying parallel, i.e. without any frustration, in the whole volume of S³.{{Efn|name=Petrie polygon of a honeycomb}} They can therefore be used as models to study the condensation of long molecules in the presence of a double twist constraint.{{Sfn|Sadoc & Charvolin|2009|loc=§1.2 The curved space approach|ps=; studies the helical orientation of molecules in crystal structures and their imperfect packings ("frustrations") in 3-dimensional space.}}</blockquote> Of course we do not find molecules condensing to close-pack the 3-sphere in our experience, and Sadoc does not say that we do. We find 3-spheres in the atomic realm (if atoms are 4-polytopes), and in the cosmic realm (as the surface boundaries of stars, and the concentric surfaces of galaxies). But in between, in the realm of ordinary experience which includes the molecular realm, ourselves and all the objects we can materially handle or observe up close including the planets, we are confined together by gravity as inertia within a curved 3-dimensional space that is no more than one atom thick in the fourth spatial dimension. That is why in the molecular realm we find only objects that occupy 3-spaces which, though infinitesimally curved in the fourth dimension, are tiny patches on whole 3-spheres of galactic size. So Sadoc's exercise is a thought experiment, like Einstein's gedankenexperiments about railroad embankments and trains moving at nearly the speed of light. It is no less illuminating, despite the symmetry it reveals not having a realization as an actual 3-sphere of actual molecules. And might not something very like it have an actual realization in the atomic realm? We know that atoms have their own complex internal structure, which we are unable to model geometrically in ordinary 3-dimensional space. Suppose such a model is impossible because an atom is actually a 4-polytope occupying a tiny spherical region of 4-dimensional space, and so we only find its constituent particles in close-packed helical orbits on the 3-sphere, in the manner of Sadoc's imaginary twisted molecules, but as real 4-dimensional helices of atomic scale. We would expect to find the atomic orbit of a fundamental particle in some discrete Hopf fibration characteristic of a symmetry group, that is, on the maximally symmetric isoclines of a discrete isoclinic rotation characteristic of some regular 4-polytope and the particle. == A theory of the Euclidean atom == <blockquote>Because quantum physics could be tested without being understood, it allowed humans to see how the universe worked without knowing why.<ref>Sebastian Junger, In My Time of Dying</ref></blockquote> ... == Light and Mass are Reflection and Rotation == The phenomena of light and mass are expressions of reflection symmetries and rotation symmetries, respectively. ... Atoms are 4-polytopes, elementary objects with SO(4) rotational symmetry. Light is .... Motion in space is the propagation of the elementary objects of light and matter in Coxeter congruent transformations by kaleidoscopic self-reflections, like the motion of self-reproducing cellular automata in [[Conway's Game of Life|Conway's game of life]]. ... Light is discrete reflections. Mass is discrete rotations. Both are group actions, expressions of intrinsic symmetries. That is all of physics. === Atoms are 4-polytopes === ... == Relativity in real space of four or more orthogonal dimensions == Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions. General relativity is Galilean relativity in a general space of four or more orthogonal dimensions, e.g. in Euclidean 4-space <math>R^4</math>, spherical 4-space <math>S^4</math>, and any orthogonal 4-manifold. Light is a consequence of symmetry group reflections at quantum scale. Gravity and the other fundamental forces are consequences of rotations, which are consequences of quantum reflections. Light is discrete reflections. Gravity and all forces are discrete rotations. Both are group actions, expressions of intrinsic symmetries. That is all of physics. Every observer may properly see themself as stationary and the universe as an ''n''-sphere with themself at the center. The curvature of these spheres is a function of the rate at which causality evolves, and can be measured by the observer as the speed of light. === Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions === ...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here... Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in three spatial dimensions. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (In general relativity, discussed below, the actual rate of physical processes varies from place to place, and those differences are neither reciprocal nor illusory.) None of these Lorentz effects are beyond geometric explanation or paradoxical. The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, successive Euclidean spaces are dimensionally analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature, is an exact expression of intrinsic symmetries: that is Nother's great discovery. === General relativity is Galilean relativity in a general space of four orthogonal dimensions === ... == Dimensional relativity == Coxeter's kinetic law of <math>n</math>-dimensional congruent Euclidean transformations may be called ''dimensional relativity'', since it captures the theories of special and general relativity entire, and has its roots in dimensional analogy. Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessable by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated. By analogy to the surface of the earth, the bounding surface of a spherical region of <math>n</math>-dimensional Euclidean space is an <math>(n-1)</math>-sphere, a spherical space of one fewer dimensions than the <math>n</math>-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean <math>n</math>-spaces of increasing <math>n</math>, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating <math>n</math>-spaces. By the degree of dimensional analogy of which they are capable, some observers see deeper into <math>n</math>-dimensional space than others. == Polycentric spherical relativity == An intelligent observer equipped with the principle of relativity may perceive the universe from any inertial reference frame, not only from their own proper perspective. We see that every observer may properly view themself as stationary and the universe as an ''n''-sphere with themself at the center observing it, perceptually equidistant from all points on its surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything. This ''polycentric model'' of the universe is a further restatement of the principle of relativity. It is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. It should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849: "The universe is a sphere whose center is wherever there is intelligence."{{Sfn|Thoreau|1849|p=349|ps=; "The universe is a sphere whose center is wherever there is intelligence." [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}} == Revolutions == The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity ''c'', with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may, or may not, all have the same origin in space and time. As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment we dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed us that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a sense related to time, at least, it must be 4-dimensional. In this work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space. Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we now observe them, any more than they lie in the three dimensional hyperplane of local space in which we find everything residing in our solar system. When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us only by virtue of how long it takes their light to reach us. We can measure their distribution around us in 4-space, but that is simply how we choose to measure them, not a finding of how they are actually distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean ''n''-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity <math>c</math>, on more or less divergent paths from each other. But only much closer observation will reveal evidence of whether everything we see lies in the same 4-space, or if it is distributed in five or more dimensions, and how it is moving there. To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity <math>c</math>, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw displacements), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw displacement has ''two'' [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity <math>c</math> in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that each galaxy's own distinct 3-sphere is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to lightspeed long ago, in whatever big bang our atoms emerged from, and have never slowed down since. == Origins of the theory == Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of the geometry of Euclidean 4-space relativity, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] contains the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and did not describe our ordinary 3-space embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.<ref>{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}</ref> He invited us to imagine "A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions", but he was careful to disclaim parenthetically that "The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice." Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal of that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.'' The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified spacetime of four dimensions. Anco and Maghadam found that <small><math>SO(4)</math></small> breaks to ... <small><math>S^3</math></small>... if the energy in the Kepler orbit is negative (an elliptical orbit), and to ... <small><math>H^3</math></small> ... Minkowski spacetime if the energy is positive (a hyperbolic orbit). Because the planets orbit on ellipses in our 3-space, Euclidean 4-space is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the truer model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position of centrality as our exclusive conception of our place in space. ...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others. The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; "Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions."}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.<ref>{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}</ref>}} == Boundaries == <blockquote>Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.<ref>{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}</ref></blockquote> Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? ''What is the nature of the boundary which confines us to just three dimensions?'' We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell. Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined motions and objects. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. A boundary is an explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force. <blockquote>The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three .... In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it. We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed "Dimensional Analogy."<ref>{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}</ref></blockquote> I believe, but I cannot prove, that we live in real space, which is Schläfli's and Coxeter's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover in imagination and then explore physically, each an astonishing new enlightenment.<ref>{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}<blockquote> :We shall not cease from exploration :And the end of all our exploring :Will be to arrive where we started :And know the place for the first time. :Through the unknown, remembered gate :When the last of earth left to discover :Is that which was the beginning; :At the source of the longest river :The voice of the hidden waterfall :And the children in the apple-tree :Not known, because not looked for :But heard, half-heard, in the stillness :Between two waves of the sea. </blockquote></ref> Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. This project is forever beginning anew. Coxeter showed us that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether showed us all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions, in which all objects with mass move ceaselessly at the constant velocity <math>c</math>, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages. <blockquote> ::::::BEECH :Where my imaginary line :Bends square in woods, an iron spine :And pile of real rocks have been founded. :And off this corner in the wild, :Where these are driven in and piled, :One tree, by being deeply wounded, :Has been impressed as Witness Tree :And made commit to memory :My proof of being not unbounded. :Thus truth's established and borne out, :Though circumstanced with dark and doubt— :Though by a world of doubt surrounded. :::::::—''The Moodie Forester''<ref>{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}</ref> </blockquote> == Appendix: Sequence of regular 4-polytopes == {{Regular convex 4-polytopes|wiki=W:|columns=7}} == ... == {{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}} {{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}} {{Efn|name=radially equilateral}} {{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as "the convex hull of the neighbouring vertices of a given vertex".{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its "radius" equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}} {{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example: {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0) {{indent|5}}({{spaces|2}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>){{spaces|3}}({{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>) {{indent|5}}(–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>){{spaces|3}}(–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>) {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)<br> is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}} {{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60° rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the "left" is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}} {{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}} {{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; "In mathematics, the path that the (1, 1) knot on the torus traces is also known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two intersecting circles that are the cross-section of a torus by a well-chosen plane cutting it. Picking one such circle and rotating it around the torus axis, the resulting family of circles can be used to rule the torus. By nesting tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the (1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles]."}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}} {{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}} {{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}} {{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}} {{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}} {{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}} {{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}} {{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}} {{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}} {{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90^o bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60^o bend, or as a straight line with one 60^o bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}} {{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; "In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)"}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}} {{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}} {{Efn|Departing from any vertex V₀ in the original great hexagon plane of isoclinic rotation P₀, the first vertex reached V₁ is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P₁. P₁ is inclined to P₀ at a 60° angle.{{Efn|P₀ and P₁ lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V₂ is 120 degrees beyond V₁ along a second {{radic|3}} chord lying in another hexagonal plane P₂ that is Clifford parallel to P₀.{{Efn|P₀ and P₂ are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V₀ and V₂ are ''two'' {{radic|3}} chords apart{{Efn|V₀ and V₂ are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V₀ and V₂ are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P₀ and P₂ are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V₁ lies in both intersecting planes P₁ and P₂, as V₀ lies in both P₀ and P₁. But P₀ and P₂ have ''no'' vertices in common; they do not intersect.) The third vertex reached V₃ is 120 degrees beyond V₂ along a third {{radic|3}} chord lying in another hexagonal plane P₃ that is Clifford parallel to P₁. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V₀ to V₃ is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}} {{Sfn|Mamone, Pileio & Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹₄.}} ==Notes== {{Regular convex 4-polytopes Notelist|wiki=W:}} ==Citations== {{Regular convex 4-polytopes Reflist|wiki=W:}} ==References== {{Refbegin}} * {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}} * {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1}} * {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}} === [[Polyscheme|Polyschemes]] === {{Regular convex 4-polytopes Refs|wiki=W:}} {{Refend}} 5pfptzrp64n611y1clcqjvpoo6lry15 2823719 2823715 2026-08-20T20:53:18Z Dc.samizdat 2856930 /* Special relativity describes Euclidean 4-space */ 2823719 wikitext text/x-wiki = Real Euclidean four-dimensional space R⁴ = {{align|center|David Brooks Christie}} {{align|center|dc@samizdat.org}} {{align|center|Draft in progress}} {{align|center|June 2023 - August 2026}} <blockquote>'''Abstract:''' The physical universe is properly visualized as a Euclidean space of four orthogonal spatial dimensions. Space itself has a fourth orthogonal dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and our planet are only 3-dimensional objects, but nonetheless we can see in four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.</blockquote> == Summary == We observe that physical space has four perpendicular dimensions, not just three; atoms are [[W:4-polytope|4-polytopes]]; the sun is a 4-ball that is round in four dimensions; everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space; and our entire 3-space manifold is translating through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions. == A theory of the Euclidean cosmos == The physical universe is properly visualized as a [[w:Four-dimensional_space|Euclidean space of four orthogonal spatial dimensions]]. Space itself has a fourth orthogonal dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planets, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. All objects with mass move inertially through Euclidean 4-space at velocity <math>c</math> as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity <math>c</math> is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space. A typical spiral galaxy such as ours is a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our galaxy appear from our viewpoint to be distributed in a cloud of elliptical spirals occupying a flattened ellipsoid region of 3-dimensional space, but they are not so confined: they are distributed within a spherical region of 4-dimensional space. The galaxy's actual shape is spherical, not a flattened ellipsoid, but it is rounder than round can be in our ordinary experience: it occupies a hyperspherical region of space. The concentric spirals of stars that we observe lie on concentric [[W:3-sphere|3-sphere]]s (4-dimensional spheres), not on concentric 2-ellipsoids (3-dimensional elliptical spirals). Our sun and solar system lies on one of those concentric 3-spheres. More generally, orbits are circular in 4-space, and elliptical in the 3-space of their elliptic hyperplane. [[File:Hypersphere.png|thumb|Rotating illustration of the 4-ball galaxy showimg its spirals of star clouds on the surface of concentric 3-spheres, obtained by reverse sterographic projection from 3D images of the galaxy.]] The galaxy as a whole, or more properly its orbital center point, is translating through 4-space at velocity <math>c</math>, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity <math>c</math> in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity <math>c</math>. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the cylinder; their trajectories are screw-displacements, the compound of a simple rotation and a linear translation. The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around a barycentric axis. It is the tremendous inertial force of stars in motion at velocity <math>c</math> that holds the cylinder of motion together. The observed universe as a whole appears to be a 3-sphere expanding radially from a central origin point at velocity <math>c</math>, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. For all observers, the conjectured origin point of the universe corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space (the same point in the same Euclidean 4-space for all observers). The big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured separately, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity <math>c</math>. All objects in our solar system except the sun itself lie within this thinest three-dimensional manifold. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. The enclosing surface of a spherical region of 4-space is itself a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. We live within such a 3-space, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience, and it contains the earth, all the planets and the 3-dimensional space between them. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our particular 3-sphere is one of the galaxy's concentric 3-spheres of spiral star-clouds. The solar system occupies a tiny patch of this filmy 4-dimensional soap-bubble of galactic size, that is thicker-skinned than the diameter of an atom only in the interior of stars and supermassive objects. Our entire 3-sphere manifold, as a 3-spherical shell within the moving 4-ball galaxy, is translating through 4-space at velocity <math>c</math> with the galaxy, in a distinct direction that is orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the galaxy's translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of rotating objects through Euclidean space by screw translation. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity <math>c</math>, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. Any moving 3-dimensional manifold that is such an evolving surface boundary is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. Every object which we find occurring naturally in the solar system other than the sun itself, even the largest of 3-dimensional objects a planet, is a three-dimensional smear of atoms no thicker than one atom in its fourth dimension, which is the direction of its linear translation through 4-space at velocity <math>c</math>. The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be "heaped up" into larger 4-dimensional objects that form a lump in its moving surface. We have little understanding of such 4-dimensional lumps thicker than one atom, since they occur naturally in our vicinity only in the interior of the sun. In fact the sun is the only such lump occurring naturally in our solar system. We refer to 4-dimensional lumps of matter as plasma, and have little experimental knowledge of their geometry or internal structure. We know that such a lump as the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know nothing about its interior 4-ball. Every such moving 3-dimensional surface boundary of matter in the observed universe is evolving in four dimensions at velocity <math>c</math>. Its current location in 4-space corr esponds to the present moment in the proper time of its inertial reference frame. Its direction of movement at velocity <math>c</math> corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from atoms to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, two orthogonal inertial motions each at the constant universal rate of transformation <math>c</math>. Every object moves relative to universal 4-coordinate space on its own distinct geodesic spiral, a screw translation trajectory that is the compound of two orthogonal inertial motions, a rotation and a translation. Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity <math>c</math> in all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is <math>c\prime = 2c</math>, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity <math>c</math>. For example, we can look across the center of our mostly-empty 4-ball galaxy and see stars in the opposite sides of its concentric 3-sphere surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math> in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper space. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space. == Symmetries == It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel & Goodman-Strauss|2008}} As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. [[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}} <blockquote>Let <small><math>\mathrm{Q}</math></small> denote a rotation, <small><math>\mathrm{R}</math></small> a reflection, <small><math>\mathrm{T}</math></small> a translation, and let <small><math>\mathrm{Q}^q \mathrm{R}^r\mathrm{T}</math></small> denote a product of several such transformations, all commutative with one another. Then <small><math>\mathrm{RT}</math></small> is a glide-reflection (in two or three dimensions), <small><math>\mathrm{QR}</math></small> is a rotary-reflection, <small><math>\mathrm{QT}</math></small> is a screw-displacement, and <small><math>\mathrm{Q^2}</math></small> is a double rotation (in four dimensions).<br> Every orthogonal transformation is expressible as:<br> :<small><math>\mathrm{Q}^q \mathrm{R}^r</math></small><br> where <small><math>(2^q + r \le n)</math></small>, the number of dimensions.<br> Transformations involving a translation are expressible as:<br> :<small><math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}</math></small><br> where <small><math>(2^q + r + 1 \le n)</math></small>.<br> For <small><math>(n = 4)</math></small> in particular, every displacement is either a double rotation <small><math>\mathrm{Q}^2</math></small>, or a screw-displacement <small><math>\mathrm{QT}</math></small> [where the rotation component <small><math>\mathrm{Q}</math></small> is a simple rotation, but the <small><math>\mathrm{QT}</math></small> is chiral like a <small><math>\mathrm{Q^2}</math></small>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <small><math>\mathrm{QRT}</math></small>.</blockquote> If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a <small><math>\mathrm{Q^2}</math></small> or a <small><math>\mathrm{QT}</math></small>, because we can view any <small><math>\mathrm{QT}</math></small> as a <small><math>\mathrm{Q^2}</math></small> in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a <small><math>\mathrm{Q^2}</math></small>. By the same principle, we can view any <small><math>\mathrm{QT}</math></small> or <small><math>\mathrm{Q^2}</math></small> as an isoclinic (equi-angled) <small><math>\mathrm{Q^2}</math></small> by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (<small><math>\mathrm{T}</math></small>) for ''one'' of the two rotations (<small><math>\mathrm{Q}</math></small>). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (<small><math>\mathrm{Q}</math></small>) up to uncertainty, and can always distinguish the direction of their own proper time translation (<small><math>\mathrm{T}</math></small>). As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebra), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group <small><math>SO(4)</math></small> [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic <small><math>SO(4)</math></small> rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, stationary atoms exhibit the <small><math>SO(4)</math></small> symmetries of the discrete isoclinic (equi-angled) double rotations (<small><math>\mathrm{Q^2}</math></small>) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]]. == Special relativity describes Euclidean 4-space == <blockquote>Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.<ref>{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}</ref></blockquote> Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional "space" because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign to the three space coordinates so spacetime is hyperbolic, not a flat Euclidean 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was first described by Einstein himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction. Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity ''c'', in some 4-space direction. This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always ''c'', as measured by all observers from any inertial reference frame. This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source. But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity ''c''. In physics as it has been universally understood, observers are not supposed to be able to move at velocity ''c''. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four. In the Euclidean relativity alternative view, however, every observer is always moving at velocity ''c'' through the universe, which is real Euclidean 4-dimensional space <small><math>\mathbb{R^4}</math></small>. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity ''c''. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and proper space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity ''c'', in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space <small><math>\mathbb{R^4}</math></small>.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity ''c'' relative to universal 4-coordinate space, so the maximum relative velocity between two observers is 2''c'' when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to ''c'', it is the same measurement in different units. Special relativity measures all velocities in a 3-space of Minkowski spacetime. Euclidean relativity measures all velocities in Euclidean 4-space.}} So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity ''c'' in Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the "speed of light" ''c'', although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity ''c'', but in at least slightly different directions. In Einstein's relativity, the invariant ''c'' is the speed of light through 3-space. In Euclidean relativity, the invariant ''c'' is the speed of matter through 4-space! The speed of light through 3-space is also perceived as ''c'' by all observers, because they are each living in a moving 3-manifold that is moving through 4-space at velocity ''c''. Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same predictions about how observers in different reference frames will perceive each other's motions in time and space, and we shall see that they also agree on the predictions of general relativity. They both describe the same geometric relations of space and time, but they describe that geometry as embedded in two very different universal host spaces: Minkowski spacetime versus Euclidean 4-space. ...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity <math>c</math> through space and proper time ...cite Yamashita{{Sfn|Yamashita|2023}} on the equivalence of special relativity and Euclidean 4-space relativity ...cite Kappraff & Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff & Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff & Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords. Euclidean relativity is not even a fringe theory; no physicists have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could "catch up" with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at ''c'' (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than ''c''. Euclidean relativity is a revolutionary theory indeed, in which ''c'' cannot possibly be the speed of light! We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for <math>\mathbb{R^4}</math> to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be <math>c\prime = 2c</math>, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate linearly along the edge of a unit 4-hypercube. This is conceivable in 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number <small><math>\sqrt{4}</math></small>. == An object's motion in space is the product of its discrete self-reflections == Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a small number of discrete self-reflections. Any action of a geometric object that transforms its position and orientation in space may be measured as a distinct group of self-reflections of the object in its own surfaces. Any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete set of local self-reflections. Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which touch (intersect each other). When a object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality. Coxeter's laws of motion are a geometric counterpart to Newton's laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures. But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. For example, they give us geometric pictures of all the possible motions of objects in four dimensional Euclidean space: <blockquote>Every orthogonal transformation in 4-space is expressible as:<br> :<small><math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t</math></small><br> where <small><math>(2^q + r + t \le 4)</math></small>. Every displacement is either a double rotation <small><math>\mathrm{Q}^2</math></small>, or a screw-displacement <small><math>\mathrm{QT}</math></small> [where the rotation component <small><math>\mathrm{Q}</math></small> is a simple rotation, but the <small><math>\mathrm{QT}</math></small> is chiral like a <small><math>\mathrm{Q^2}</math></small>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <small><math>\mathrm{QRT}</math></small>.</blockquote> While this description should be understood as simple geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (<small><math>\mathrm{Q}</math></small>), reflection (<small><math>\mathrm{R}</math></small>) and translation (<small><math>\mathrm{T}</math></small>) are just what they are in three-dimensional space, but double rotation (<small><math>\mathrm{Q}^2</math></small>) is something new and unprecedented in our physical experience, because double rotations cannot occur until you have four or more dimensions of space to rotate in. ...to readers who have not studied Coxeter (almost all readers including TAC), the blockquote above is "just math", not visualizable geometry...but I could describe Coxeter's congruent transformations in 4-space here geometrically: I could say clearly what they mean in spatial terms, in language anyone can understand, because they don't require any math to be understood; the "math" here is really just simple pictures (reflections and rotations); even double rotations can be visualized by dimensional analogy, as compounds of simple rotations...since even most physicists are unacquainted with Coxeter geometry, it might be useful to do this here... == Light propagates through 4-space at twice its apparent velocity ''c''== Coxeter's geometric laws of motion apply to all objects with mass in 4-dimensional Euclidean space, but we find there is an additional kind of displacement which applies only to massless particles such as photons. Light quanta (photons) translate through 4-space by 4-dimensional reflection <small><math>\mathrm{R}^4</math></small>, which may be termed a double translation <small><math>\mathrm{T}^2</math></small>, a pure translation via two pairs of parallel reflections, without any rotation component <small><math>\mathrm{Q}</math></small>. Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by <small><math>\mathrm{QT}</math></small>, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic <small><math>\mathrm{Q^2}</math></small>, an isoclinically rotating object such as an atom. A simple rotation <small><math>\mathrm{Q}</math></small> or simple translation <small><math>\mathrm{T}</math></small> is a double reflection <small><math>\mathrm{R^2}</math></small>, so a <small><math>\mathrm{QT}</math></small> or <small><math>\mathrm{Q^2}</math></small> is also an <small><math>\mathrm{R^4}</math></small>, but not with the same group of reflection angles as a light signal <small><math>\mathrm{R^4}</math></small>. A translation <small><math>\mathrm{T = R^2}</math></small> is a double reflection in two parallel planes, and a rotation <small><math>\mathrm{Q = R^2}</math></small> is a double reflection in two intersecting planes, as in a <small><math>\mathrm{QT = R^4}</math></small> which is both at once. A double translation <small><math>\mathrm{T^2 = R^4}</math></small> is two double reflections in pairs of parallel planes at once, a reflection in four or more non-intersecting parallel planes; it is all translation and no rotation. In a <small><math>\mathrm{T^2}</math></small> all the motion goes to translation, so the translation goes twice as far as the simple translation <small><math>\mathrm{T}</math></small> in a <small><math>\mathrm{QT}</math></small>. A double translation <small><math>\mathrm{T^2 = R^4}</math></small> is the opposite of a double rotation <small><math>\mathrm{Q^2 = R^4}</math></small>, which is stationary but rotates twice as fast as the simple rotation <small><math>\mathrm{Q}</math></small> in a <small><math>\mathrm{QT}</math></small>. The product of the two translations in a <small><math>\mathrm{T^2}</math></small> is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple <small><math>\mathrm{T}</math></small> over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double-the-distance translation, but without any rotation component, so it cannot carry any mass with it. A <small><math>\mathrm{T^2}</math></small> cannot reposition a 4-polytope the way a <small><math>\mathrm{QT}</math></small> does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter. ...lensing of double translations <small><math>\mathrm{T^2 = R^4}</math></small> in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet... == The Kepler problem is framed in Euclidean 4-space == The [[W:Kepler problem|Kepler problem]] is named for [[W:Johannes Kepler|Johannes Kepler]], arguably the greatest geometer since the ancients up to [[w:Ludwig Schläfli|Ludwig Schläfli]], who proposed [[W:Kepler's laws of planetary motion|Kepler's laws of planetary motion]] which solved the problem of the orbits of the planets, and investigated the types of forces that would result in orbits obeying those laws. Those forces were later identified by [[W:Isaac Newton|Isaac Newton]] in his[[W:Philosophiæ Naturalis Principia Mathematica| Principia]], where he proves what today might be called the "inverse Kepler problem": the orbit characteristics require the force to depend on the inverse square of the distance.<ref>{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton & Company|isbn=978-0393039184}}</ref> The inverse square law behind the Kepler problem is the [[W:Central force|central force]] law which governs not only [[W:Newtonian gravity|Newtonian gravity]] and celestial orbits, but also the motion of two charged particles in [[W:Coulomb’s law|Coulomb’s law]] of [[W:Electrostatics|electrostatics]]; it applies to attractive or repulsive forces. Problems in which two bodies interact by a central force that varies as the [[W:Inverse square law|inverse square]] of the distance between them are called Kepler problems. Thus the [[W:Hydrogen atom|hydrogen atom]] is a Kepler problem, since it comprises two charged particles interacting by Coulomb's law, another inverse-square central force. Using classical mechanics, the solution to a Kepler problem can be expressed as a [[W:Kepler orbit|Kepler orbit]] using six kinematical variables or [[W:Orbital elements|orbital elements]]. The solution conserves an orbital element called the [[W:Laplace–Runge–Lenz vector|Laplace–Runge–Lenz (LRL) vector]], a [[W:Constant of motion|constant of motion]], meaning that it is the same no matter where it is calculated on the orbit. The LRL vector was essential in the first quantum mechanical derivation of the [[W:Atomic emission spectrum|spectrum]] of the hydrogen atom, but this approach has rarely been used since the development of the [[W:Schrödinger equation|Schrödinger equation]]. The conservation of the LRL vector corresponds to the <small><math>SO(4)</math></small> symmetry, by Nother's theorem. The LRL vector lies orthogonal to both the orbital plane and the angular momentum vector of the Kepler orbit; we observe that it lies in a fourth orthogonal dimension. Fock in 1935<ref>V. Fock, Zur Theorie des Wasserstoffatoms, Zeitschrift für Physik. 98 (3-4) (1935), 145–154.</ref> and Moser in 1970<ref>J. Moser, Regularization of Kepler’s problem and the averaging method on a manifold, Commun. Pure Appl. 23 (1970), 609–636</ref> observed that the Kepler problem is mathematically equivalent to non-affine geodesic motion (a particle moving freely) on the surface of a 3-sphere, so that the whole problem is symmetric under certain rotations of the four-dimensional space. This higher-dimensional symmetry results in two well-known properties of the Kepler problem: the momentum vector always moves in a perfect circle and, for a given total energy, all such velocity circles intersect each other in the same two points. ... Relativity establishes that an orbit in space is viewed in a different way in each distinct inertial reference frame. Depending on the choice of reference frame, the same Kepler system may be seen to be performing any one of a sequence of relativistically equivalent rotations in 4-space, on a continuum from an isoclinic rotation (Q²) in the orbit's proper reference frame, to a screw transfer (QT) with a simple rotation component (Q) and a translation component (T) at velocity <math>c</math>, in the universal reference frame of 4-coordinate space wherein every object is seen to be translating at velocity <math>c</math>. In reference frames between these two limit cases, the orbit is seen to be performing a double rotation (Q²) at two unequal, completely orthogonal angular rates of rotation: an elliptical double rotation. These include the reference frames of most typical observers, who are moving slowly relative to the observed orbital system's reference frame (their relative motion is a small fraction of the speed of light). ...this is probably misplaced here and should not interrupt the discussion at this point: ...These typical observations agree closely with the predictions of special relativity, because the non-isoclinic elliptical (Q²) resembles a (QT), since one of its two completely orthogonal rotations (Q) has such a long period that it is almost indistinguishable from a straight translation (T). All orbits in 4-space are isoclinic in their own reference frame. Orbiting objects in their own proper Kepler systems follow circular geodesic isoclines through 4-space. Orbits in 4-space are perfectly circular in their own reference frame, as Copernicus assumed the orbits of planets to be. It is the orbit's path through the 3-space of its elliptic hyperplane that is an ellipse, as Kepler found it to be. ...cite Jesper Goransson's very concise paper The geodesic circle that an orbiting object follows through 4-space in the proper reference frame of its own Kepler system is not a simple great circle which turns in two orthogonal dimensions. It is a helical great circle that turns in four orthogonal dimensions at once.{{Efn|Geodesic orbits in 4-space are not simple 2-dimensional great circles; they are helical 4-dimensional great circles that curve in all four dimensions at once. Their circular trajectories are helixes which we call ''isoclines'', since they are the paths taken by points on a rigid object undergoing isoclinic rotation.}} Such circles lie outside our physical experience, since our local space has only three orthogonal dimensions. Nonetheless we can visualize them in imagination, because their helical, circular shape is perfectly well defined by the kinematical variables of the Kepler orbit. The real physical correlates of abstract orthogonal planes and rotation angles are already familiar to us viscerally in our body-language of physical experience, since we are endowed biologically with highly evolved visual signal processing engines. These enable us to see and understand spatial relations and motions, including rotations, without even thinking about angles and orthogonal planes. This physical endowment is an inborn capacity for dimensional analogy which our biologic evolution has provided. All our instinctive spatial reasoning is by dimensional analogy from flat 2-dimensional retinal images to 3-dimensional scenes, using our powerful inborn visualization capacities of reverse stereographic projection and pattern recognition. We humans are thus very well equipped with everything we need to see in four-dimensional space, except experience. ... Recently Anco and Moghadam found that through Noether’s theorem in reverse, the LRL vector gives rise to a corresponding infinitesimal dynamical symmetry on the kinematical variables, which they show to be the semi-direct product of <small><math>SO(3)</math></small> and <small><math>\mathbb{R^3}</math></small>, in contrast to the <small><math>SO(4)</math></small> symmetry group generated by the LRL symmetries and the rotations.{{Sfn|Anco|Moghadam|2026|ps=; The physically relevant part of the LRL vector is its direction ... since its magnitude is just a function of energy and angular momentum.}} This remarkable symmetry breaking is expressive of the ''dimensional relativity'' between ordinary 3-space <small><math>\mathbb{R^3}</math></small>, spherical space <small><math>S^3</math></small> and Euclidean space <small><math>\mathbb{R^4}</math></small>. Consider a hydrogen atom in a Kepler orbit: for example, a hydrogen atom moving freely in space in an orbit around the sun. It is a ''double'' Kepler problem: an electrostatic Kepler problem within itself, and a gravitational Kepler problem in its environment. The ''single'' electrostatic Kepler problem of a hydrogen atom moving freely in space beyond any gravitational influence is a problem in special relativity. In our Euclidean 4-space model, this atom viewed as stationary in its own proper reference frame exhibits an <small><math>SO(4)</math></small> rotation symmetry corresponding to an isoclinic double rotation (<small><math>\mathrm{Q^2}</math></small>). The fourth dimension in this reference frame is the atom's proper time vector; it has constant velocity <math>c</math> and constant direction. From the point of view of our universal 4-coordinate space (which cannot be the proper inertial reference frame of any physical observer, all of whom are moving relative to it at velocity ''c''), the entire Kepler system (the atom) is translating through 4-space via a screw translation (<small><math>\mathrm{QT}</math></small>) at constant velocity <math>c</math>. From this viewpoint the atom has only a simple <small><math>SO(3)</math></small> rotation component (<small><math>\mathrm{Q}</math></small>), breaking its stationary <small><math>SO(4)</math></small> isoclinic rotation symmetry (<small><math>\mathrm{Q^2}</math></small>). Because each discrete part of the rotating atom moves along a helical trajectory through 4-space, the atom is in orbit around a barycentric axis (like a star in a galaxy), but only in a tiny orbit within its own radius, which is its inertial domain of rotation. The straight 4-dimensional cylinder it progresses along at velocity <math>c</math> is very narrow: only the diameter of the rotating atom itself. The gravitational Kepler problem of a hydrogen atom in a Kepler orbit around the sun is a problem in general relativity. In our 4-space model, this atom viewed in its own proper reference frame exhibits the same <small><math>SO(4)</math></small> rotation symmetry as it did in the electrostatic Kepler problem where the atom was translating linearly through space. The Kepler system in this case is not just the atom; it is the entire solar system. The LRL vector of this Kepler system is the proper time vector of the atom's inertial reference frame; once again it has constant velocity ''and constant direction''. Although the momentum vector moves in a perfect circle as the atom orbits the sun, the 4-space LRL vector does not move at all: it is a constant of motion, of linear motion (<small><math>\mathrm{T}</math></small>) of the Kepler system (the entire solar system in this case) in a constant 4-space direction, the proper time direction of the system. The direction of the system's proper time vector would vary under some kinds of acceleration of the atom, but it is constant under this kind of orbital acceleration. It continues to point in the same direction, like a 4-space compass needle, as the atom winds its way along its spiral path around the axis of the sun's straight-line translation through 4-space at velocity <math>c</math>. This compass needle always points in the direction the sun is moving, not the direction the atom is moving at any instant. ...Its Kepler orbit around the sun is its <small><math>SO(3)</math></small> rotation component (<small><math>\mathrm{Q}</math></small>). Although the atom is moving on a geodesic circle in the second problem, by the [[equivalence principle]] the difference in the state of the atomic systems in these two problems cannot be observed by examining the atoms alone. Even from another inertial reference frame, where the atom in the second problem is seen to be translating through 4-space via a wide screw translation (<small><math>\mathrm{QT}</math></small>) around the sun's axis of motion, there is still no difference between the two problems which can be detected by examining only the atoms within their own proper reference frames (even over time), because the LRL vector (<small><math>\mathrm{T}</math></small>) is a constant of motion of the entire system in both cases. ...Anco and Maghadam found that <small><math>SO(4)</math></small>) breaks to ... <small><math>S^3</math></small>)... if the energy in the Kepler orbit is negative (an elliptical orbit), and to ... <small><math>H^3</math></small>) ... Minkowski spacetime if the energy is positive (a hyperbolic orbit). ... Finally we consider a third problem in which a hydrogen atom enters the solar system as a comet, loops around the sun and exits the solar system again. This atom... ... As Hamilton found when he discovered the quaternions, we see that it is necessary to admit a fourth dimension to the system in order to properly model the problem: in Hamilton's case the general problem of ..., and in our case the Kepler problem. These are instances of the same problem in 4-dimensional Euclidean geometry, and indeed a solution to the Kepler problem in quaternions (the four Cartesian coordinates of Euclidean 4-space) is a solution to it in our model of the 4-coordinate Euclidean cosmos. == Distribution of stars in our galaxy == The stars in our own galaxy appear to us to be a rotating spiral cluster in 3-dimensional space. By assuming that light from them reaches us on straight lines through space, by assuming that we can measure their distance from us by its red shift, and by assuming that they are distributed in three dimensions of space, we have plotted their locations in 3-space. If we abandon the last of those three assumptions, we can just as easily reinterpret that dataset to plot their distribution around us in 4-dimensional space, and see how they actually lie. When we perform this experiment on the data for the stars in our galaxy, do we indeed find that they are distributed non-uniformly in various concentric spirals, but the spirals lie on the surface of various 3-spheres, rather than in elliptical orbits as we saw them in 3-space? That would be an expected consequence of the special rotational symmetry group of 4-space <small><math>SO(4)</math></small>, in which circular (isoclinic) orbits are the geodesics (shortest rotational paths) rather than elliptical (non-equi-angled double rotation) orbits. ...have to perform this experiment somehow, at least as a conclusive thought experiment, before I publish this paper... == Rotations == The [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotations]] of the convex [[W:regular 4-polytope|regular 4-polytope]]s are usually described as discrete rotations of a rigid object. For example, the rigid [[24-cell]] can rotate in a [[24-cell#Great hexagons|hexagonal]] (6-vertex) central [[24-cell#Planes of rotation|plane of rotation]]. A 4-dimensional [[24-cell#Isoclinic rotations|''isoclinic'' rotation]] (as distinct from a [[24-cell#Simple rotations|''simple'' rotation]] like the ones that occur in 3-dimensional space) is a ''diagonal'' rotation in multiple [[W:Clifford parallel|Clifford parallel]] [[24-cell#Geodesics|central planes]] of rotation at once. It is diagonal because it is a [[W:SO(4)#Double rotations|double rotation]]: in addition to rotating in parallel (like wheels), the multiple planes of rotation also tilt sideways in the completely orthogonal plane of rotation (like coins flipping) into each other's planes. Consequently, the path taken by each vertex is a [[24-cell#Helical hexagrams and their isoclines|twisted helical circle]], rather than the ordinary flat great circle a vertex follows in a simple rotation. In a rigid 4-polytope rotating isoclinically, ''all'' the vertices lie in one of the parallel planes of rotation, so all the vertices move in parallel along Clifford parallel twisting circular paths. [[24-cell#Clifford parallel polytopes|Clifford parallel planes]] are not parallel in the normal sense of parallel planes in three dimensions; the vertices are all moving in different directions around the [[W:3-sphere|3-sphere]]. In one complete 360° isoclinic revolution, a rigid 4-polytope turns itself inside out. This is sufficiently different from the simple rotations of rigid bodies in our 3-dimensional experience that a [[24-cell#Rotations|detailed description]] enabling the reader to properly visualize its counter-intuitive consequences runs to many pages and illustrations, with many accompanying pages of explanatory notes on surprising phenomena that arise in 4-dimensional space: [[24-cell#Great squares|completely orthogonal planes]], [[24-cell#Clifford parallel polytopes|Clifford parallelism]]{{Efn|name=Clifford parallels}} and [[W:Hopf fibration|Hopf fiber bundles]], [[24-cell#Isoclinic rotations|isoclinic geodesic paths]], and [[24-cell#Double rotations|chiral (mirror image) pairs of rotations]], among other complexities. Moreover, the characteristic rotations of the various regular 4-polytopes are all different; each is a unique surprise. [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|The 6 regular convex 4-polytopes]] have different numbers of vertices (5, 8, 16, 24, 120 and 600 respectively) and those with fewer vertices occur inscribed in those with more vertices (with one exception), with the result that the more complex 4-polytopes subsume the kinds of rotations characteristic of their less complex predecessors, as well as each having a characteristic kind of rotation not found in their predecessors. None of these symmetries is to be found in 3-dimensional space, although their simpler 3-dimensional analogues are all present there. [[W:Euclidean geometry#Higher dimensions|Four dimensional Euclidean space]] is more complicated (and more interesting) than three dimensional space because there is more room in it, in which unprecedented things can happen. It subsumes 3-dimensional space, with all of the symmetries we are accustomed to, and adds astonishing new surprises. These are hard for us to visualize, because the only way we can experience them is in our imagination; we have no body of sensory experience in 4-dimensional space to draw upon, other than our evolution in time. For that reason (our difficulty in visualizing them), descriptions of isoclinic rotations usually begin and end with rigid rotations: [[24-cell#Isoclinic rotations|for example]], all 24 vertices of a single rigid 24-cell rotating in unison, with 6 vertices evenly spaced around each of 4 Clifford parallel twisted circles.{{Efn|name=360 degree geodesic path visiting 3 hexagonal planes}} But that is only the simplest case, which is easiest for us to understand. Compound and [[W:Kinematics|kinematic]] 24-cells (with moving parts) are even more interesting (and more complicated) than the rotation of a single rigid 24-cell. To begin with, when we examine the individual parts of a single rigid 24-cell that are moving in an isoclinic rotation, such as the orbits of individual vertices, we can imagine a case where fewer than 24 point-objects are orbiting on those twisted circular paths at once. [[24-cell#Reflections|For example]], if we imagine just 8 point-objects, evenly spaced around the 24-cell at [[24-cell#Reciprocal constructions from 8-cell and 16-cell|the 8 vertices that lie on the 4 coordinate axes]], and rotate them isoclinically along exactly the same orbits they would take in the above-mentioned rotation of a rigid 24-cell, then in the course of a single 360° rotation the 8 point-objects will trace out the whole 24-cell, with just one point-object reaching each of the 24 vertex positions just once, and no point-object colliding with (or even crossing the path of) any other at any time. This is an example of a discrete Hopf fibration. But it is still an example of a rigid object in a discrete isoclinic rotation: a rigid 8-vertex object (called the 4-[[W:orthoplex|orthoplex]] or [[16-cell]]) performing one half of the characteristic rotation of the 24-cell. We can also imagine ''combining'' distinct isoclinic rotations. What happens when multiple point-objects are orbiting at once, but do ''not'' all follow the Clifford parallel paths characteristic of the ''same'' distinct rigid rotation? What happens when we combine orbits from distinct rotations characteristic of different 4-polytopes, for example when different rigid 4-polytopes are concentric and rotating simultaneously in their characteristic ways? What kinds of such hybrid rotations are possible in the same 3-sphere shell without collisions? In adjacent concentric shells without asymmetric imbalance? What sort of [[Kinematics of the cuboctahedron|kinematic polytopes]] do they trace out, and how do their [[24-cell#Clifford parallel polytopes|component parts]] relate to each other as they move? Is there (sometimes) some kind of mutual stability amid their lack of combined rigidity? Visualizing isoclinic rotations (rigid and otherwise) allows us to explore such questions of [[W:kinematics|kinematics]], and where dynamic stabilities arise, of [[wikipedia:kinetics (physics)|kinetics]]. In four dimensions, we discover that space has more room in it than we have experienced, which permits previously unimagined motions. Even 3-space is more commodious than we thought; when it is curved and lies embedded in a higher-dimensional space, it permits previously impossible symmetric packings. Sadoc studied double-twisted 3-dimensional molecules, and imagined them embedded in 4-dimensional space as the Hopf fibrations of regular 4-polytopes. He found that these molecules would close-pack on the 3-sphere perfectly without exhibiting any torsion, although their packing in ordinary flat 3-space is imperfect, "frustrated" by their twisted geometry. <blockquote>The frustration, which arises when the molecular orientation is transported along the two [spiral] AB paths of figure 1 [double twist helix], is imposed by the very topological nature of the Euclidean space R³. It would not occur if the molecules were embedded in the non-Euclidean space of the [[W:3-sphere|3-sphere]] S³, or hypersphere. This space with a homogeneous positive curvature can indeed be described by equidistant and uniformly twisted fibers, along which the molecules can be aligned without any conflict between compactness and [[W:torsion of a curve|torsion]].... The fibres of this [[W:Hopf fibration|Hopf fibration]] are great circles of S³, the whole family of which is also called the [[W:Clifford parallel|Clifford parallel]]s.{{Efn|name=Clifford parallels}} Two of these fibers are C_∞ symmetry axes for the whole fibration; each fibre makes one turn around each axis and regularly rotates when moving from one axis to another.{{Efn|name=helical geodesic}} These fibers build a double twist configuration while staying parallel, i.e. without any frustration, in the whole volume of S³.{{Efn|name=Petrie polygon of a honeycomb}} They can therefore be used as models to study the condensation of long molecules in the presence of a double twist constraint.{{Sfn|Sadoc & Charvolin|2009|loc=§1.2 The curved space approach|ps=; studies the helical orientation of molecules in crystal structures and their imperfect packings ("frustrations") in 3-dimensional space.}}</blockquote> Of course we do not find molecules condensing to close-pack the 3-sphere in our experience, and Sadoc does not say that we do. We find 3-spheres in the atomic realm (if atoms are 4-polytopes), and in the cosmic realm (as the surface boundaries of stars, and the concentric surfaces of galaxies). But in between, in the realm of ordinary experience which includes the molecular realm, ourselves and all the objects we can materially handle or observe up close including the planets, we are confined together by gravity as inertia within a curved 3-dimensional space that is no more than one atom thick in the fourth spatial dimension. That is why in the molecular realm we find only objects that occupy 3-spaces which, though infinitesimally curved in the fourth dimension, are tiny patches on whole 3-spheres of galactic size. So Sadoc's exercise is a thought experiment, like Einstein's gedankenexperiments about railroad embankments and trains moving at nearly the speed of light. It is no less illuminating, despite the symmetry it reveals not having a realization as an actual 3-sphere of actual molecules. And might not something very like it have an actual realization in the atomic realm? We know that atoms have their own complex internal structure, which we are unable to model geometrically in ordinary 3-dimensional space. Suppose such a model is impossible because an atom is actually a 4-polytope occupying a tiny spherical region of 4-dimensional space, and so we only find its constituent particles in close-packed helical orbits on the 3-sphere, in the manner of Sadoc's imaginary twisted molecules, but as real 4-dimensional helices of atomic scale. We would expect to find the atomic orbit of a fundamental particle in some discrete Hopf fibration characteristic of a symmetry group, that is, on the maximally symmetric isoclines of a discrete isoclinic rotation characteristic of some regular 4-polytope and the particle. == A theory of the Euclidean atom == <blockquote>Because quantum physics could be tested without being understood, it allowed humans to see how the universe worked without knowing why.<ref>Sebastian Junger, In My Time of Dying</ref></blockquote> ... == Light and Mass are Reflection and Rotation == The phenomena of light and mass are expressions of reflection symmetries and rotation symmetries, respectively. ... Atoms are 4-polytopes, elementary objects with SO(4) rotational symmetry. Light is .... Motion in space is the propagation of the elementary objects of light and matter in Coxeter congruent transformations by kaleidoscopic self-reflections, like the motion of self-reproducing cellular automata in [[Conway's Game of Life|Conway's game of life]]. ... Light is discrete reflections. Mass is discrete rotations. Both are group actions, expressions of intrinsic symmetries. That is all of physics. === Atoms are 4-polytopes === ... == Relativity in real space of four or more orthogonal dimensions == Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions. General relativity is Galilean relativity in a general space of four or more orthogonal dimensions, e.g. in Euclidean 4-space <math>R^4</math>, spherical 4-space <math>S^4</math>, and any orthogonal 4-manifold. Light is a consequence of symmetry group reflections at quantum scale. Gravity and the other fundamental forces are consequences of rotations, which are consequences of quantum reflections. Light is discrete reflections. Gravity and all forces are discrete rotations. Both are group actions, expressions of intrinsic symmetries. That is all of physics. Every observer may properly see themself as stationary and the universe as an ''n''-sphere with themself at the center. The curvature of these spheres is a function of the rate at which causality evolves, and can be measured by the observer as the speed of light. === Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions === ...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here... Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in three spatial dimensions. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (In general relativity, discussed below, the actual rate of physical processes varies from place to place, and those differences are neither reciprocal nor illusory.) None of these Lorentz effects are beyond geometric explanation or paradoxical. The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, successive Euclidean spaces are dimensionally analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature, is an exact expression of intrinsic symmetries: that is Nother's great discovery. === General relativity is Galilean relativity in a general space of four orthogonal dimensions === ... == Dimensional relativity == Coxeter's kinetic law of <math>n</math>-dimensional congruent Euclidean transformations may be called ''dimensional relativity'', since it captures the theories of special and general relativity entire, and has its roots in dimensional analogy. Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessable by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated. By analogy to the surface of the earth, the bounding surface of a spherical region of <math>n</math>-dimensional Euclidean space is an <math>(n-1)</math>-sphere, a spherical space of one fewer dimensions than the <math>n</math>-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean <math>n</math>-spaces of increasing <math>n</math>, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating <math>n</math>-spaces. By the degree of dimensional analogy of which they are capable, some observers see deeper into <math>n</math>-dimensional space than others. == Polycentric spherical relativity == An intelligent observer equipped with the principle of relativity may perceive the universe from any inertial reference frame, not only from their own proper perspective. We see that every observer may properly view themself as stationary and the universe as an ''n''-sphere with themself at the center observing it, perceptually equidistant from all points on its surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything. This ''polycentric model'' of the universe is a further restatement of the principle of relativity. It is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. It should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849: "The universe is a sphere whose center is wherever there is intelligence."{{Sfn|Thoreau|1849|p=349|ps=; "The universe is a sphere whose center is wherever there is intelligence." [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}} == Revolutions == The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity ''c'', with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may, or may not, all have the same origin in space and time. As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment we dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed us that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a sense related to time, at least, it must be 4-dimensional. In this work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space. Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we now observe them, any more than they lie in the three dimensional hyperplane of local space in which we find everything residing in our solar system. When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us only by virtue of how long it takes their light to reach us. We can measure their distribution around us in 4-space, but that is simply how we choose to measure them, not a finding of how they are actually distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean ''n''-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity <math>c</math>, on more or less divergent paths from each other. But only much closer observation will reveal evidence of whether everything we see lies in the same 4-space, or if it is distributed in five or more dimensions, and how it is moving there. To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity <math>c</math>, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw displacements), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw displacement has ''two'' [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity <math>c</math> in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that each galaxy's own distinct 3-sphere is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to lightspeed long ago, in whatever big bang our atoms emerged from, and have never slowed down since. == Origins of the theory == Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of the geometry of Euclidean 4-space relativity, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] contains the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and did not describe our ordinary 3-space embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.<ref>{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}</ref> He invited us to imagine "A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions", but he was careful to disclaim parenthetically that "The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice." Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal of that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.'' The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified spacetime of four dimensions. Anco and Maghadam found that <small><math>SO(4)</math></small> breaks to ... <small><math>S^3</math></small>... if the energy in the Kepler orbit is negative (an elliptical orbit), and to ... <small><math>H^3</math></small> ... Minkowski spacetime if the energy is positive (a hyperbolic orbit). Because the planets orbit on ellipses in our 3-space, Euclidean 4-space is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the truer model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position of centrality as our exclusive conception of our place in space. ...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others. The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; "Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions."}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.<ref>{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}</ref>}} == Boundaries == <blockquote>Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.<ref>{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}</ref></blockquote> Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? ''What is the nature of the boundary which confines us to just three dimensions?'' We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell. Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined motions and objects. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. A boundary is an explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force. <blockquote>The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three .... In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it. We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed "Dimensional Analogy."<ref>{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}</ref></blockquote> I believe, but I cannot prove, that we live in real space, which is Schläfli's and Coxeter's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover in imagination and then explore physically, each an astonishing new enlightenment.<ref>{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}<blockquote> :We shall not cease from exploration :And the end of all our exploring :Will be to arrive where we started :And know the place for the first time. :Through the unknown, remembered gate :When the last of earth left to discover :Is that which was the beginning; :At the source of the longest river :The voice of the hidden waterfall :And the children in the apple-tree :Not known, because not looked for :But heard, half-heard, in the stillness :Between two waves of the sea. </blockquote></ref> Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. This project is forever beginning anew. Coxeter showed us that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether showed us all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions, in which all objects with mass move ceaselessly at the constant velocity <math>c</math>, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages. <blockquote> ::::::BEECH :Where my imaginary line :Bends square in woods, an iron spine :And pile of real rocks have been founded. :And off this corner in the wild, :Where these are driven in and piled, :One tree, by being deeply wounded, :Has been impressed as Witness Tree :And made commit to memory :My proof of being not unbounded. :Thus truth's established and borne out, :Though circumstanced with dark and doubt— :Though by a world of doubt surrounded. :::::::—''The Moodie Forester''<ref>{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}</ref> </blockquote> == Appendix: Sequence of regular 4-polytopes == {{Regular convex 4-polytopes|wiki=W:|columns=7}} == ... == {{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}} {{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}} {{Efn|name=radially equilateral}} {{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as "the convex hull of the neighbouring vertices of a given vertex".{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its "radius" equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}} {{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example: {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0) {{indent|5}}({{spaces|2}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>){{spaces|3}}({{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>) {{indent|5}}(–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>){{spaces|3}}(–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>) {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)<br> is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}} {{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60° rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the "left" is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}} {{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}} {{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; "In mathematics, the path that the (1, 1) knot on the torus traces is also known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two intersecting circles that are the cross-section of a torus by a well-chosen plane cutting it. Picking one such circle and rotating it around the torus axis, the resulting family of circles can be used to rule the torus. By nesting tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the (1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles]."}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}} {{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}} {{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}} {{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}} {{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}} {{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}} {{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}} {{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}} {{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}} {{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90^o bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60^o bend, or as a straight line with one 60^o bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}} {{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; "In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)"}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}} {{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}} {{Efn|Departing from any vertex V₀ in the original great hexagon plane of isoclinic rotation P₀, the first vertex reached V₁ is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P₁. P₁ is inclined to P₀ at a 60° angle.{{Efn|P₀ and P₁ lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V₂ is 120 degrees beyond V₁ along a second {{radic|3}} chord lying in another hexagonal plane P₂ that is Clifford parallel to P₀.{{Efn|P₀ and P₂ are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V₀ and V₂ are ''two'' {{radic|3}} chords apart{{Efn|V₀ and V₂ are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V₀ and V₂ are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P₀ and P₂ are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V₁ lies in both intersecting planes P₁ and P₂, as V₀ lies in both P₀ and P₁. But P₀ and P₂ have ''no'' vertices in common; they do not intersect.) The third vertex reached V₃ is 120 degrees beyond V₂ along a third {{radic|3}} chord lying in another hexagonal plane P₃ that is Clifford parallel to P₁. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V₀ to V₃ is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}} {{Sfn|Mamone, Pileio & Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹₄.}} ==Notes== {{Regular convex 4-polytopes Notelist|wiki=W:}} ==Citations== {{Regular convex 4-polytopes Reflist|wiki=W:}} ==References== {{Refbegin}} * {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}} * {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1}} * {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}} === [[Polyscheme|Polyschemes]] === {{Regular convex 4-polytopes Refs|wiki=W:}} {{Refend}} cpeuqexw09d6cosoh477owmimahas50 2823724 2823719 2026-08-20T20:59:45Z Dc.samizdat 2856930 /* A theory of the Euclidean cosmos */ 2823724 wikitext text/x-wiki = Real Euclidean four-dimensional space R⁴ = {{align|center|David Brooks Christie}} {{align|center|dc@samizdat.org}} {{align|center|Draft in progress}} {{align|center|June 2023 - August 2026}} <blockquote>'''Abstract:''' The physical universe is properly visualized as a Euclidean space of four orthogonal spatial dimensions. Space itself has a fourth orthogonal dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and our planet are only 3-dimensional objects, but nonetheless we can see in four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.</blockquote> == Summary == We observe that physical space has four perpendicular dimensions, not just three; atoms are [[W:4-polytope|4-polytopes]]; the sun is a 4-ball that is round in four dimensions; everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space; and our entire 3-space manifold is translating through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions. == A theory of the Euclidean cosmos == The physical universe is properly visualized as a [[w:Four-dimensional_space|Euclidean space of four orthogonal spatial dimensions]]. Space itself has a fourth orthogonal dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planets, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. All objects with mass move inertially through Euclidean 4-space at velocity <math>c</math> as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity <math>c</math> is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space. A typical spiral galaxy such as ours is a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our galaxy appear from our viewpoint to be distributed in a cloud of elliptical spirals occupying a flattened ellipsoid region of 3-dimensional space, but they are not so confined: they are distributed within a spherical region of 4-dimensional space. The galaxy's actual shape is spherical, not a flattened ellipsoid, but it is rounder than round can be in our ordinary experience: it occupies a hyperspherical region of space. The concentric spirals of stars that we observe lie on concentric [[W:3-sphere|3-sphere]]s (4-dimensional spheres), not on concentric 2-ellipsoids (3-dimensional elliptical spirals). Our sun and solar system lies on one of those concentric 3-spheres. More generally, orbits are circular in 4-space, and elliptical in the 3-space of their elliptic hyperplane. [[File:Hypersphere.png|thumb|Rotating illustration of the 4-ball galaxy showimg its spirals of star clouds on the surface of concentric 3-spheres, obtained by reverse sterographic projection from 3D images of the galaxy.]] The galaxy as a whole, or more properly its orbital center point, is translating through 4-space at velocity <math>c</math>, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity <math>c</math> in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity <math>c</math>. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the cylinder; their trajectories are screw-displacements, the compound of a simple rotation and a linear translation. The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around a barycentric axis. It is the tremendous inertial force of stars in motion at velocity <math>c</math> that holds the cylinder of motion together. The observed universe as a whole appears to be a 3-sphere expanding radially from a central origin point at velocity <math>c</math>, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. For all observers, the conjectured origin point of the universe corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space (the same point in the same Euclidean 4-space for all observers). The big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured separately, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity <math>c</math>. All objects in our solar system except the sun itself lie within this thinest three-dimensional manifold. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. The enclosing surface of a spherical region of 4-space is itself a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. We live within such a 3-space, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience, and it contains the earth, all the planets and the 3-dimensional space between them. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our particular 3-sphere is one of the galaxy's concentric 3-spheres of spiral star-clouds. The solar system occupies a tiny patch of this filmy 4-dimensional soap-bubble of galactic size, that is thicker-skinned than the diameter of an atom only in the interior of stars and supermassive objects. Our entire 3-sphere manifold, as a 3-spherical shell within the moving 4-ball galaxy, is translating through 4-space at velocity <math>c</math> with the galaxy, in a distinct direction that is orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the galaxy's translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of rotating objects through Euclidean space by screw translation. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity <math>c</math>, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. Any moving 3-dimensional manifold that is such an evolving surface boundary is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. Every object which we find occurring naturally in the solar system other than the sun itself, even the largest of 3-dimensional objects a planet, is a three-dimensional smear of atoms no thicker than one atom in its fourth dimension, which is the direction of its linear translation through 4-space at velocity <math>c</math>. The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be "heaped up" into larger 4-dimensional objects that form a lump in its moving surface. We have little understanding of such 4-dimensional lumps thicker than one atom, since they occur naturally in our vicinity only in the interior of the sun. In fact the sun is the only such lump occurring naturally in our solar system. We refer to 4-dimensional lumps of matter as plasma, and have little experimental knowledge of their geometry or internal structure. We know that such a lump as the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know nothing about its interior 4-ball. Every such moving 3-dimensional surface boundary of matter in the observed universe is evolving in four dimensions at velocity <math>c</math>. Its current location in 4-space corresponds to the present moment in the proper time of its inertial reference frame. Its direction of movement at velocity <math>c</math> corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from atoms to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, two orthogonal inertial motions each at the constant universal rate of transformation <math>c</math>. Every object moves relative to universal 4-coordinate space on its own distinct geodesic spiral, a screw translation trajectory that is the compound of two orthogonal inertial motions, a rotation and a translation. Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity <math>c</math> in all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is <math>c\prime = 2c</math>, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity <math>c</math>. For example, we can look across the center of our mostly-empty 4-ball galaxy and see stars in the opposite sides of its concentric 3-sphere surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math> in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper space. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space. == Symmetries == It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel & Goodman-Strauss|2008}} As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. [[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}} <blockquote>Let <small><math>\mathrm{Q}</math></small> denote a rotation, <small><math>\mathrm{R}</math></small> a reflection, <small><math>\mathrm{T}</math></small> a translation, and let <small><math>\mathrm{Q}^q \mathrm{R}^r\mathrm{T}</math></small> denote a product of several such transformations, all commutative with one another. Then <small><math>\mathrm{RT}</math></small> is a glide-reflection (in two or three dimensions), <small><math>\mathrm{QR}</math></small> is a rotary-reflection, <small><math>\mathrm{QT}</math></small> is a screw-displacement, and <small><math>\mathrm{Q^2}</math></small> is a double rotation (in four dimensions).<br> Every orthogonal transformation is expressible as:<br> :<small><math>\mathrm{Q}^q \mathrm{R}^r</math></small><br> where <small><math>(2^q + r \le n)</math></small>, the number of dimensions.<br> Transformations involving a translation are expressible as:<br> :<small><math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}</math></small><br> where <small><math>(2^q + r + 1 \le n)</math></small>.<br> For <small><math>(n = 4)</math></small> in particular, every displacement is either a double rotation <small><math>\mathrm{Q}^2</math></small>, or a screw-displacement <small><math>\mathrm{QT}</math></small> [where the rotation component <small><math>\mathrm{Q}</math></small> is a simple rotation, but the <small><math>\mathrm{QT}</math></small> is chiral like a <small><math>\mathrm{Q^2}</math></small>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <small><math>\mathrm{QRT}</math></small>.</blockquote> If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a <small><math>\mathrm{Q^2}</math></small> or a <small><math>\mathrm{QT}</math></small>, because we can view any <small><math>\mathrm{QT}</math></small> as a <small><math>\mathrm{Q^2}</math></small> in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a <small><math>\mathrm{Q^2}</math></small>. By the same principle, we can view any <small><math>\mathrm{QT}</math></small> or <small><math>\mathrm{Q^2}</math></small> as an isoclinic (equi-angled) <small><math>\mathrm{Q^2}</math></small> by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (<small><math>\mathrm{T}</math></small>) for ''one'' of the two rotations (<small><math>\mathrm{Q}</math></small>). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (<small><math>\mathrm{Q}</math></small>) up to uncertainty, and can always distinguish the direction of their own proper time translation (<small><math>\mathrm{T}</math></small>). As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebra), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group <small><math>SO(4)</math></small> [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic <small><math>SO(4)</math></small> rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, stationary atoms exhibit the <small><math>SO(4)</math></small> symmetries of the discrete isoclinic (equi-angled) double rotations (<small><math>\mathrm{Q^2}</math></small>) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]]. == Special relativity describes Euclidean 4-space == <blockquote>Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.<ref>{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}</ref></blockquote> Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional "space" because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign to the three space coordinates so spacetime is hyperbolic, not a flat Euclidean 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was first described by Einstein himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction. Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity ''c'', in some 4-space direction. This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always ''c'', as measured by all observers from any inertial reference frame. This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source. But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity ''c''. In physics as it has been universally understood, observers are not supposed to be able to move at velocity ''c''. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four. In the Euclidean relativity alternative view, however, every observer is always moving at velocity ''c'' through the universe, which is real Euclidean 4-dimensional space <small><math>\mathbb{R^4}</math></small>. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity ''c''. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and proper space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity ''c'', in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space <small><math>\mathbb{R^4}</math></small>.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity ''c'' relative to universal 4-coordinate space, so the maximum relative velocity between two observers is 2''c'' when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to ''c'', it is the same measurement in different units. Special relativity measures all velocities in a 3-space of Minkowski spacetime. Euclidean relativity measures all velocities in Euclidean 4-space.}} So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity ''c'' in Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the "speed of light" ''c'', although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity ''c'', but in at least slightly different directions. In Einstein's relativity, the invariant ''c'' is the speed of light through 3-space. In Euclidean relativity, the invariant ''c'' is the speed of matter through 4-space! The speed of light through 3-space is also perceived as ''c'' by all observers, because they are each living in a moving 3-manifold that is moving through 4-space at velocity ''c''. Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same predictions about how observers in different reference frames will perceive each other's motions in time and space, and we shall see that they also agree on the predictions of general relativity. They both describe the same geometric relations of space and time, but they describe that geometry as embedded in two very different universal host spaces: Minkowski spacetime versus Euclidean 4-space. ...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity <math>c</math> through space and proper time ...cite Yamashita{{Sfn|Yamashita|2023}} on the equivalence of special relativity and Euclidean 4-space relativity ...cite Kappraff & Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff & Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff & Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords. Euclidean relativity is not even a fringe theory; no physicists have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could "catch up" with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at ''c'' (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than ''c''. Euclidean relativity is a revolutionary theory indeed, in which ''c'' cannot possibly be the speed of light! We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for <math>\mathbb{R^4}</math> to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be <math>c\prime = 2c</math>, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate linearly along the edge of a unit 4-hypercube. This is conceivable in 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number <small><math>\sqrt{4}</math></small>. == An object's motion in space is the product of its discrete self-reflections == Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a small number of discrete self-reflections. Any action of a geometric object that transforms its position and orientation in space may be measured as a distinct group of self-reflections of the object in its own surfaces. Any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete set of local self-reflections. Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which touch (intersect each other). When a object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality. Coxeter's laws of motion are a geometric counterpart to Newton's laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures. But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. For example, they give us geometric pictures of all the possible motions of objects in four dimensional Euclidean space: <blockquote>Every orthogonal transformation in 4-space is expressible as:<br> :<small><math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t</math></small><br> where <small><math>(2^q + r + t \le 4)</math></small>. Every displacement is either a double rotation <small><math>\mathrm{Q}^2</math></small>, or a screw-displacement <small><math>\mathrm{QT}</math></small> [where the rotation component <small><math>\mathrm{Q}</math></small> is a simple rotation, but the <small><math>\mathrm{QT}</math></small> is chiral like a <small><math>\mathrm{Q^2}</math></small>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <small><math>\mathrm{QRT}</math></small>.</blockquote> While this description should be understood as simple geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (<small><math>\mathrm{Q}</math></small>), reflection (<small><math>\mathrm{R}</math></small>) and translation (<small><math>\mathrm{T}</math></small>) are just what they are in three-dimensional space, but double rotation (<small><math>\mathrm{Q}^2</math></small>) is something new and unprecedented in our physical experience, because double rotations cannot occur until you have four or more dimensions of space to rotate in. ...to readers who have not studied Coxeter (almost all readers including TAC), the blockquote above is "just math", not visualizable geometry...but I could describe Coxeter's congruent transformations in 4-space here geometrically: I could say clearly what they mean in spatial terms, in language anyone can understand, because they don't require any math to be understood; the "math" here is really just simple pictures (reflections and rotations); even double rotations can be visualized by dimensional analogy, as compounds of simple rotations...since even most physicists are unacquainted with Coxeter geometry, it might be useful to do this here... == Light propagates through 4-space at twice its apparent velocity ''c''== Coxeter's geometric laws of motion apply to all objects with mass in 4-dimensional Euclidean space, but we find there is an additional kind of displacement which applies only to massless particles such as photons. Light quanta (photons) translate through 4-space by 4-dimensional reflection <small><math>\mathrm{R}^4</math></small>, which may be termed a double translation <small><math>\mathrm{T}^2</math></small>, a pure translation via two pairs of parallel reflections, without any rotation component <small><math>\mathrm{Q}</math></small>. Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by <small><math>\mathrm{QT}</math></small>, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic <small><math>\mathrm{Q^2}</math></small>, an isoclinically rotating object such as an atom. A simple rotation <small><math>\mathrm{Q}</math></small> or simple translation <small><math>\mathrm{T}</math></small> is a double reflection <small><math>\mathrm{R^2}</math></small>, so a <small><math>\mathrm{QT}</math></small> or <small><math>\mathrm{Q^2}</math></small> is also an <small><math>\mathrm{R^4}</math></small>, but not with the same group of reflection angles as a light signal <small><math>\mathrm{R^4}</math></small>. A translation <small><math>\mathrm{T = R^2}</math></small> is a double reflection in two parallel planes, and a rotation <small><math>\mathrm{Q = R^2}</math></small> is a double reflection in two intersecting planes, as in a <small><math>\mathrm{QT = R^4}</math></small> which is both at once. A double translation <small><math>\mathrm{T^2 = R^4}</math></small> is two double reflections in pairs of parallel planes at once, a reflection in four or more non-intersecting parallel planes; it is all translation and no rotation. In a <small><math>\mathrm{T^2}</math></small> all the motion goes to translation, so the translation goes twice as far as the simple translation <small><math>\mathrm{T}</math></small> in a <small><math>\mathrm{QT}</math></small>. A double translation <small><math>\mathrm{T^2 = R^4}</math></small> is the opposite of a double rotation <small><math>\mathrm{Q^2 = R^4}</math></small>, which is stationary but rotates twice as fast as the simple rotation <small><math>\mathrm{Q}</math></small> in a <small><math>\mathrm{QT}</math></small>. The product of the two translations in a <small><math>\mathrm{T^2}</math></small> is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple <small><math>\mathrm{T}</math></small> over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double-the-distance translation, but without any rotation component, so it cannot carry any mass with it. A <small><math>\mathrm{T^2}</math></small> cannot reposition a 4-polytope the way a <small><math>\mathrm{QT}</math></small> does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter. ...lensing of double translations <small><math>\mathrm{T^2 = R^4}</math></small> in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet... == The Kepler problem is framed in Euclidean 4-space == The [[W:Kepler problem|Kepler problem]] is named for [[W:Johannes Kepler|Johannes Kepler]], arguably the greatest geometer since the ancients up to [[w:Ludwig Schläfli|Ludwig Schläfli]], who proposed [[W:Kepler's laws of planetary motion|Kepler's laws of planetary motion]] which solved the problem of the orbits of the planets, and investigated the types of forces that would result in orbits obeying those laws. Those forces were later identified by [[W:Isaac Newton|Isaac Newton]] in his[[W:Philosophiæ Naturalis Principia Mathematica| Principia]], where he proves what today might be called the "inverse Kepler problem": the orbit characteristics require the force to depend on the inverse square of the distance.<ref>{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton & Company|isbn=978-0393039184}}</ref> The inverse square law behind the Kepler problem is the [[W:Central force|central force]] law which governs not only [[W:Newtonian gravity|Newtonian gravity]] and celestial orbits, but also the motion of two charged particles in [[W:Coulomb’s law|Coulomb’s law]] of [[W:Electrostatics|electrostatics]]; it applies to attractive or repulsive forces. Problems in which two bodies interact by a central force that varies as the [[W:Inverse square law|inverse square]] of the distance between them are called Kepler problems. Thus the [[W:Hydrogen atom|hydrogen atom]] is a Kepler problem, since it comprises two charged particles interacting by Coulomb's law, another inverse-square central force. Using classical mechanics, the solution to a Kepler problem can be expressed as a [[W:Kepler orbit|Kepler orbit]] using six kinematical variables or [[W:Orbital elements|orbital elements]]. The solution conserves an orbital element called the [[W:Laplace–Runge–Lenz vector|Laplace–Runge–Lenz (LRL) vector]], a [[W:Constant of motion|constant of motion]], meaning that it is the same no matter where it is calculated on the orbit. The LRL vector was essential in the first quantum mechanical derivation of the [[W:Atomic emission spectrum|spectrum]] of the hydrogen atom, but this approach has rarely been used since the development of the [[W:Schrödinger equation|Schrödinger equation]]. The conservation of the LRL vector corresponds to the <small><math>SO(4)</math></small> symmetry, by Nother's theorem. The LRL vector lies orthogonal to both the orbital plane and the angular momentum vector of the Kepler orbit; we observe that it lies in a fourth orthogonal dimension. Fock in 1935<ref>V. Fock, Zur Theorie des Wasserstoffatoms, Zeitschrift für Physik. 98 (3-4) (1935), 145–154.</ref> and Moser in 1970<ref>J. Moser, Regularization of Kepler’s problem and the averaging method on a manifold, Commun. Pure Appl. 23 (1970), 609–636</ref> observed that the Kepler problem is mathematically equivalent to non-affine geodesic motion (a particle moving freely) on the surface of a 3-sphere, so that the whole problem is symmetric under certain rotations of the four-dimensional space. This higher-dimensional symmetry results in two well-known properties of the Kepler problem: the momentum vector always moves in a perfect circle and, for a given total energy, all such velocity circles intersect each other in the same two points. ... Relativity establishes that an orbit in space is viewed in a different way in each distinct inertial reference frame. Depending on the choice of reference frame, the same Kepler system may be seen to be performing any one of a sequence of relativistically equivalent rotations in 4-space, on a continuum from an isoclinic rotation (Q²) in the orbit's proper reference frame, to a screw transfer (QT) with a simple rotation component (Q) and a translation component (T) at velocity <math>c</math>, in the universal reference frame of 4-coordinate space wherein every object is seen to be translating at velocity <math>c</math>. In reference frames between these two limit cases, the orbit is seen to be performing a double rotation (Q²) at two unequal, completely orthogonal angular rates of rotation: an elliptical double rotation. These include the reference frames of most typical observers, who are moving slowly relative to the observed orbital system's reference frame (their relative motion is a small fraction of the speed of light). ...this is probably misplaced here and should not interrupt the discussion at this point: ...These typical observations agree closely with the predictions of special relativity, because the non-isoclinic elliptical (Q²) resembles a (QT), since one of its two completely orthogonal rotations (Q) has such a long period that it is almost indistinguishable from a straight translation (T). All orbits in 4-space are isoclinic in their own reference frame. Orbiting objects in their own proper Kepler systems follow circular geodesic isoclines through 4-space. Orbits in 4-space are perfectly circular in their own reference frame, as Copernicus assumed the orbits of planets to be. It is the orbit's path through the 3-space of its elliptic hyperplane that is an ellipse, as Kepler found it to be. ...cite Jesper Goransson's very concise paper The geodesic circle that an orbiting object follows through 4-space in the proper reference frame of its own Kepler system is not a simple great circle which turns in two orthogonal dimensions. It is a helical great circle that turns in four orthogonal dimensions at once.{{Efn|Geodesic orbits in 4-space are not simple 2-dimensional great circles; they are helical 4-dimensional great circles that curve in all four dimensions at once. Their circular trajectories are helixes which we call ''isoclines'', since they are the paths taken by points on a rigid object undergoing isoclinic rotation.}} Such circles lie outside our physical experience, since our local space has only three orthogonal dimensions. Nonetheless we can visualize them in imagination, because their helical, circular shape is perfectly well defined by the kinematical variables of the Kepler orbit. The real physical correlates of abstract orthogonal planes and rotation angles are already familiar to us viscerally in our body-language of physical experience, since we are endowed biologically with highly evolved visual signal processing engines. These enable us to see and understand spatial relations and motions, including rotations, without even thinking about angles and orthogonal planes. This physical endowment is an inborn capacity for dimensional analogy which our biologic evolution has provided. All our instinctive spatial reasoning is by dimensional analogy from flat 2-dimensional retinal images to 3-dimensional scenes, using our powerful inborn visualization capacities of reverse stereographic projection and pattern recognition. We humans are thus very well equipped with everything we need to see in four-dimensional space, except experience. ... Recently Anco and Moghadam found that through Noether’s theorem in reverse, the LRL vector gives rise to a corresponding infinitesimal dynamical symmetry on the kinematical variables, which they show to be the semi-direct product of <small><math>SO(3)</math></small> and <small><math>\mathbb{R^3}</math></small>, in contrast to the <small><math>SO(4)</math></small> symmetry group generated by the LRL symmetries and the rotations.{{Sfn|Anco|Moghadam|2026|ps=; The physically relevant part of the LRL vector is its direction ... since its magnitude is just a function of energy and angular momentum.}} This remarkable symmetry breaking is expressive of the ''dimensional relativity'' between ordinary 3-space <small><math>\mathbb{R^3}</math></small>, spherical space <small><math>S^3</math></small> and Euclidean space <small><math>\mathbb{R^4}</math></small>. Consider a hydrogen atom in a Kepler orbit: for example, a hydrogen atom moving freely in space in an orbit around the sun. It is a ''double'' Kepler problem: an electrostatic Kepler problem within itself, and a gravitational Kepler problem in its environment. The ''single'' electrostatic Kepler problem of a hydrogen atom moving freely in space beyond any gravitational influence is a problem in special relativity. In our Euclidean 4-space model, this atom viewed as stationary in its own proper reference frame exhibits an <small><math>SO(4)</math></small> rotation symmetry corresponding to an isoclinic double rotation (<small><math>\mathrm{Q^2}</math></small>). The fourth dimension in this reference frame is the atom's proper time vector; it has constant velocity <math>c</math> and constant direction. From the point of view of our universal 4-coordinate space (which cannot be the proper inertial reference frame of any physical observer, all of whom are moving relative to it at velocity ''c''), the entire Kepler system (the atom) is translating through 4-space via a screw translation (<small><math>\mathrm{QT}</math></small>) at constant velocity <math>c</math>. From this viewpoint the atom has only a simple <small><math>SO(3)</math></small> rotation component (<small><math>\mathrm{Q}</math></small>), breaking its stationary <small><math>SO(4)</math></small> isoclinic rotation symmetry (<small><math>\mathrm{Q^2}</math></small>). Because each discrete part of the rotating atom moves along a helical trajectory through 4-space, the atom is in orbit around a barycentric axis (like a star in a galaxy), but only in a tiny orbit within its own radius, which is its inertial domain of rotation. The straight 4-dimensional cylinder it progresses along at velocity <math>c</math> is very narrow: only the diameter of the rotating atom itself. The gravitational Kepler problem of a hydrogen atom in a Kepler orbit around the sun is a problem in general relativity. In our 4-space model, this atom viewed in its own proper reference frame exhibits the same <small><math>SO(4)</math></small> rotation symmetry as it did in the electrostatic Kepler problem where the atom was translating linearly through space. The Kepler system in this case is not just the atom; it is the entire solar system. The LRL vector of this Kepler system is the proper time vector of the atom's inertial reference frame; once again it has constant velocity ''and constant direction''. Although the momentum vector moves in a perfect circle as the atom orbits the sun, the 4-space LRL vector does not move at all: it is a constant of motion, of linear motion (<small><math>\mathrm{T}</math></small>) of the Kepler system (the entire solar system in this case) in a constant 4-space direction, the proper time direction of the system. The direction of the system's proper time vector would vary under some kinds of acceleration of the atom, but it is constant under this kind of orbital acceleration. It continues to point in the same direction, like a 4-space compass needle, as the atom winds its way along its spiral path around the axis of the sun's straight-line translation through 4-space at velocity <math>c</math>. This compass needle always points in the direction the sun is moving, not the direction the atom is moving at any instant. ...Its Kepler orbit around the sun is its <small><math>SO(3)</math></small> rotation component (<small><math>\mathrm{Q}</math></small>). Although the atom is moving on a geodesic circle in the second problem, by the [[equivalence principle]] the difference in the state of the atomic systems in these two problems cannot be observed by examining the atoms alone. Even from another inertial reference frame, where the atom in the second problem is seen to be translating through 4-space via a wide screw translation (<small><math>\mathrm{QT}</math></small>) around the sun's axis of motion, there is still no difference between the two problems which can be detected by examining only the atoms within their own proper reference frames (even over time), because the LRL vector (<small><math>\mathrm{T}</math></small>) is a constant of motion of the entire system in both cases. ...Anco and Maghadam found that <small><math>SO(4)</math></small>) breaks to ... <small><math>S^3</math></small>)... if the energy in the Kepler orbit is negative (an elliptical orbit), and to ... <small><math>H^3</math></small>) ... Minkowski spacetime if the energy is positive (a hyperbolic orbit). ... Finally we consider a third problem in which a hydrogen atom enters the solar system as a comet, loops around the sun and exits the solar system again. This atom... ... As Hamilton found when he discovered the quaternions, we see that it is necessary to admit a fourth dimension to the system in order to properly model the problem: in Hamilton's case the general problem of ..., and in our case the Kepler problem. These are instances of the same problem in 4-dimensional Euclidean geometry, and indeed a solution to the Kepler problem in quaternions (the four Cartesian coordinates of Euclidean 4-space) is a solution to it in our model of the 4-coordinate Euclidean cosmos. == Distribution of stars in our galaxy == The stars in our own galaxy appear to us to be a rotating spiral cluster in 3-dimensional space. By assuming that light from them reaches us on straight lines through space, by assuming that we can measure their distance from us by its red shift, and by assuming that they are distributed in three dimensions of space, we have plotted their locations in 3-space. If we abandon the last of those three assumptions, we can just as easily reinterpret that dataset to plot their distribution around us in 4-dimensional space, and see how they actually lie. When we perform this experiment on the data for the stars in our galaxy, do we indeed find that they are distributed non-uniformly in various concentric spirals, but the spirals lie on the surface of various 3-spheres, rather than in elliptical orbits as we saw them in 3-space? That would be an expected consequence of the special rotational symmetry group of 4-space <small><math>SO(4)</math></small>, in which circular (isoclinic) orbits are the geodesics (shortest rotational paths) rather than elliptical (non-equi-angled double rotation) orbits. ...have to perform this experiment somehow, at least as a conclusive thought experiment, before I publish this paper... == Rotations == The [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotations]] of the convex [[W:regular 4-polytope|regular 4-polytope]]s are usually described as discrete rotations of a rigid object. For example, the rigid [[24-cell]] can rotate in a [[24-cell#Great hexagons|hexagonal]] (6-vertex) central [[24-cell#Planes of rotation|plane of rotation]]. A 4-dimensional [[24-cell#Isoclinic rotations|''isoclinic'' rotation]] (as distinct from a [[24-cell#Simple rotations|''simple'' rotation]] like the ones that occur in 3-dimensional space) is a ''diagonal'' rotation in multiple [[W:Clifford parallel|Clifford parallel]] [[24-cell#Geodesics|central planes]] of rotation at once. It is diagonal because it is a [[W:SO(4)#Double rotations|double rotation]]: in addition to rotating in parallel (like wheels), the multiple planes of rotation also tilt sideways in the completely orthogonal plane of rotation (like coins flipping) into each other's planes. Consequently, the path taken by each vertex is a [[24-cell#Helical hexagrams and their isoclines|twisted helical circle]], rather than the ordinary flat great circle a vertex follows in a simple rotation. In a rigid 4-polytope rotating isoclinically, ''all'' the vertices lie in one of the parallel planes of rotation, so all the vertices move in parallel along Clifford parallel twisting circular paths. [[24-cell#Clifford parallel polytopes|Clifford parallel planes]] are not parallel in the normal sense of parallel planes in three dimensions; the vertices are all moving in different directions around the [[W:3-sphere|3-sphere]]. In one complete 360° isoclinic revolution, a rigid 4-polytope turns itself inside out. This is sufficiently different from the simple rotations of rigid bodies in our 3-dimensional experience that a [[24-cell#Rotations|detailed description]] enabling the reader to properly visualize its counter-intuitive consequences runs to many pages and illustrations, with many accompanying pages of explanatory notes on surprising phenomena that arise in 4-dimensional space: [[24-cell#Great squares|completely orthogonal planes]], [[24-cell#Clifford parallel polytopes|Clifford parallelism]]{{Efn|name=Clifford parallels}} and [[W:Hopf fibration|Hopf fiber bundles]], [[24-cell#Isoclinic rotations|isoclinic geodesic paths]], and [[24-cell#Double rotations|chiral (mirror image) pairs of rotations]], among other complexities. Moreover, the characteristic rotations of the various regular 4-polytopes are all different; each is a unique surprise. [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|The 6 regular convex 4-polytopes]] have different numbers of vertices (5, 8, 16, 24, 120 and 600 respectively) and those with fewer vertices occur inscribed in those with more vertices (with one exception), with the result that the more complex 4-polytopes subsume the kinds of rotations characteristic of their less complex predecessors, as well as each having a characteristic kind of rotation not found in their predecessors. None of these symmetries is to be found in 3-dimensional space, although their simpler 3-dimensional analogues are all present there. [[W:Euclidean geometry#Higher dimensions|Four dimensional Euclidean space]] is more complicated (and more interesting) than three dimensional space because there is more room in it, in which unprecedented things can happen. It subsumes 3-dimensional space, with all of the symmetries we are accustomed to, and adds astonishing new surprises. These are hard for us to visualize, because the only way we can experience them is in our imagination; we have no body of sensory experience in 4-dimensional space to draw upon, other than our evolution in time. For that reason (our difficulty in visualizing them), descriptions of isoclinic rotations usually begin and end with rigid rotations: [[24-cell#Isoclinic rotations|for example]], all 24 vertices of a single rigid 24-cell rotating in unison, with 6 vertices evenly spaced around each of 4 Clifford parallel twisted circles.{{Efn|name=360 degree geodesic path visiting 3 hexagonal planes}} But that is only the simplest case, which is easiest for us to understand. Compound and [[W:Kinematics|kinematic]] 24-cells (with moving parts) are even more interesting (and more complicated) than the rotation of a single rigid 24-cell. To begin with, when we examine the individual parts of a single rigid 24-cell that are moving in an isoclinic rotation, such as the orbits of individual vertices, we can imagine a case where fewer than 24 point-objects are orbiting on those twisted circular paths at once. [[24-cell#Reflections|For example]], if we imagine just 8 point-objects, evenly spaced around the 24-cell at [[24-cell#Reciprocal constructions from 8-cell and 16-cell|the 8 vertices that lie on the 4 coordinate axes]], and rotate them isoclinically along exactly the same orbits they would take in the above-mentioned rotation of a rigid 24-cell, then in the course of a single 360° rotation the 8 point-objects will trace out the whole 24-cell, with just one point-object reaching each of the 24 vertex positions just once, and no point-object colliding with (or even crossing the path of) any other at any time. This is an example of a discrete Hopf fibration. But it is still an example of a rigid object in a discrete isoclinic rotation: a rigid 8-vertex object (called the 4-[[W:orthoplex|orthoplex]] or [[16-cell]]) performing one half of the characteristic rotation of the 24-cell. We can also imagine ''combining'' distinct isoclinic rotations. What happens when multiple point-objects are orbiting at once, but do ''not'' all follow the Clifford parallel paths characteristic of the ''same'' distinct rigid rotation? What happens when we combine orbits from distinct rotations characteristic of different 4-polytopes, for example when different rigid 4-polytopes are concentric and rotating simultaneously in their characteristic ways? What kinds of such hybrid rotations are possible in the same 3-sphere shell without collisions? In adjacent concentric shells without asymmetric imbalance? What sort of [[Kinematics of the cuboctahedron|kinematic polytopes]] do they trace out, and how do their [[24-cell#Clifford parallel polytopes|component parts]] relate to each other as they move? Is there (sometimes) some kind of mutual stability amid their lack of combined rigidity? Visualizing isoclinic rotations (rigid and otherwise) allows us to explore such questions of [[W:kinematics|kinematics]], and where dynamic stabilities arise, of [[wikipedia:kinetics (physics)|kinetics]]. In four dimensions, we discover that space has more room in it than we have experienced, which permits previously unimagined motions. Even 3-space is more commodious than we thought; when it is curved and lies embedded in a higher-dimensional space, it permits previously impossible symmetric packings. Sadoc studied double-twisted 3-dimensional molecules, and imagined them embedded in 4-dimensional space as the Hopf fibrations of regular 4-polytopes. He found that these molecules would close-pack on the 3-sphere perfectly without exhibiting any torsion, although their packing in ordinary flat 3-space is imperfect, "frustrated" by their twisted geometry. <blockquote>The frustration, which arises when the molecular orientation is transported along the two [spiral] AB paths of figure 1 [double twist helix], is imposed by the very topological nature of the Euclidean space R³. It would not occur if the molecules were embedded in the non-Euclidean space of the [[W:3-sphere|3-sphere]] S³, or hypersphere. This space with a homogeneous positive curvature can indeed be described by equidistant and uniformly twisted fibers, along which the molecules can be aligned without any conflict between compactness and [[W:torsion of a curve|torsion]].... The fibres of this [[W:Hopf fibration|Hopf fibration]] are great circles of S³, the whole family of which is also called the [[W:Clifford parallel|Clifford parallel]]s.{{Efn|name=Clifford parallels}} Two of these fibers are C_∞ symmetry axes for the whole fibration; each fibre makes one turn around each axis and regularly rotates when moving from one axis to another.{{Efn|name=helical geodesic}} These fibers build a double twist configuration while staying parallel, i.e. without any frustration, in the whole volume of S³.{{Efn|name=Petrie polygon of a honeycomb}} They can therefore be used as models to study the condensation of long molecules in the presence of a double twist constraint.{{Sfn|Sadoc & Charvolin|2009|loc=§1.2 The curved space approach|ps=; studies the helical orientation of molecules in crystal structures and their imperfect packings ("frustrations") in 3-dimensional space.}}</blockquote> Of course we do not find molecules condensing to close-pack the 3-sphere in our experience, and Sadoc does not say that we do. We find 3-spheres in the atomic realm (if atoms are 4-polytopes), and in the cosmic realm (as the surface boundaries of stars, and the concentric surfaces of galaxies). But in between, in the realm of ordinary experience which includes the molecular realm, ourselves and all the objects we can materially handle or observe up close including the planets, we are confined together by gravity as inertia within a curved 3-dimensional space that is no more than one atom thick in the fourth spatial dimension. That is why in the molecular realm we find only objects that occupy 3-spaces which, though infinitesimally curved in the fourth dimension, are tiny patches on whole 3-spheres of galactic size. So Sadoc's exercise is a thought experiment, like Einstein's gedankenexperiments about railroad embankments and trains moving at nearly the speed of light. It is no less illuminating, despite the symmetry it reveals not having a realization as an actual 3-sphere of actual molecules. And might not something very like it have an actual realization in the atomic realm? We know that atoms have their own complex internal structure, which we are unable to model geometrically in ordinary 3-dimensional space. Suppose such a model is impossible because an atom is actually a 4-polytope occupying a tiny spherical region of 4-dimensional space, and so we only find its constituent particles in close-packed helical orbits on the 3-sphere, in the manner of Sadoc's imaginary twisted molecules, but as real 4-dimensional helices of atomic scale. We would expect to find the atomic orbit of a fundamental particle in some discrete Hopf fibration characteristic of a symmetry group, that is, on the maximally symmetric isoclines of a discrete isoclinic rotation characteristic of some regular 4-polytope and the particle. == A theory of the Euclidean atom == <blockquote>Because quantum physics could be tested without being understood, it allowed humans to see how the universe worked without knowing why.<ref>Sebastian Junger, In My Time of Dying</ref></blockquote> ... == Light and Mass are Reflection and Rotation == The phenomena of light and mass are expressions of reflection symmetries and rotation symmetries, respectively. ... Atoms are 4-polytopes, elementary objects with SO(4) rotational symmetry. Light is .... Motion in space is the propagation of the elementary objects of light and matter in Coxeter congruent transformations by kaleidoscopic self-reflections, like the motion of self-reproducing cellular automata in [[Conway's Game of Life|Conway's game of life]]. ... Light is discrete reflections. Mass is discrete rotations. Both are group actions, expressions of intrinsic symmetries. That is all of physics. === Atoms are 4-polytopes === ... == Relativity in real space of four or more orthogonal dimensions == Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions. General relativity is Galilean relativity in a general space of four or more orthogonal dimensions, e.g. in Euclidean 4-space <math>R^4</math>, spherical 4-space <math>S^4</math>, and any orthogonal 4-manifold. Light is a consequence of symmetry group reflections at quantum scale. Gravity and the other fundamental forces are consequences of rotations, which are consequences of quantum reflections. Light is discrete reflections. Gravity and all forces are discrete rotations. Both are group actions, expressions of intrinsic symmetries. That is all of physics. Every observer may properly see themself as stationary and the universe as an ''n''-sphere with themself at the center. The curvature of these spheres is a function of the rate at which causality evolves, and can be measured by the observer as the speed of light. === Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions === ...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here... Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in three spatial dimensions. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (In general relativity, discussed below, the actual rate of physical processes varies from place to place, and those differences are neither reciprocal nor illusory.) None of these Lorentz effects are beyond geometric explanation or paradoxical. The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, successive Euclidean spaces are dimensionally analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature, is an exact expression of intrinsic symmetries: that is Nother's great discovery. === General relativity is Galilean relativity in a general space of four orthogonal dimensions === ... == Dimensional relativity == Coxeter's kinetic law of <math>n</math>-dimensional congruent Euclidean transformations may be called ''dimensional relativity'', since it captures the theories of special and general relativity entire, and has its roots in dimensional analogy. Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessable by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated. By analogy to the surface of the earth, the bounding surface of a spherical region of <math>n</math>-dimensional Euclidean space is an <math>(n-1)</math>-sphere, a spherical space of one fewer dimensions than the <math>n</math>-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean <math>n</math>-spaces of increasing <math>n</math>, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating <math>n</math>-spaces. By the degree of dimensional analogy of which they are capable, some observers see deeper into <math>n</math>-dimensional space than others. == Polycentric spherical relativity == An intelligent observer equipped with the principle of relativity may perceive the universe from any inertial reference frame, not only from their own proper perspective. We see that every observer may properly view themself as stationary and the universe as an ''n''-sphere with themself at the center observing it, perceptually equidistant from all points on its surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything. This ''polycentric model'' of the universe is a further restatement of the principle of relativity. It is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. It should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849: "The universe is a sphere whose center is wherever there is intelligence."{{Sfn|Thoreau|1849|p=349|ps=; "The universe is a sphere whose center is wherever there is intelligence." [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}} == Revolutions == The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity ''c'', with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may, or may not, all have the same origin in space and time. As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment we dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed us that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a sense related to time, at least, it must be 4-dimensional. In this work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space. Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we now observe them, any more than they lie in the three dimensional hyperplane of local space in which we find everything residing in our solar system. When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us only by virtue of how long it takes their light to reach us. We can measure their distribution around us in 4-space, but that is simply how we choose to measure them, not a finding of how they are actually distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean ''n''-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity <math>c</math>, on more or less divergent paths from each other. But only much closer observation will reveal evidence of whether everything we see lies in the same 4-space, or if it is distributed in five or more dimensions, and how it is moving there. To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity <math>c</math>, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw displacements), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw displacement has ''two'' [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity <math>c</math> in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that each galaxy's own distinct 3-sphere is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to lightspeed long ago, in whatever big bang our atoms emerged from, and have never slowed down since. == Origins of the theory == Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of the geometry of Euclidean 4-space relativity, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] contains the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and did not describe our ordinary 3-space embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.<ref>{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}</ref> He invited us to imagine "A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions", but he was careful to disclaim parenthetically that "The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice." Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal of that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.'' The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified spacetime of four dimensions. Anco and Maghadam found that <small><math>SO(4)</math></small> breaks to ... <small><math>S^3</math></small>... if the energy in the Kepler orbit is negative (an elliptical orbit), and to ... <small><math>H^3</math></small> ... Minkowski spacetime if the energy is positive (a hyperbolic orbit). Because the planets orbit on ellipses in our 3-space, Euclidean 4-space is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the truer model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position of centrality as our exclusive conception of our place in space. ...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others. The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; "Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions."}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.<ref>{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}</ref>}} == Boundaries == <blockquote>Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.<ref>{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}</ref></blockquote> Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? ''What is the nature of the boundary which confines us to just three dimensions?'' We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell. Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined motions and objects. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. A boundary is an explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force. <blockquote>The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three .... In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it. We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed "Dimensional Analogy."<ref>{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}</ref></blockquote> I believe, but I cannot prove, that we live in real space, which is Schläfli's and Coxeter's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover in imagination and then explore physically, each an astonishing new enlightenment.<ref>{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}<blockquote> :We shall not cease from exploration :And the end of all our exploring :Will be to arrive where we started :And know the place for the first time. :Through the unknown, remembered gate :When the last of earth left to discover :Is that which was the beginning; :At the source of the longest river :The voice of the hidden waterfall :And the children in the apple-tree :Not known, because not looked for :But heard, half-heard, in the stillness :Between two waves of the sea. </blockquote></ref> Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. This project is forever beginning anew. Coxeter showed us that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether showed us all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions, in which all objects with mass move ceaselessly at the constant velocity <math>c</math>, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages. <blockquote> ::::::BEECH :Where my imaginary line :Bends square in woods, an iron spine :And pile of real rocks have been founded. :And off this corner in the wild, :Where these are driven in and piled, :One tree, by being deeply wounded, :Has been impressed as Witness Tree :And made commit to memory :My proof of being not unbounded. :Thus truth's established and borne out, :Though circumstanced with dark and doubt— :Though by a world of doubt surrounded. :::::::—''The Moodie Forester''<ref>{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}</ref> </blockquote> == Appendix: Sequence of regular 4-polytopes == {{Regular convex 4-polytopes|wiki=W:|columns=7}} == ... == {{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}} {{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}} {{Efn|name=radially equilateral}} {{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as "the convex hull of the neighbouring vertices of a given vertex".{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its "radius" equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}} {{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example: {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0) {{indent|5}}({{spaces|2}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>){{spaces|3}}({{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>) {{indent|5}}(–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>){{spaces|3}}(–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>) {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)<br> is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}} {{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60° rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the "left" is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}} {{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}} {{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; "In mathematics, the path that the (1, 1) knot on the torus traces is also known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two intersecting circles that are the cross-section of a torus by a well-chosen plane cutting it. Picking one such circle and rotating it around the torus axis, the resulting family of circles can be used to rule the torus. By nesting tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the (1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles]."}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}} {{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}} {{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}} {{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}} {{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}} {{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}} {{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}} {{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}} {{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}} {{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90^o bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60^o bend, or as a straight line with one 60^o bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}} {{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; "In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)"}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}} {{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}} {{Efn|Departing from any vertex V₀ in the original great hexagon plane of isoclinic rotation P₀, the first vertex reached V₁ is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P₁. P₁ is inclined to P₀ at a 60° angle.{{Efn|P₀ and P₁ lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V₂ is 120 degrees beyond V₁ along a second {{radic|3}} chord lying in another hexagonal plane P₂ that is Clifford parallel to P₀.{{Efn|P₀ and P₂ are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V₀ and V₂ are ''two'' {{radic|3}} chords apart{{Efn|V₀ and V₂ are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V₀ and V₂ are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P₀ and P₂ are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V₁ lies in both intersecting planes P₁ and P₂, as V₀ lies in both P₀ and P₁. But P₀ and P₂ have ''no'' vertices in common; they do not intersect.) The third vertex reached V₃ is 120 degrees beyond V₂ along a third {{radic|3}} chord lying in another hexagonal plane P₃ that is Clifford parallel to P₁. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V₀ to V₃ is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}} {{Sfn|Mamone, Pileio & Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹₄.}} ==Notes== {{Regular convex 4-polytopes Notelist|wiki=W:}} ==Citations== {{Regular convex 4-polytopes Reflist|wiki=W:}} ==References== {{Refbegin}} * {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}} * {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1}} * {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}} === [[Polyscheme|Polyschemes]] === {{Regular convex 4-polytopes Refs|wiki=W:}} {{Refend}} btwr84vxzp61b0cdqmh4mlsmxeb27p7 2823726 2823724 2026-08-20T21:02:33Z Dc.samizdat 2856930 /* A theory of the Euclidean cosmos */ 2823726 wikitext text/x-wiki = Real Euclidean four-dimensional space R⁴ = {{align|center|David Brooks Christie}} {{align|center|dc@samizdat.org}} {{align|center|Draft in progress}} {{align|center|June 2023 - August 2026}} <blockquote>'''Abstract:''' The physical universe is properly visualized as a Euclidean space of four orthogonal spatial dimensions. Space itself has a fourth orthogonal dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and our planet are only 3-dimensional objects, but nonetheless we can see in four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.</blockquote> == Summary == We observe that physical space has four perpendicular dimensions, not just three; atoms are [[W:4-polytope|4-polytopes]]; the sun is a 4-ball that is round in four dimensions; everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space; and our entire 3-space manifold is translating through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions. == A theory of the Euclidean cosmos == The physical universe is properly visualized as a [[w:Four-dimensional_space|Euclidean space of four orthogonal spatial dimensions]]. Space itself has a fourth orthogonal dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planets, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. All objects with mass move inertially through Euclidean 4-space at velocity <math>c</math> as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity <math>c</math> is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space. A typical spiral galaxy such as ours is a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our galaxy appear from our viewpoint to be distributed in a cloud of elliptical spirals occupying a flattened ellipsoid region of 3-dimensional space, but they are not so confined: they are distributed within a spherical region of 4-dimensional space. The galaxy's actual shape is spherical, not a flattened ellipsoid, but it is rounder than round can be in our ordinary experience: it occupies a hyperspherical region of space. The concentric spirals of stars that we observe lie on concentric [[W:3-sphere|3-sphere]]s (4-dimensional spheres), not on concentric 2-ellipsoids (3-dimensional elliptical spirals). Our sun and solar system lies on one of those concentric 3-spheres. More generally, orbits are circular in 4-space, and elliptical in the 3-space of their elliptic hyperplane. [[File:Hypersphere.png|thumb|[Placeholder image for:]Rotating illustration of the 4-ball galaxy showing its spirals of star clouds on the surface of concentric 3-spheres, obtained by reverse sterographic projection from 3D images of the galaxy.]] The galaxy as a whole, or more properly its orbital center point, is translating through 4-space at velocity <math>c</math>, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity <math>c</math> in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity <math>c</math>. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the cylinder; their trajectories are screw-displacements, the compound of a simple rotation and a linear translation. The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around a barycentric axis. It is the tremendous inertial force of stars in motion at velocity <math>c</math> that holds the cylinder of motion together. The observed universe as a whole appears to be a 3-sphere expanding radially from a central origin point at velocity <math>c</math>, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. For all observers, the conjectured origin point of the universe corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space (the same point in the same Euclidean 4-space for all observers). The big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured separately, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity <math>c</math>. All objects in our solar system except the sun itself lie within this thinest three-dimensional manifold. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. The enclosing surface of a spherical region of 4-space is itself a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. We live within such a 3-space, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience, and it contains the earth, all the planets and the 3-dimensional space between them. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our particular 3-sphere is one of the galaxy's concentric 3-spheres of spiral star-clouds. The solar system occupies a tiny patch of this filmy 4-dimensional soap-bubble of galactic size, that is thicker-skinned than the diameter of an atom only in the interior of stars and supermassive objects. Our entire 3-sphere manifold, as a 3-spherical shell within the moving 4-ball galaxy, is translating through 4-space at velocity <math>c</math> with the galaxy, in a distinct direction that is orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the galaxy's translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of rotating objects through Euclidean space by screw translation. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity <math>c</math>, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. Any moving 3-dimensional manifold that is such an evolving surface boundary is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. Every object which we find occurring naturally in the solar system other than the sun itself, even the largest of 3-dimensional objects a planet, is a three-dimensional smear of atoms no thicker than one atom in its fourth dimension, which is the direction of its linear translation through 4-space at velocity <math>c</math>. The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be "heaped up" into larger 4-dimensional objects that form a lump in its moving surface. We have little understanding of such 4-dimensional lumps thicker than one atom, since they occur naturally in our vicinity only in the interior of the sun. In fact the sun is the only such lump occurring naturally in our solar system. We refer to 4-dimensional lumps of matter as plasma, and have little experimental knowledge of their geometry or internal structure. We know that such a lump as the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know nothing about its interior 4-ball. Every such moving 3-dimensional surface boundary of matter in the observed universe is evolving in four dimensions at velocity <math>c</math>. Its current location in 4-space corresponds to the present moment in the proper time of its inertial reference frame. Its direction of movement at velocity <math>c</math> corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from atoms to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, two orthogonal inertial motions each at the constant universal rate of transformation <math>c</math>. Every object moves relative to universal 4-coordinate space on its own distinct geodesic spiral, a screw translation trajectory that is the compound of two orthogonal inertial motions, a rotation and a translation. Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity <math>c</math> in all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is <math>c\prime = 2c</math>, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity <math>c</math>. For example, we can look across the center of our mostly-empty 4-ball galaxy and see stars in the opposite sides of its concentric 3-sphere surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math> in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper space. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space. == Symmetries == It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel & Goodman-Strauss|2008}} As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. [[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}} <blockquote>Let <small><math>\mathrm{Q}</math></small> denote a rotation, <small><math>\mathrm{R}</math></small> a reflection, <small><math>\mathrm{T}</math></small> a translation, and let <small><math>\mathrm{Q}^q \mathrm{R}^r\mathrm{T}</math></small> denote a product of several such transformations, all commutative with one another. Then <small><math>\mathrm{RT}</math></small> is a glide-reflection (in two or three dimensions), <small><math>\mathrm{QR}</math></small> is a rotary-reflection, <small><math>\mathrm{QT}</math></small> is a screw-displacement, and <small><math>\mathrm{Q^2}</math></small> is a double rotation (in four dimensions).<br> Every orthogonal transformation is expressible as:<br> :<small><math>\mathrm{Q}^q \mathrm{R}^r</math></small><br> where <small><math>(2^q + r \le n)</math></small>, the number of dimensions.<br> Transformations involving a translation are expressible as:<br> :<small><math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}</math></small><br> where <small><math>(2^q + r + 1 \le n)</math></small>.<br> For <small><math>(n = 4)</math></small> in particular, every displacement is either a double rotation <small><math>\mathrm{Q}^2</math></small>, or a screw-displacement <small><math>\mathrm{QT}</math></small> [where the rotation component <small><math>\mathrm{Q}</math></small> is a simple rotation, but the <small><math>\mathrm{QT}</math></small> is chiral like a <small><math>\mathrm{Q^2}</math></small>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <small><math>\mathrm{QRT}</math></small>.</blockquote> If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a <small><math>\mathrm{Q^2}</math></small> or a <small><math>\mathrm{QT}</math></small>, because we can view any <small><math>\mathrm{QT}</math></small> as a <small><math>\mathrm{Q^2}</math></small> in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a <small><math>\mathrm{Q^2}</math></small>. By the same principle, we can view any <small><math>\mathrm{QT}</math></small> or <small><math>\mathrm{Q^2}</math></small> as an isoclinic (equi-angled) <small><math>\mathrm{Q^2}</math></small> by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (<small><math>\mathrm{T}</math></small>) for ''one'' of the two rotations (<small><math>\mathrm{Q}</math></small>). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (<small><math>\mathrm{Q}</math></small>) up to uncertainty, and can always distinguish the direction of their own proper time translation (<small><math>\mathrm{T}</math></small>). As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebra), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group <small><math>SO(4)</math></small> [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic <small><math>SO(4)</math></small> rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, stationary atoms exhibit the <small><math>SO(4)</math></small> symmetries of the discrete isoclinic (equi-angled) double rotations (<small><math>\mathrm{Q^2}</math></small>) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]]. == Special relativity describes Euclidean 4-space == <blockquote>Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.<ref>{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}</ref></blockquote> Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional "space" because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign to the three space coordinates so spacetime is hyperbolic, not a flat Euclidean 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was first described by Einstein himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction. Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity ''c'', in some 4-space direction. This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always ''c'', as measured by all observers from any inertial reference frame. This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source. But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity ''c''. In physics as it has been universally understood, observers are not supposed to be able to move at velocity ''c''. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four. In the Euclidean relativity alternative view, however, every observer is always moving at velocity ''c'' through the universe, which is real Euclidean 4-dimensional space <small><math>\mathbb{R^4}</math></small>. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity ''c''. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and proper space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity ''c'', in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space <small><math>\mathbb{R^4}</math></small>.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity ''c'' relative to universal 4-coordinate space, so the maximum relative velocity between two observers is 2''c'' when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to ''c'', it is the same measurement in different units. Special relativity measures all velocities in a 3-space of Minkowski spacetime. Euclidean relativity measures all velocities in Euclidean 4-space.}} So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity ''c'' in Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the "speed of light" ''c'', although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity ''c'', but in at least slightly different directions. In Einstein's relativity, the invariant ''c'' is the speed of light through 3-space. In Euclidean relativity, the invariant ''c'' is the speed of matter through 4-space! The speed of light through 3-space is also perceived as ''c'' by all observers, because they are each living in a moving 3-manifold that is moving through 4-space at velocity ''c''. Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same predictions about how observers in different reference frames will perceive each other's motions in time and space, and we shall see that they also agree on the predictions of general relativity. They both describe the same geometric relations of space and time, but they describe that geometry as embedded in two very different universal host spaces: Minkowski spacetime versus Euclidean 4-space. ...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity <math>c</math> through space and proper time ...cite Yamashita{{Sfn|Yamashita|2023}} on the equivalence of special relativity and Euclidean 4-space relativity ...cite Kappraff & Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff & Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff & Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords. Euclidean relativity is not even a fringe theory; no physicists have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could "catch up" with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at ''c'' (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than ''c''. Euclidean relativity is a revolutionary theory indeed, in which ''c'' cannot possibly be the speed of light! We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for <math>\mathbb{R^4}</math> to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be <math>c\prime = 2c</math>, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate linearly along the edge of a unit 4-hypercube. This is conceivable in 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number <small><math>\sqrt{4}</math></small>. == An object's motion in space is the product of its discrete self-reflections == Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a small number of discrete self-reflections. Any action of a geometric object that transforms its position and orientation in space may be measured as a distinct group of self-reflections of the object in its own surfaces. Any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete set of local self-reflections. Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which touch (intersect each other). When a object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality. Coxeter's laws of motion are a geometric counterpart to Newton's laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures. But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. For example, they give us geometric pictures of all the possible motions of objects in four dimensional Euclidean space: <blockquote>Every orthogonal transformation in 4-space is expressible as:<br> :<small><math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t</math></small><br> where <small><math>(2^q + r + t \le 4)</math></small>. Every displacement is either a double rotation <small><math>\mathrm{Q}^2</math></small>, or a screw-displacement <small><math>\mathrm{QT}</math></small> [where the rotation component <small><math>\mathrm{Q}</math></small> is a simple rotation, but the <small><math>\mathrm{QT}</math></small> is chiral like a <small><math>\mathrm{Q^2}</math></small>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <small><math>\mathrm{QRT}</math></small>.</blockquote> While this description should be understood as simple geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (<small><math>\mathrm{Q}</math></small>), reflection (<small><math>\mathrm{R}</math></small>) and translation (<small><math>\mathrm{T}</math></small>) are just what they are in three-dimensional space, but double rotation (<small><math>\mathrm{Q}^2</math></small>) is something new and unprecedented in our physical experience, because double rotations cannot occur until you have four or more dimensions of space to rotate in. ...to readers who have not studied Coxeter (almost all readers including TAC), the blockquote above is "just math", not visualizable geometry...but I could describe Coxeter's congruent transformations in 4-space here geometrically: I could say clearly what they mean in spatial terms, in language anyone can understand, because they don't require any math to be understood; the "math" here is really just simple pictures (reflections and rotations); even double rotations can be visualized by dimensional analogy, as compounds of simple rotations...since even most physicists are unacquainted with Coxeter geometry, it might be useful to do this here... == Light propagates through 4-space at twice its apparent velocity ''c''== Coxeter's geometric laws of motion apply to all objects with mass in 4-dimensional Euclidean space, but we find there is an additional kind of displacement which applies only to massless particles such as photons. Light quanta (photons) translate through 4-space by 4-dimensional reflection <small><math>\mathrm{R}^4</math></small>, which may be termed a double translation <small><math>\mathrm{T}^2</math></small>, a pure translation via two pairs of parallel reflections, without any rotation component <small><math>\mathrm{Q}</math></small>. Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by <small><math>\mathrm{QT}</math></small>, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic <small><math>\mathrm{Q^2}</math></small>, an isoclinically rotating object such as an atom. A simple rotation <small><math>\mathrm{Q}</math></small> or simple translation <small><math>\mathrm{T}</math></small> is a double reflection <small><math>\mathrm{R^2}</math></small>, so a <small><math>\mathrm{QT}</math></small> or <small><math>\mathrm{Q^2}</math></small> is also an <small><math>\mathrm{R^4}</math></small>, but not with the same group of reflection angles as a light signal <small><math>\mathrm{R^4}</math></small>. A translation <small><math>\mathrm{T = R^2}</math></small> is a double reflection in two parallel planes, and a rotation <small><math>\mathrm{Q = R^2}</math></small> is a double reflection in two intersecting planes, as in a <small><math>\mathrm{QT = R^4}</math></small> which is both at once. A double translation <small><math>\mathrm{T^2 = R^4}</math></small> is two double reflections in pairs of parallel planes at once, a reflection in four or more non-intersecting parallel planes; it is all translation and no rotation. In a <small><math>\mathrm{T^2}</math></small> all the motion goes to translation, so the translation goes twice as far as the simple translation <small><math>\mathrm{T}</math></small> in a <small><math>\mathrm{QT}</math></small>. A double translation <small><math>\mathrm{T^2 = R^4}</math></small> is the opposite of a double rotation <small><math>\mathrm{Q^2 = R^4}</math></small>, which is stationary but rotates twice as fast as the simple rotation <small><math>\mathrm{Q}</math></small> in a <small><math>\mathrm{QT}</math></small>. The product of the two translations in a <small><math>\mathrm{T^2}</math></small> is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple <small><math>\mathrm{T}</math></small> over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double-the-distance translation, but without any rotation component, so it cannot carry any mass with it. A <small><math>\mathrm{T^2}</math></small> cannot reposition a 4-polytope the way a <small><math>\mathrm{QT}</math></small> does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter. ...lensing of double translations <small><math>\mathrm{T^2 = R^4}</math></small> in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet... == The Kepler problem is framed in Euclidean 4-space == The [[W:Kepler problem|Kepler problem]] is named for [[W:Johannes Kepler|Johannes Kepler]], arguably the greatest geometer since the ancients up to [[w:Ludwig Schläfli|Ludwig Schläfli]], who proposed [[W:Kepler's laws of planetary motion|Kepler's laws of planetary motion]] which solved the problem of the orbits of the planets, and investigated the types of forces that would result in orbits obeying those laws. Those forces were later identified by [[W:Isaac Newton|Isaac Newton]] in his[[W:Philosophiæ Naturalis Principia Mathematica| Principia]], where he proves what today might be called the "inverse Kepler problem": the orbit characteristics require the force to depend on the inverse square of the distance.<ref>{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton & Company|isbn=978-0393039184}}</ref> The inverse square law behind the Kepler problem is the [[W:Central force|central force]] law which governs not only [[W:Newtonian gravity|Newtonian gravity]] and celestial orbits, but also the motion of two charged particles in [[W:Coulomb’s law|Coulomb’s law]] of [[W:Electrostatics|electrostatics]]; it applies to attractive or repulsive forces. Problems in which two bodies interact by a central force that varies as the [[W:Inverse square law|inverse square]] of the distance between them are called Kepler problems. Thus the [[W:Hydrogen atom|hydrogen atom]] is a Kepler problem, since it comprises two charged particles interacting by Coulomb's law, another inverse-square central force. Using classical mechanics, the solution to a Kepler problem can be expressed as a [[W:Kepler orbit|Kepler orbit]] using six kinematical variables or [[W:Orbital elements|orbital elements]]. The solution conserves an orbital element called the [[W:Laplace–Runge–Lenz vector|Laplace–Runge–Lenz (LRL) vector]], a [[W:Constant of motion|constant of motion]], meaning that it is the same no matter where it is calculated on the orbit. The LRL vector was essential in the first quantum mechanical derivation of the [[W:Atomic emission spectrum|spectrum]] of the hydrogen atom, but this approach has rarely been used since the development of the [[W:Schrödinger equation|Schrödinger equation]]. The conservation of the LRL vector corresponds to the <small><math>SO(4)</math></small> symmetry, by Nother's theorem. The LRL vector lies orthogonal to both the orbital plane and the angular momentum vector of the Kepler orbit; we observe that it lies in a fourth orthogonal dimension. Fock in 1935<ref>V. Fock, Zur Theorie des Wasserstoffatoms, Zeitschrift für Physik. 98 (3-4) (1935), 145–154.</ref> and Moser in 1970<ref>J. Moser, Regularization of Kepler’s problem and the averaging method on a manifold, Commun. Pure Appl. 23 (1970), 609–636</ref> observed that the Kepler problem is mathematically equivalent to non-affine geodesic motion (a particle moving freely) on the surface of a 3-sphere, so that the whole problem is symmetric under certain rotations of the four-dimensional space. This higher-dimensional symmetry results in two well-known properties of the Kepler problem: the momentum vector always moves in a perfect circle and, for a given total energy, all such velocity circles intersect each other in the same two points. ... Relativity establishes that an orbit in space is viewed in a different way in each distinct inertial reference frame. Depending on the choice of reference frame, the same Kepler system may be seen to be performing any one of a sequence of relativistically equivalent rotations in 4-space, on a continuum from an isoclinic rotation (Q²) in the orbit's proper reference frame, to a screw transfer (QT) with a simple rotation component (Q) and a translation component (T) at velocity <math>c</math>, in the universal reference frame of 4-coordinate space wherein every object is seen to be translating at velocity <math>c</math>. In reference frames between these two limit cases, the orbit is seen to be performing a double rotation (Q²) at two unequal, completely orthogonal angular rates of rotation: an elliptical double rotation. These include the reference frames of most typical observers, who are moving slowly relative to the observed orbital system's reference frame (their relative motion is a small fraction of the speed of light). ...this is probably misplaced here and should not interrupt the discussion at this point: ...These typical observations agree closely with the predictions of special relativity, because the non-isoclinic elliptical (Q²) resembles a (QT), since one of its two completely orthogonal rotations (Q) has such a long period that it is almost indistinguishable from a straight translation (T). All orbits in 4-space are isoclinic in their own reference frame. Orbiting objects in their own proper Kepler systems follow circular geodesic isoclines through 4-space. Orbits in 4-space are perfectly circular in their own reference frame, as Copernicus assumed the orbits of planets to be. It is the orbit's path through the 3-space of its elliptic hyperplane that is an ellipse, as Kepler found it to be. ...cite Jesper Goransson's very concise paper The geodesic circle that an orbiting object follows through 4-space in the proper reference frame of its own Kepler system is not a simple great circle which turns in two orthogonal dimensions. It is a helical great circle that turns in four orthogonal dimensions at once.{{Efn|Geodesic orbits in 4-space are not simple 2-dimensional great circles; they are helical 4-dimensional great circles that curve in all four dimensions at once. Their circular trajectories are helixes which we call ''isoclines'', since they are the paths taken by points on a rigid object undergoing isoclinic rotation.}} Such circles lie outside our physical experience, since our local space has only three orthogonal dimensions. Nonetheless we can visualize them in imagination, because their helical, circular shape is perfectly well defined by the kinematical variables of the Kepler orbit. The real physical correlates of abstract orthogonal planes and rotation angles are already familiar to us viscerally in our body-language of physical experience, since we are endowed biologically with highly evolved visual signal processing engines. These enable us to see and understand spatial relations and motions, including rotations, without even thinking about angles and orthogonal planes. This physical endowment is an inborn capacity for dimensional analogy which our biologic evolution has provided. All our instinctive spatial reasoning is by dimensional analogy from flat 2-dimensional retinal images to 3-dimensional scenes, using our powerful inborn visualization capacities of reverse stereographic projection and pattern recognition. We humans are thus very well equipped with everything we need to see in four-dimensional space, except experience. ... Recently Anco and Moghadam found that through Noether’s theorem in reverse, the LRL vector gives rise to a corresponding infinitesimal dynamical symmetry on the kinematical variables, which they show to be the semi-direct product of <small><math>SO(3)</math></small> and <small><math>\mathbb{R^3}</math></small>, in contrast to the <small><math>SO(4)</math></small> symmetry group generated by the LRL symmetries and the rotations.{{Sfn|Anco|Moghadam|2026|ps=; The physically relevant part of the LRL vector is its direction ... since its magnitude is just a function of energy and angular momentum.}} This remarkable symmetry breaking is expressive of the ''dimensional relativity'' between ordinary 3-space <small><math>\mathbb{R^3}</math></small>, spherical space <small><math>S^3</math></small> and Euclidean space <small><math>\mathbb{R^4}</math></small>. Consider a hydrogen atom in a Kepler orbit: for example, a hydrogen atom moving freely in space in an orbit around the sun. It is a ''double'' Kepler problem: an electrostatic Kepler problem within itself, and a gravitational Kepler problem in its environment. The ''single'' electrostatic Kepler problem of a hydrogen atom moving freely in space beyond any gravitational influence is a problem in special relativity. In our Euclidean 4-space model, this atom viewed as stationary in its own proper reference frame exhibits an <small><math>SO(4)</math></small> rotation symmetry corresponding to an isoclinic double rotation (<small><math>\mathrm{Q^2}</math></small>). The fourth dimension in this reference frame is the atom's proper time vector; it has constant velocity <math>c</math> and constant direction. From the point of view of our universal 4-coordinate space (which cannot be the proper inertial reference frame of any physical observer, all of whom are moving relative to it at velocity ''c''), the entire Kepler system (the atom) is translating through 4-space via a screw translation (<small><math>\mathrm{QT}</math></small>) at constant velocity <math>c</math>. From this viewpoint the atom has only a simple <small><math>SO(3)</math></small> rotation component (<small><math>\mathrm{Q}</math></small>), breaking its stationary <small><math>SO(4)</math></small> isoclinic rotation symmetry (<small><math>\mathrm{Q^2}</math></small>). Because each discrete part of the rotating atom moves along a helical trajectory through 4-space, the atom is in orbit around a barycentric axis (like a star in a galaxy), but only in a tiny orbit within its own radius, which is its inertial domain of rotation. The straight 4-dimensional cylinder it progresses along at velocity <math>c</math> is very narrow: only the diameter of the rotating atom itself. The gravitational Kepler problem of a hydrogen atom in a Kepler orbit around the sun is a problem in general relativity. In our 4-space model, this atom viewed in its own proper reference frame exhibits the same <small><math>SO(4)</math></small> rotation symmetry as it did in the electrostatic Kepler problem where the atom was translating linearly through space. The Kepler system in this case is not just the atom; it is the entire solar system. The LRL vector of this Kepler system is the proper time vector of the atom's inertial reference frame; once again it has constant velocity ''and constant direction''. Although the momentum vector moves in a perfect circle as the atom orbits the sun, the 4-space LRL vector does not move at all: it is a constant of motion, of linear motion (<small><math>\mathrm{T}</math></small>) of the Kepler system (the entire solar system in this case) in a constant 4-space direction, the proper time direction of the system. The direction of the system's proper time vector would vary under some kinds of acceleration of the atom, but it is constant under this kind of orbital acceleration. It continues to point in the same direction, like a 4-space compass needle, as the atom winds its way along its spiral path around the axis of the sun's straight-line translation through 4-space at velocity <math>c</math>. This compass needle always points in the direction the sun is moving, not the direction the atom is moving at any instant. ...Its Kepler orbit around the sun is its <small><math>SO(3)</math></small> rotation component (<small><math>\mathrm{Q}</math></small>). Although the atom is moving on a geodesic circle in the second problem, by the [[equivalence principle]] the difference in the state of the atomic systems in these two problems cannot be observed by examining the atoms alone. Even from another inertial reference frame, where the atom in the second problem is seen to be translating through 4-space via a wide screw translation (<small><math>\mathrm{QT}</math></small>) around the sun's axis of motion, there is still no difference between the two problems which can be detected by examining only the atoms within their own proper reference frames (even over time), because the LRL vector (<small><math>\mathrm{T}</math></small>) is a constant of motion of the entire system in both cases. ...Anco and Maghadam found that <small><math>SO(4)</math></small>) breaks to ... <small><math>S^3</math></small>)... if the energy in the Kepler orbit is negative (an elliptical orbit), and to ... <small><math>H^3</math></small>) ... Minkowski spacetime if the energy is positive (a hyperbolic orbit). ... Finally we consider a third problem in which a hydrogen atom enters the solar system as a comet, loops around the sun and exits the solar system again. This atom... ... As Hamilton found when he discovered the quaternions, we see that it is necessary to admit a fourth dimension to the system in order to properly model the problem: in Hamilton's case the general problem of ..., and in our case the Kepler problem. These are instances of the same problem in 4-dimensional Euclidean geometry, and indeed a solution to the Kepler problem in quaternions (the four Cartesian coordinates of Euclidean 4-space) is a solution to it in our model of the 4-coordinate Euclidean cosmos. == Distribution of stars in our galaxy == The stars in our own galaxy appear to us to be a rotating spiral cluster in 3-dimensional space. By assuming that light from them reaches us on straight lines through space, by assuming that we can measure their distance from us by its red shift, and by assuming that they are distributed in three dimensions of space, we have plotted their locations in 3-space. If we abandon the last of those three assumptions, we can just as easily reinterpret that dataset to plot their distribution around us in 4-dimensional space, and see how they actually lie. When we perform this experiment on the data for the stars in our galaxy, do we indeed find that they are distributed non-uniformly in various concentric spirals, but the spirals lie on the surface of various 3-spheres, rather than in elliptical orbits as we saw them in 3-space? That would be an expected consequence of the special rotational symmetry group of 4-space <small><math>SO(4)</math></small>, in which circular (isoclinic) orbits are the geodesics (shortest rotational paths) rather than elliptical (non-equi-angled double rotation) orbits. ...have to perform this experiment somehow, at least as a conclusive thought experiment, before I publish this paper... == Rotations == The [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotations]] of the convex [[W:regular 4-polytope|regular 4-polytope]]s are usually described as discrete rotations of a rigid object. For example, the rigid [[24-cell]] can rotate in a [[24-cell#Great hexagons|hexagonal]] (6-vertex) central [[24-cell#Planes of rotation|plane of rotation]]. A 4-dimensional [[24-cell#Isoclinic rotations|''isoclinic'' rotation]] (as distinct from a [[24-cell#Simple rotations|''simple'' rotation]] like the ones that occur in 3-dimensional space) is a ''diagonal'' rotation in multiple [[W:Clifford parallel|Clifford parallel]] [[24-cell#Geodesics|central planes]] of rotation at once. It is diagonal because it is a [[W:SO(4)#Double rotations|double rotation]]: in addition to rotating in parallel (like wheels), the multiple planes of rotation also tilt sideways in the completely orthogonal plane of rotation (like coins flipping) into each other's planes. Consequently, the path taken by each vertex is a [[24-cell#Helical hexagrams and their isoclines|twisted helical circle]], rather than the ordinary flat great circle a vertex follows in a simple rotation. In a rigid 4-polytope rotating isoclinically, ''all'' the vertices lie in one of the parallel planes of rotation, so all the vertices move in parallel along Clifford parallel twisting circular paths. [[24-cell#Clifford parallel polytopes|Clifford parallel planes]] are not parallel in the normal sense of parallel planes in three dimensions; the vertices are all moving in different directions around the [[W:3-sphere|3-sphere]]. In one complete 360° isoclinic revolution, a rigid 4-polytope turns itself inside out. This is sufficiently different from the simple rotations of rigid bodies in our 3-dimensional experience that a [[24-cell#Rotations|detailed description]] enabling the reader to properly visualize its counter-intuitive consequences runs to many pages and illustrations, with many accompanying pages of explanatory notes on surprising phenomena that arise in 4-dimensional space: [[24-cell#Great squares|completely orthogonal planes]], [[24-cell#Clifford parallel polytopes|Clifford parallelism]]{{Efn|name=Clifford parallels}} and [[W:Hopf fibration|Hopf fiber bundles]], [[24-cell#Isoclinic rotations|isoclinic geodesic paths]], and [[24-cell#Double rotations|chiral (mirror image) pairs of rotations]], among other complexities. Moreover, the characteristic rotations of the various regular 4-polytopes are all different; each is a unique surprise. [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|The 6 regular convex 4-polytopes]] have different numbers of vertices (5, 8, 16, 24, 120 and 600 respectively) and those with fewer vertices occur inscribed in those with more vertices (with one exception), with the result that the more complex 4-polytopes subsume the kinds of rotations characteristic of their less complex predecessors, as well as each having a characteristic kind of rotation not found in their predecessors. None of these symmetries is to be found in 3-dimensional space, although their simpler 3-dimensional analogues are all present there. [[W:Euclidean geometry#Higher dimensions|Four dimensional Euclidean space]] is more complicated (and more interesting) than three dimensional space because there is more room in it, in which unprecedented things can happen. It subsumes 3-dimensional space, with all of the symmetries we are accustomed to, and adds astonishing new surprises. These are hard for us to visualize, because the only way we can experience them is in our imagination; we have no body of sensory experience in 4-dimensional space to draw upon, other than our evolution in time. For that reason (our difficulty in visualizing them), descriptions of isoclinic rotations usually begin and end with rigid rotations: [[24-cell#Isoclinic rotations|for example]], all 24 vertices of a single rigid 24-cell rotating in unison, with 6 vertices evenly spaced around each of 4 Clifford parallel twisted circles.{{Efn|name=360 degree geodesic path visiting 3 hexagonal planes}} But that is only the simplest case, which is easiest for us to understand. Compound and [[W:Kinematics|kinematic]] 24-cells (with moving parts) are even more interesting (and more complicated) than the rotation of a single rigid 24-cell. To begin with, when we examine the individual parts of a single rigid 24-cell that are moving in an isoclinic rotation, such as the orbits of individual vertices, we can imagine a case where fewer than 24 point-objects are orbiting on those twisted circular paths at once. [[24-cell#Reflections|For example]], if we imagine just 8 point-objects, evenly spaced around the 24-cell at [[24-cell#Reciprocal constructions from 8-cell and 16-cell|the 8 vertices that lie on the 4 coordinate axes]], and rotate them isoclinically along exactly the same orbits they would take in the above-mentioned rotation of a rigid 24-cell, then in the course of a single 360° rotation the 8 point-objects will trace out the whole 24-cell, with just one point-object reaching each of the 24 vertex positions just once, and no point-object colliding with (or even crossing the path of) any other at any time. This is an example of a discrete Hopf fibration. But it is still an example of a rigid object in a discrete isoclinic rotation: a rigid 8-vertex object (called the 4-[[W:orthoplex|orthoplex]] or [[16-cell]]) performing one half of the characteristic rotation of the 24-cell. We can also imagine ''combining'' distinct isoclinic rotations. What happens when multiple point-objects are orbiting at once, but do ''not'' all follow the Clifford parallel paths characteristic of the ''same'' distinct rigid rotation? What happens when we combine orbits from distinct rotations characteristic of different 4-polytopes, for example when different rigid 4-polytopes are concentric and rotating simultaneously in their characteristic ways? What kinds of such hybrid rotations are possible in the same 3-sphere shell without collisions? In adjacent concentric shells without asymmetric imbalance? What sort of [[Kinematics of the cuboctahedron|kinematic polytopes]] do they trace out, and how do their [[24-cell#Clifford parallel polytopes|component parts]] relate to each other as they move? Is there (sometimes) some kind of mutual stability amid their lack of combined rigidity? Visualizing isoclinic rotations (rigid and otherwise) allows us to explore such questions of [[W:kinematics|kinematics]], and where dynamic stabilities arise, of [[wikipedia:kinetics (physics)|kinetics]]. In four dimensions, we discover that space has more room in it than we have experienced, which permits previously unimagined motions. Even 3-space is more commodious than we thought; when it is curved and lies embedded in a higher-dimensional space, it permits previously impossible symmetric packings. Sadoc studied double-twisted 3-dimensional molecules, and imagined them embedded in 4-dimensional space as the Hopf fibrations of regular 4-polytopes. He found that these molecules would close-pack on the 3-sphere perfectly without exhibiting any torsion, although their packing in ordinary flat 3-space is imperfect, "frustrated" by their twisted geometry. <blockquote>The frustration, which arises when the molecular orientation is transported along the two [spiral] AB paths of figure 1 [double twist helix], is imposed by the very topological nature of the Euclidean space R³. It would not occur if the molecules were embedded in the non-Euclidean space of the [[W:3-sphere|3-sphere]] S³, or hypersphere. This space with a homogeneous positive curvature can indeed be described by equidistant and uniformly twisted fibers, along which the molecules can be aligned without any conflict between compactness and [[W:torsion of a curve|torsion]].... The fibres of this [[W:Hopf fibration|Hopf fibration]] are great circles of S³, the whole family of which is also called the [[W:Clifford parallel|Clifford parallel]]s.{{Efn|name=Clifford parallels}} Two of these fibers are C_∞ symmetry axes for the whole fibration; each fibre makes one turn around each axis and regularly rotates when moving from one axis to another.{{Efn|name=helical geodesic}} These fibers build a double twist configuration while staying parallel, i.e. without any frustration, in the whole volume of S³.{{Efn|name=Petrie polygon of a honeycomb}} They can therefore be used as models to study the condensation of long molecules in the presence of a double twist constraint.{{Sfn|Sadoc & Charvolin|2009|loc=§1.2 The curved space approach|ps=; studies the helical orientation of molecules in crystal structures and their imperfect packings ("frustrations") in 3-dimensional space.}}</blockquote> Of course we do not find molecules condensing to close-pack the 3-sphere in our experience, and Sadoc does not say that we do. We find 3-spheres in the atomic realm (if atoms are 4-polytopes), and in the cosmic realm (as the surface boundaries of stars, and the concentric surfaces of galaxies). But in between, in the realm of ordinary experience which includes the molecular realm, ourselves and all the objects we can materially handle or observe up close including the planets, we are confined together by gravity as inertia within a curved 3-dimensional space that is no more than one atom thick in the fourth spatial dimension. That is why in the molecular realm we find only objects that occupy 3-spaces which, though infinitesimally curved in the fourth dimension, are tiny patches on whole 3-spheres of galactic size. So Sadoc's exercise is a thought experiment, like Einstein's gedankenexperiments about railroad embankments and trains moving at nearly the speed of light. It is no less illuminating, despite the symmetry it reveals not having a realization as an actual 3-sphere of actual molecules. And might not something very like it have an actual realization in the atomic realm? We know that atoms have their own complex internal structure, which we are unable to model geometrically in ordinary 3-dimensional space. Suppose such a model is impossible because an atom is actually a 4-polytope occupying a tiny spherical region of 4-dimensional space, and so we only find its constituent particles in close-packed helical orbits on the 3-sphere, in the manner of Sadoc's imaginary twisted molecules, but as real 4-dimensional helices of atomic scale. We would expect to find the atomic orbit of a fundamental particle in some discrete Hopf fibration characteristic of a symmetry group, that is, on the maximally symmetric isoclines of a discrete isoclinic rotation characteristic of some regular 4-polytope and the particle. == A theory of the Euclidean atom == <blockquote>Because quantum physics could be tested without being understood, it allowed humans to see how the universe worked without knowing why.<ref>Sebastian Junger, In My Time of Dying</ref></blockquote> ... == Light and Mass are Reflection and Rotation == The phenomena of light and mass are expressions of reflection symmetries and rotation symmetries, respectively. ... Atoms are 4-polytopes, elementary objects with SO(4) rotational symmetry. Light is .... Motion in space is the propagation of the elementary objects of light and matter in Coxeter congruent transformations by kaleidoscopic self-reflections, like the motion of self-reproducing cellular automata in [[Conway's Game of Life|Conway's game of life]]. ... Light is discrete reflections. Mass is discrete rotations. Both are group actions, expressions of intrinsic symmetries. That is all of physics. === Atoms are 4-polytopes === ... == Relativity in real space of four or more orthogonal dimensions == Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions. General relativity is Galilean relativity in a general space of four or more orthogonal dimensions, e.g. in Euclidean 4-space <math>R^4</math>, spherical 4-space <math>S^4</math>, and any orthogonal 4-manifold. Light is a consequence of symmetry group reflections at quantum scale. Gravity and the other fundamental forces are consequences of rotations, which are consequences of quantum reflections. Light is discrete reflections. Gravity and all forces are discrete rotations. Both are group actions, expressions of intrinsic symmetries. That is all of physics. Every observer may properly see themself as stationary and the universe as an ''n''-sphere with themself at the center. The curvature of these spheres is a function of the rate at which causality evolves, and can be measured by the observer as the speed of light. === Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions === ...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here... Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in three spatial dimensions. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (In general relativity, discussed below, the actual rate of physical processes varies from place to place, and those differences are neither reciprocal nor illusory.) None of these Lorentz effects are beyond geometric explanation or paradoxical. The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, successive Euclidean spaces are dimensionally analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature, is an exact expression of intrinsic symmetries: that is Nother's great discovery. === General relativity is Galilean relativity in a general space of four orthogonal dimensions === ... == Dimensional relativity == Coxeter's kinetic law of <math>n</math>-dimensional congruent Euclidean transformations may be called ''dimensional relativity'', since it captures the theories of special and general relativity entire, and has its roots in dimensional analogy. Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessable by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated. By analogy to the surface of the earth, the bounding surface of a spherical region of <math>n</math>-dimensional Euclidean space is an <math>(n-1)</math>-sphere, a spherical space of one fewer dimensions than the <math>n</math>-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean <math>n</math>-spaces of increasing <math>n</math>, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating <math>n</math>-spaces. By the degree of dimensional analogy of which they are capable, some observers see deeper into <math>n</math>-dimensional space than others. == Polycentric spherical relativity == An intelligent observer equipped with the principle of relativity may perceive the universe from any inertial reference frame, not only from their own proper perspective. We see that every observer may properly view themself as stationary and the universe as an ''n''-sphere with themself at the center observing it, perceptually equidistant from all points on its surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything. This ''polycentric model'' of the universe is a further restatement of the principle of relativity. It is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. It should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849: "The universe is a sphere whose center is wherever there is intelligence."{{Sfn|Thoreau|1849|p=349|ps=; "The universe is a sphere whose center is wherever there is intelligence." [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}} == Revolutions == The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity ''c'', with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may, or may not, all have the same origin in space and time. As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment we dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed us that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a sense related to time, at least, it must be 4-dimensional. In this work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space. Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we now observe them, any more than they lie in the three dimensional hyperplane of local space in which we find everything residing in our solar system. When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us only by virtue of how long it takes their light to reach us. We can measure their distribution around us in 4-space, but that is simply how we choose to measure them, not a finding of how they are actually distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean ''n''-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity <math>c</math>, on more or less divergent paths from each other. But only much closer observation will reveal evidence of whether everything we see lies in the same 4-space, or if it is distributed in five or more dimensions, and how it is moving there. To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity <math>c</math>, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw displacements), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw displacement has ''two'' [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity <math>c</math> in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that each galaxy's own distinct 3-sphere is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to lightspeed long ago, in whatever big bang our atoms emerged from, and have never slowed down since. == Origins of the theory == Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of the geometry of Euclidean 4-space relativity, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] contains the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and did not describe our ordinary 3-space embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.<ref>{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}</ref> He invited us to imagine "A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions", but he was careful to disclaim parenthetically that "The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice." Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal of that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.'' The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified spacetime of four dimensions. Anco and Maghadam found that <small><math>SO(4)</math></small> breaks to ... <small><math>S^3</math></small>... if the energy in the Kepler orbit is negative (an elliptical orbit), and to ... <small><math>H^3</math></small> ... Minkowski spacetime if the energy is positive (a hyperbolic orbit). Because the planets orbit on ellipses in our 3-space, Euclidean 4-space is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the truer model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position of centrality as our exclusive conception of our place in space. ...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others. The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; "Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions."}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.<ref>{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}</ref>}} == Boundaries == <blockquote>Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.<ref>{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}</ref></blockquote> Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? ''What is the nature of the boundary which confines us to just three dimensions?'' We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell. Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined motions and objects. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. A boundary is an explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force. <blockquote>The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three .... In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it. We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed "Dimensional Analogy."<ref>{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}</ref></blockquote> I believe, but I cannot prove, that we live in real space, which is Schläfli's and Coxeter's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover in imagination and then explore physically, each an astonishing new enlightenment.<ref>{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}<blockquote> :We shall not cease from exploration :And the end of all our exploring :Will be to arrive where we started :And know the place for the first time. :Through the unknown, remembered gate :When the last of earth left to discover :Is that which was the beginning; :At the source of the longest river :The voice of the hidden waterfall :And the children in the apple-tree :Not known, because not looked for :But heard, half-heard, in the stillness :Between two waves of the sea. </blockquote></ref> Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. This project is forever beginning anew. Coxeter showed us that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether showed us all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions, in which all objects with mass move ceaselessly at the constant velocity <math>c</math>, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages. <blockquote> ::::::BEECH :Where my imaginary line :Bends square in woods, an iron spine :And pile of real rocks have been founded. :And off this corner in the wild, :Where these are driven in and piled, :One tree, by being deeply wounded, :Has been impressed as Witness Tree :And made commit to memory :My proof of being not unbounded. :Thus truth's established and borne out, :Though circumstanced with dark and doubt— :Though by a world of doubt surrounded. :::::::—''The Moodie Forester''<ref>{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}</ref> </blockquote> == Appendix: Sequence of regular 4-polytopes == {{Regular convex 4-polytopes|wiki=W:|columns=7}} == ... == {{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}} {{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}} {{Efn|name=radially equilateral}} {{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as "the convex hull of the neighbouring vertices of a given vertex".{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its "radius" equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}} {{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example: {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0) {{indent|5}}({{spaces|2}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>){{spaces|3}}({{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>) {{indent|5}}(–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>){{spaces|3}}(–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>) {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)<br> is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}} {{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60° rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the "left" is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}} {{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}} {{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; "In mathematics, the path that the (1, 1) knot on the torus traces is also known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two intersecting circles that are the cross-section of a torus by a well-chosen plane cutting it. Picking one such circle and rotating it around the torus axis, the resulting family of circles can be used to rule the torus. By nesting tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the (1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles]."}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}} {{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}} {{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}} {{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}} {{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}} {{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}} {{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}} {{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}} {{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}} {{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90^o bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60^o bend, or as a straight line with one 60^o bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}} {{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; "In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)"}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}} {{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}} {{Efn|Departing from any vertex V₀ in the original great hexagon plane of isoclinic rotation P₀, the first vertex reached V₁ is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P₁. P₁ is inclined to P₀ at a 60° angle.{{Efn|P₀ and P₁ lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V₂ is 120 degrees beyond V₁ along a second {{radic|3}} chord lying in another hexagonal plane P₂ that is Clifford parallel to P₀.{{Efn|P₀ and P₂ are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V₀ and V₂ are ''two'' {{radic|3}} chords apart{{Efn|V₀ and V₂ are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V₀ and V₂ are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P₀ and P₂ are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V₁ lies in both intersecting planes P₁ and P₂, as V₀ lies in both P₀ and P₁. But P₀ and P₂ have ''no'' vertices in common; they do not intersect.) The third vertex reached V₃ is 120 degrees beyond V₂ along a third {{radic|3}} chord lying in another hexagonal plane P₃ that is Clifford parallel to P₁. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V₀ to V₃ is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}} {{Sfn|Mamone, Pileio & Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹₄.}} ==Notes== {{Regular convex 4-polytopes Notelist|wiki=W:}} ==Citations== {{Regular convex 4-polytopes Reflist|wiki=W:}} ==References== {{Refbegin}} * {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}} * {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1}} * {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}} === [[Polyscheme|Polyschemes]] === {{Regular convex 4-polytopes Refs|wiki=W:}} {{Refend}} df8jjdvopak3ocfqitdmlqbkzxawa5f 2823727 2823726 2026-08-20T21:06:26Z Dc.samizdat 2856930 /* A theory of the Euclidean cosmos */ 2823727 wikitext text/x-wiki = Real Euclidean four-dimensional space R⁴ = {{align|center|David Brooks Christie}} {{align|center|dc@samizdat.org}} {{align|center|Draft in progress}} {{align|center|June 2023 - August 2026}} <blockquote>'''Abstract:''' The physical universe is properly visualized as a Euclidean space of four orthogonal spatial dimensions. Space itself has a fourth orthogonal dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and our planet are only 3-dimensional objects, but nonetheless we can see in four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.</blockquote> == Summary == We observe that physical space has four perpendicular dimensions, not just three; atoms are [[W:4-polytope|4-polytopes]]; the sun is a 4-ball that is round in four dimensions; everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space; and our entire 3-space manifold is translating through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions. == A theory of the Euclidean cosmos == The physical universe is properly visualized as a [[w:Four-dimensional_space|Euclidean space of four orthogonal spatial dimensions]]. Space itself has a fourth orthogonal dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planets, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. All objects with mass move inertially through Euclidean 4-space at velocity <math>c</math> as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity <math>c</math> is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space. A typical spiral galaxy such as ours is a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our galaxy appear from our viewpoint to be distributed in a cloud of elliptical spirals occupying a disk-like ellipsoid region of 3-dimensional space, but they are not so confined: they are distributed within a spherical region of 4-dimensional space. The galaxy's actual shape is spherical, not a flattened ellipsoid, but it is rounder than round can be in our ordinary experience: it occupies a hyperspherical region of space. The concentric spirals of stars that we observe lie on concentric [[W:3-sphere|3-sphere]]s (4-dimensional spheres), not on concentric 2-ellipsoids (3-dimensional elliptical spirals). Our sun and solar system lies on one of those concentric 3-spheres. More generally, orbits are circular in 4-space, and elliptical in the 3-space of their elliptic hyperplane. [[File:Hypersphere.png|thumb|[Placeholder image for:]Rotating illustration of the 4-ball galaxy showing its spirals of star clouds on the surface of concentric 3-spheres, obtained by reverse sterographic projection from 3D images of the galaxy.]] The galaxy as a whole, or more properly its orbital center point, is translating through 4-space at velocity <math>c</math>, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity <math>c</math> in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity <math>c</math>. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the cylinder; their trajectories are screw-displacements, the compound of a simple rotation and a linear translation. The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around a barycentric axis. It is the tremendous inertial force of stars in motion at velocity <math>c</math> that holds the cylinder of motion together. The observed universe as a whole appears to be a 3-sphere expanding radially from a central origin point at velocity <math>c</math>, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. For all observers, the conjectured origin point of the universe corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space (the same point in the same Euclidean 4-space for all observers). The big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured separately, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity <math>c</math>. All objects in our solar system except the sun itself lie within this thinest three-dimensional manifold. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. The enclosing surface of a spherical region of 4-space is itself a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. We live within such a 3-space, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience, and it contains the earth, all the planets and the 3-dimensional space between them. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our particular 3-sphere is one of the galaxy's concentric 3-spheres of spiral star-clouds. The solar system occupies a tiny patch of this filmy 4-dimensional soap-bubble of galactic size, that is thicker-skinned than the diameter of an atom only in the interior of stars and supermassive objects. Our entire 3-sphere manifold, as a 3-spherical shell within the moving 4-ball galaxy, is translating through 4-space at velocity <math>c</math> with the galaxy, in a distinct direction that is orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the galaxy's translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of rotating objects through Euclidean space by screw translation. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity <math>c</math>, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. Any moving 3-dimensional manifold that is such an evolving surface boundary is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. Every object which we find occurring naturally in the solar system other than the sun itself, even the largest of 3-dimensional objects a planet, is a three-dimensional smear of atoms no thicker than one atom in its fourth dimension, which is the direction of its linear translation through 4-space at velocity <math>c</math>. The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be "heaped up" into larger 4-dimensional objects that form a lump in its moving surface. We have little understanding of such 4-dimensional lumps thicker than one atom, since they occur naturally in our vicinity only in the interior of the sun. In fact the sun is the only such lump occurring naturally in our solar system. We refer to 4-dimensional lumps of matter as plasma, and have little experimental knowledge of their geometry or internal structure. We know that such a lump as the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know nothing about its interior 4-ball. Every such moving 3-dimensional surface boundary of matter in the observed universe is evolving in four dimensions at velocity <math>c</math>. Its current location in 4-space corresponds to the present moment in the proper time of its inertial reference frame. Its direction of movement at velocity <math>c</math> corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from atoms to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, two orthogonal inertial motions each at the constant universal rate of transformation <math>c</math>. Every object moves relative to universal 4-coordinate space on its own distinct geodesic spiral, a screw translation trajectory that is the compound of two orthogonal inertial motions, a rotation and a translation. Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity <math>c</math> in all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is <math>c\prime = 2c</math>, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity <math>c</math>. For example, we can look across the center of our mostly-empty 4-ball galaxy and see stars in the opposite sides of its concentric 3-sphere surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math> in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper space. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space. == Symmetries == It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel & Goodman-Strauss|2008}} As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. [[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}} <blockquote>Let <small><math>\mathrm{Q}</math></small> denote a rotation, <small><math>\mathrm{R}</math></small> a reflection, <small><math>\mathrm{T}</math></small> a translation, and let <small><math>\mathrm{Q}^q \mathrm{R}^r\mathrm{T}</math></small> denote a product of several such transformations, all commutative with one another. Then <small><math>\mathrm{RT}</math></small> is a glide-reflection (in two or three dimensions), <small><math>\mathrm{QR}</math></small> is a rotary-reflection, <small><math>\mathrm{QT}</math></small> is a screw-displacement, and <small><math>\mathrm{Q^2}</math></small> is a double rotation (in four dimensions).<br> Every orthogonal transformation is expressible as:<br> :<small><math>\mathrm{Q}^q \mathrm{R}^r</math></small><br> where <small><math>(2^q + r \le n)</math></small>, the number of dimensions.<br> Transformations involving a translation are expressible as:<br> :<small><math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}</math></small><br> where <small><math>(2^q + r + 1 \le n)</math></small>.<br> For <small><math>(n = 4)</math></small> in particular, every displacement is either a double rotation <small><math>\mathrm{Q}^2</math></small>, or a screw-displacement <small><math>\mathrm{QT}</math></small> [where the rotation component <small><math>\mathrm{Q}</math></small> is a simple rotation, but the <small><math>\mathrm{QT}</math></small> is chiral like a <small><math>\mathrm{Q^2}</math></small>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <small><math>\mathrm{QRT}</math></small>.</blockquote> If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a <small><math>\mathrm{Q^2}</math></small> or a <small><math>\mathrm{QT}</math></small>, because we can view any <small><math>\mathrm{QT}</math></small> as a <small><math>\mathrm{Q^2}</math></small> in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a <small><math>\mathrm{Q^2}</math></small>. By the same principle, we can view any <small><math>\mathrm{QT}</math></small> or <small><math>\mathrm{Q^2}</math></small> as an isoclinic (equi-angled) <small><math>\mathrm{Q^2}</math></small> by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (<small><math>\mathrm{T}</math></small>) for ''one'' of the two rotations (<small><math>\mathrm{Q}</math></small>). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (<small><math>\mathrm{Q}</math></small>) up to uncertainty, and can always distinguish the direction of their own proper time translation (<small><math>\mathrm{T}</math></small>). As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebra), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group <small><math>SO(4)</math></small> [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic <small><math>SO(4)</math></small> rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, stationary atoms exhibit the <small><math>SO(4)</math></small> symmetries of the discrete isoclinic (equi-angled) double rotations (<small><math>\mathrm{Q^2}</math></small>) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]]. == Special relativity describes Euclidean 4-space == <blockquote>Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.<ref>{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}</ref></blockquote> Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional "space" because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign to the three space coordinates so spacetime is hyperbolic, not a flat Euclidean 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was first described by Einstein himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction. Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity ''c'', in some 4-space direction. This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always ''c'', as measured by all observers from any inertial reference frame. This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source. But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity ''c''. In physics as it has been universally understood, observers are not supposed to be able to move at velocity ''c''. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four. In the Euclidean relativity alternative view, however, every observer is always moving at velocity ''c'' through the universe, which is real Euclidean 4-dimensional space <small><math>\mathbb{R^4}</math></small>. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity ''c''. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and proper space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity ''c'', in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space <small><math>\mathbb{R^4}</math></small>.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity ''c'' relative to universal 4-coordinate space, so the maximum relative velocity between two observers is 2''c'' when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to ''c'', it is the same measurement in different units. Special relativity measures all velocities in a 3-space of Minkowski spacetime. Euclidean relativity measures all velocities in Euclidean 4-space.}} So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity ''c'' in Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the "speed of light" ''c'', although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity ''c'', but in at least slightly different directions. In Einstein's relativity, the invariant ''c'' is the speed of light through 3-space. In Euclidean relativity, the invariant ''c'' is the speed of matter through 4-space! The speed of light through 3-space is also perceived as ''c'' by all observers, because they are each living in a moving 3-manifold that is moving through 4-space at velocity ''c''. Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same predictions about how observers in different reference frames will perceive each other's motions in time and space, and we shall see that they also agree on the predictions of general relativity. They both describe the same geometric relations of space and time, but they describe that geometry as embedded in two very different universal host spaces: Minkowski spacetime versus Euclidean 4-space. ...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity <math>c</math> through space and proper time ...cite Yamashita{{Sfn|Yamashita|2023}} on the equivalence of special relativity and Euclidean 4-space relativity ...cite Kappraff & Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff & Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff & Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords. Euclidean relativity is not even a fringe theory; no physicists have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could "catch up" with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at ''c'' (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than ''c''. Euclidean relativity is a revolutionary theory indeed, in which ''c'' cannot possibly be the speed of light! We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for <math>\mathbb{R^4}</math> to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be <math>c\prime = 2c</math>, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate linearly along the edge of a unit 4-hypercube. This is conceivable in 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number <small><math>\sqrt{4}</math></small>. == An object's motion in space is the product of its discrete self-reflections == Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a small number of discrete self-reflections. Any action of a geometric object that transforms its position and orientation in space may be measured as a distinct group of self-reflections of the object in its own surfaces. Any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete set of local self-reflections. Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which touch (intersect each other). When a object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality. Coxeter's laws of motion are a geometric counterpart to Newton's laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures. But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. For example, they give us geometric pictures of all the possible motions of objects in four dimensional Euclidean space: <blockquote>Every orthogonal transformation in 4-space is expressible as:<br> :<small><math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t</math></small><br> where <small><math>(2^q + r + t \le 4)</math></small>. Every displacement is either a double rotation <small><math>\mathrm{Q}^2</math></small>, or a screw-displacement <small><math>\mathrm{QT}</math></small> [where the rotation component <small><math>\mathrm{Q}</math></small> is a simple rotation, but the <small><math>\mathrm{QT}</math></small> is chiral like a <small><math>\mathrm{Q^2}</math></small>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <small><math>\mathrm{QRT}</math></small>.</blockquote> While this description should be understood as simple geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (<small><math>\mathrm{Q}</math></small>), reflection (<small><math>\mathrm{R}</math></small>) and translation (<small><math>\mathrm{T}</math></small>) are just what they are in three-dimensional space, but double rotation (<small><math>\mathrm{Q}^2</math></small>) is something new and unprecedented in our physical experience, because double rotations cannot occur until you have four or more dimensions of space to rotate in. ...to readers who have not studied Coxeter (almost all readers including TAC), the blockquote above is "just math", not visualizable geometry...but I could describe Coxeter's congruent transformations in 4-space here geometrically: I could say clearly what they mean in spatial terms, in language anyone can understand, because they don't require any math to be understood; the "math" here is really just simple pictures (reflections and rotations); even double rotations can be visualized by dimensional analogy, as compounds of simple rotations...since even most physicists are unacquainted with Coxeter geometry, it might be useful to do this here... == Light propagates through 4-space at twice its apparent velocity ''c''== Coxeter's geometric laws of motion apply to all objects with mass in 4-dimensional Euclidean space, but we find there is an additional kind of displacement which applies only to massless particles such as photons. Light quanta (photons) translate through 4-space by 4-dimensional reflection <small><math>\mathrm{R}^4</math></small>, which may be termed a double translation <small><math>\mathrm{T}^2</math></small>, a pure translation via two pairs of parallel reflections, without any rotation component <small><math>\mathrm{Q}</math></small>. Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by <small><math>\mathrm{QT}</math></small>, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic <small><math>\mathrm{Q^2}</math></small>, an isoclinically rotating object such as an atom. A simple rotation <small><math>\mathrm{Q}</math></small> or simple translation <small><math>\mathrm{T}</math></small> is a double reflection <small><math>\mathrm{R^2}</math></small>, so a <small><math>\mathrm{QT}</math></small> or <small><math>\mathrm{Q^2}</math></small> is also an <small><math>\mathrm{R^4}</math></small>, but not with the same group of reflection angles as a light signal <small><math>\mathrm{R^4}</math></small>. A translation <small><math>\mathrm{T = R^2}</math></small> is a double reflection in two parallel planes, and a rotation <small><math>\mathrm{Q = R^2}</math></small> is a double reflection in two intersecting planes, as in a <small><math>\mathrm{QT = R^4}</math></small> which is both at once. A double translation <small><math>\mathrm{T^2 = R^4}</math></small> is two double reflections in pairs of parallel planes at once, a reflection in four or more non-intersecting parallel planes; it is all translation and no rotation. In a <small><math>\mathrm{T^2}</math></small> all the motion goes to translation, so the translation goes twice as far as the simple translation <small><math>\mathrm{T}</math></small> in a <small><math>\mathrm{QT}</math></small>. A double translation <small><math>\mathrm{T^2 = R^4}</math></small> is the opposite of a double rotation <small><math>\mathrm{Q^2 = R^4}</math></small>, which is stationary but rotates twice as fast as the simple rotation <small><math>\mathrm{Q}</math></small> in a <small><math>\mathrm{QT}</math></small>. The product of the two translations in a <small><math>\mathrm{T^2}</math></small> is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple <small><math>\mathrm{T}</math></small> over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double-the-distance translation, but without any rotation component, so it cannot carry any mass with it. A <small><math>\mathrm{T^2}</math></small> cannot reposition a 4-polytope the way a <small><math>\mathrm{QT}</math></small> does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter. ...lensing of double translations <small><math>\mathrm{T^2 = R^4}</math></small> in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet... == The Kepler problem is framed in Euclidean 4-space == The [[W:Kepler problem|Kepler problem]] is named for [[W:Johannes Kepler|Johannes Kepler]], arguably the greatest geometer since the ancients up to [[w:Ludwig Schläfli|Ludwig Schläfli]], who proposed [[W:Kepler's laws of planetary motion|Kepler's laws of planetary motion]] which solved the problem of the orbits of the planets, and investigated the types of forces that would result in orbits obeying those laws. Those forces were later identified by [[W:Isaac Newton|Isaac Newton]] in his[[W:Philosophiæ Naturalis Principia Mathematica| Principia]], where he proves what today might be called the "inverse Kepler problem": the orbit characteristics require the force to depend on the inverse square of the distance.<ref>{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton & Company|isbn=978-0393039184}}</ref> The inverse square law behind the Kepler problem is the [[W:Central force|central force]] law which governs not only [[W:Newtonian gravity|Newtonian gravity]] and celestial orbits, but also the motion of two charged particles in [[W:Coulomb’s law|Coulomb’s law]] of [[W:Electrostatics|electrostatics]]; it applies to attractive or repulsive forces. Problems in which two bodies interact by a central force that varies as the [[W:Inverse square law|inverse square]] of the distance between them are called Kepler problems. Thus the [[W:Hydrogen atom|hydrogen atom]] is a Kepler problem, since it comprises two charged particles interacting by Coulomb's law, another inverse-square central force. Using classical mechanics, the solution to a Kepler problem can be expressed as a [[W:Kepler orbit|Kepler orbit]] using six kinematical variables or [[W:Orbital elements|orbital elements]]. The solution conserves an orbital element called the [[W:Laplace–Runge–Lenz vector|Laplace–Runge–Lenz (LRL) vector]], a [[W:Constant of motion|constant of motion]], meaning that it is the same no matter where it is calculated on the orbit. The LRL vector was essential in the first quantum mechanical derivation of the [[W:Atomic emission spectrum|spectrum]] of the hydrogen atom, but this approach has rarely been used since the development of the [[W:Schrödinger equation|Schrödinger equation]]. The conservation of the LRL vector corresponds to the <small><math>SO(4)</math></small> symmetry, by Nother's theorem. The LRL vector lies orthogonal to both the orbital plane and the angular momentum vector of the Kepler orbit; we observe that it lies in a fourth orthogonal dimension. Fock in 1935<ref>V. Fock, Zur Theorie des Wasserstoffatoms, Zeitschrift für Physik. 98 (3-4) (1935), 145–154.</ref> and Moser in 1970<ref>J. Moser, Regularization of Kepler’s problem and the averaging method on a manifold, Commun. Pure Appl. 23 (1970), 609–636</ref> observed that the Kepler problem is mathematically equivalent to non-affine geodesic motion (a particle moving freely) on the surface of a 3-sphere, so that the whole problem is symmetric under certain rotations of the four-dimensional space. This higher-dimensional symmetry results in two well-known properties of the Kepler problem: the momentum vector always moves in a perfect circle and, for a given total energy, all such velocity circles intersect each other in the same two points. ... Relativity establishes that an orbit in space is viewed in a different way in each distinct inertial reference frame. Depending on the choice of reference frame, the same Kepler system may be seen to be performing any one of a sequence of relativistically equivalent rotations in 4-space, on a continuum from an isoclinic rotation (Q²) in the orbit's proper reference frame, to a screw transfer (QT) with a simple rotation component (Q) and a translation component (T) at velocity <math>c</math>, in the universal reference frame of 4-coordinate space wherein every object is seen to be translating at velocity <math>c</math>. In reference frames between these two limit cases, the orbit is seen to be performing a double rotation (Q²) at two unequal, completely orthogonal angular rates of rotation: an elliptical double rotation. These include the reference frames of most typical observers, who are moving slowly relative to the observed orbital system's reference frame (their relative motion is a small fraction of the speed of light). ...this is probably misplaced here and should not interrupt the discussion at this point: ...These typical observations agree closely with the predictions of special relativity, because the non-isoclinic elliptical (Q²) resembles a (QT), since one of its two completely orthogonal rotations (Q) has such a long period that it is almost indistinguishable from a straight translation (T). All orbits in 4-space are isoclinic in their own reference frame. Orbiting objects in their own proper Kepler systems follow circular geodesic isoclines through 4-space. Orbits in 4-space are perfectly circular in their own reference frame, as Copernicus assumed the orbits of planets to be. It is the orbit's path through the 3-space of its elliptic hyperplane that is an ellipse, as Kepler found it to be. ...cite Jesper Goransson's very concise paper The geodesic circle that an orbiting object follows through 4-space in the proper reference frame of its own Kepler system is not a simple great circle which turns in two orthogonal dimensions. It is a helical great circle that turns in four orthogonal dimensions at once.{{Efn|Geodesic orbits in 4-space are not simple 2-dimensional great circles; they are helical 4-dimensional great circles that curve in all four dimensions at once. Their circular trajectories are helixes which we call ''isoclines'', since they are the paths taken by points on a rigid object undergoing isoclinic rotation.}} Such circles lie outside our physical experience, since our local space has only three orthogonal dimensions. Nonetheless we can visualize them in imagination, because their helical, circular shape is perfectly well defined by the kinematical variables of the Kepler orbit. The real physical correlates of abstract orthogonal planes and rotation angles are already familiar to us viscerally in our body-language of physical experience, since we are endowed biologically with highly evolved visual signal processing engines. These enable us to see and understand spatial relations and motions, including rotations, without even thinking about angles and orthogonal planes. This physical endowment is an inborn capacity for dimensional analogy which our biologic evolution has provided. All our instinctive spatial reasoning is by dimensional analogy from flat 2-dimensional retinal images to 3-dimensional scenes, using our powerful inborn visualization capacities of reverse stereographic projection and pattern recognition. We humans are thus very well equipped with everything we need to see in four-dimensional space, except experience. ... Recently Anco and Moghadam found that through Noether’s theorem in reverse, the LRL vector gives rise to a corresponding infinitesimal dynamical symmetry on the kinematical variables, which they show to be the semi-direct product of <small><math>SO(3)</math></small> and <small><math>\mathbb{R^3}</math></small>, in contrast to the <small><math>SO(4)</math></small> symmetry group generated by the LRL symmetries and the rotations.{{Sfn|Anco|Moghadam|2026|ps=; The physically relevant part of the LRL vector is its direction ... since its magnitude is just a function of energy and angular momentum.}} This remarkable symmetry breaking is expressive of the ''dimensional relativity'' between ordinary 3-space <small><math>\mathbb{R^3}</math></small>, spherical space <small><math>S^3</math></small> and Euclidean space <small><math>\mathbb{R^4}</math></small>. Consider a hydrogen atom in a Kepler orbit: for example, a hydrogen atom moving freely in space in an orbit around the sun. It is a ''double'' Kepler problem: an electrostatic Kepler problem within itself, and a gravitational Kepler problem in its environment. The ''single'' electrostatic Kepler problem of a hydrogen atom moving freely in space beyond any gravitational influence is a problem in special relativity. In our Euclidean 4-space model, this atom viewed as stationary in its own proper reference frame exhibits an <small><math>SO(4)</math></small> rotation symmetry corresponding to an isoclinic double rotation (<small><math>\mathrm{Q^2}</math></small>). The fourth dimension in this reference frame is the atom's proper time vector; it has constant velocity <math>c</math> and constant direction. From the point of view of our universal 4-coordinate space (which cannot be the proper inertial reference frame of any physical observer, all of whom are moving relative to it at velocity ''c''), the entire Kepler system (the atom) is translating through 4-space via a screw translation (<small><math>\mathrm{QT}</math></small>) at constant velocity <math>c</math>. From this viewpoint the atom has only a simple <small><math>SO(3)</math></small> rotation component (<small><math>\mathrm{Q}</math></small>), breaking its stationary <small><math>SO(4)</math></small> isoclinic rotation symmetry (<small><math>\mathrm{Q^2}</math></small>). Because each discrete part of the rotating atom moves along a helical trajectory through 4-space, the atom is in orbit around a barycentric axis (like a star in a galaxy), but only in a tiny orbit within its own radius, which is its inertial domain of rotation. The straight 4-dimensional cylinder it progresses along at velocity <math>c</math> is very narrow: only the diameter of the rotating atom itself. The gravitational Kepler problem of a hydrogen atom in a Kepler orbit around the sun is a problem in general relativity. In our 4-space model, this atom viewed in its own proper reference frame exhibits the same <small><math>SO(4)</math></small> rotation symmetry as it did in the electrostatic Kepler problem where the atom was translating linearly through space. The Kepler system in this case is not just the atom; it is the entire solar system. The LRL vector of this Kepler system is the proper time vector of the atom's inertial reference frame; once again it has constant velocity ''and constant direction''. Although the momentum vector moves in a perfect circle as the atom orbits the sun, the 4-space LRL vector does not move at all: it is a constant of motion, of linear motion (<small><math>\mathrm{T}</math></small>) of the Kepler system (the entire solar system in this case) in a constant 4-space direction, the proper time direction of the system. The direction of the system's proper time vector would vary under some kinds of acceleration of the atom, but it is constant under this kind of orbital acceleration. It continues to point in the same direction, like a 4-space compass needle, as the atom winds its way along its spiral path around the axis of the sun's straight-line translation through 4-space at velocity <math>c</math>. This compass needle always points in the direction the sun is moving, not the direction the atom is moving at any instant. ...Its Kepler orbit around the sun is its <small><math>SO(3)</math></small> rotation component (<small><math>\mathrm{Q}</math></small>). Although the atom is moving on a geodesic circle in the second problem, by the [[equivalence principle]] the difference in the state of the atomic systems in these two problems cannot be observed by examining the atoms alone. Even from another inertial reference frame, where the atom in the second problem is seen to be translating through 4-space via a wide screw translation (<small><math>\mathrm{QT}</math></small>) around the sun's axis of motion, there is still no difference between the two problems which can be detected by examining only the atoms within their own proper reference frames (even over time), because the LRL vector (<small><math>\mathrm{T}</math></small>) is a constant of motion of the entire system in both cases. ...Anco and Maghadam found that <small><math>SO(4)</math></small>) breaks to ... <small><math>S^3</math></small>)... if the energy in the Kepler orbit is negative (an elliptical orbit), and to ... <small><math>H^3</math></small>) ... Minkowski spacetime if the energy is positive (a hyperbolic orbit). ... Finally we consider a third problem in which a hydrogen atom enters the solar system as a comet, loops around the sun and exits the solar system again. This atom... ... As Hamilton found when he discovered the quaternions, we see that it is necessary to admit a fourth dimension to the system in order to properly model the problem: in Hamilton's case the general problem of ..., and in our case the Kepler problem. These are instances of the same problem in 4-dimensional Euclidean geometry, and indeed a solution to the Kepler problem in quaternions (the four Cartesian coordinates of Euclidean 4-space) is a solution to it in our model of the 4-coordinate Euclidean cosmos. == Distribution of stars in our galaxy == The stars in our own galaxy appear to us to be a rotating spiral cluster in 3-dimensional space. By assuming that light from them reaches us on straight lines through space, by assuming that we can measure their distance from us by its red shift, and by assuming that they are distributed in three dimensions of space, we have plotted their locations in 3-space. If we abandon the last of those three assumptions, we can just as easily reinterpret that dataset to plot their distribution around us in 4-dimensional space, and see how they actually lie. When we perform this experiment on the data for the stars in our galaxy, do we indeed find that they are distributed non-uniformly in various concentric spirals, but the spirals lie on the surface of various 3-spheres, rather than in elliptical orbits as we saw them in 3-space? That would be an expected consequence of the special rotational symmetry group of 4-space <small><math>SO(4)</math></small>, in which circular (isoclinic) orbits are the geodesics (shortest rotational paths) rather than elliptical (non-equi-angled double rotation) orbits. ...have to perform this experiment somehow, at least as a conclusive thought experiment, before I publish this paper... == Rotations == The [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotations]] of the convex [[W:regular 4-polytope|regular 4-polytope]]s are usually described as discrete rotations of a rigid object. For example, the rigid [[24-cell]] can rotate in a [[24-cell#Great hexagons|hexagonal]] (6-vertex) central [[24-cell#Planes of rotation|plane of rotation]]. A 4-dimensional [[24-cell#Isoclinic rotations|''isoclinic'' rotation]] (as distinct from a [[24-cell#Simple rotations|''simple'' rotation]] like the ones that occur in 3-dimensional space) is a ''diagonal'' rotation in multiple [[W:Clifford parallel|Clifford parallel]] [[24-cell#Geodesics|central planes]] of rotation at once. It is diagonal because it is a [[W:SO(4)#Double rotations|double rotation]]: in addition to rotating in parallel (like wheels), the multiple planes of rotation also tilt sideways in the completely orthogonal plane of rotation (like coins flipping) into each other's planes. Consequently, the path taken by each vertex is a [[24-cell#Helical hexagrams and their isoclines|twisted helical circle]], rather than the ordinary flat great circle a vertex follows in a simple rotation. In a rigid 4-polytope rotating isoclinically, ''all'' the vertices lie in one of the parallel planes of rotation, so all the vertices move in parallel along Clifford parallel twisting circular paths. [[24-cell#Clifford parallel polytopes|Clifford parallel planes]] are not parallel in the normal sense of parallel planes in three dimensions; the vertices are all moving in different directions around the [[W:3-sphere|3-sphere]]. In one complete 360° isoclinic revolution, a rigid 4-polytope turns itself inside out. This is sufficiently different from the simple rotations of rigid bodies in our 3-dimensional experience that a [[24-cell#Rotations|detailed description]] enabling the reader to properly visualize its counter-intuitive consequences runs to many pages and illustrations, with many accompanying pages of explanatory notes on surprising phenomena that arise in 4-dimensional space: [[24-cell#Great squares|completely orthogonal planes]], [[24-cell#Clifford parallel polytopes|Clifford parallelism]]{{Efn|name=Clifford parallels}} and [[W:Hopf fibration|Hopf fiber bundles]], [[24-cell#Isoclinic rotations|isoclinic geodesic paths]], and [[24-cell#Double rotations|chiral (mirror image) pairs of rotations]], among other complexities. Moreover, the characteristic rotations of the various regular 4-polytopes are all different; each is a unique surprise. [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|The 6 regular convex 4-polytopes]] have different numbers of vertices (5, 8, 16, 24, 120 and 600 respectively) and those with fewer vertices occur inscribed in those with more vertices (with one exception), with the result that the more complex 4-polytopes subsume the kinds of rotations characteristic of their less complex predecessors, as well as each having a characteristic kind of rotation not found in their predecessors. None of these symmetries is to be found in 3-dimensional space, although their simpler 3-dimensional analogues are all present there. [[W:Euclidean geometry#Higher dimensions|Four dimensional Euclidean space]] is more complicated (and more interesting) than three dimensional space because there is more room in it, in which unprecedented things can happen. It subsumes 3-dimensional space, with all of the symmetries we are accustomed to, and adds astonishing new surprises. These are hard for us to visualize, because the only way we can experience them is in our imagination; we have no body of sensory experience in 4-dimensional space to draw upon, other than our evolution in time. For that reason (our difficulty in visualizing them), descriptions of isoclinic rotations usually begin and end with rigid rotations: [[24-cell#Isoclinic rotations|for example]], all 24 vertices of a single rigid 24-cell rotating in unison, with 6 vertices evenly spaced around each of 4 Clifford parallel twisted circles.{{Efn|name=360 degree geodesic path visiting 3 hexagonal planes}} But that is only the simplest case, which is easiest for us to understand. Compound and [[W:Kinematics|kinematic]] 24-cells (with moving parts) are even more interesting (and more complicated) than the rotation of a single rigid 24-cell. To begin with, when we examine the individual parts of a single rigid 24-cell that are moving in an isoclinic rotation, such as the orbits of individual vertices, we can imagine a case where fewer than 24 point-objects are orbiting on those twisted circular paths at once. [[24-cell#Reflections|For example]], if we imagine just 8 point-objects, evenly spaced around the 24-cell at [[24-cell#Reciprocal constructions from 8-cell and 16-cell|the 8 vertices that lie on the 4 coordinate axes]], and rotate them isoclinically along exactly the same orbits they would take in the above-mentioned rotation of a rigid 24-cell, then in the course of a single 360° rotation the 8 point-objects will trace out the whole 24-cell, with just one point-object reaching each of the 24 vertex positions just once, and no point-object colliding with (or even crossing the path of) any other at any time. This is an example of a discrete Hopf fibration. But it is still an example of a rigid object in a discrete isoclinic rotation: a rigid 8-vertex object (called the 4-[[W:orthoplex|orthoplex]] or [[16-cell]]) performing one half of the characteristic rotation of the 24-cell. We can also imagine ''combining'' distinct isoclinic rotations. What happens when multiple point-objects are orbiting at once, but do ''not'' all follow the Clifford parallel paths characteristic of the ''same'' distinct rigid rotation? What happens when we combine orbits from distinct rotations characteristic of different 4-polytopes, for example when different rigid 4-polytopes are concentric and rotating simultaneously in their characteristic ways? What kinds of such hybrid rotations are possible in the same 3-sphere shell without collisions? In adjacent concentric shells without asymmetric imbalance? What sort of [[Kinematics of the cuboctahedron|kinematic polytopes]] do they trace out, and how do their [[24-cell#Clifford parallel polytopes|component parts]] relate to each other as they move? Is there (sometimes) some kind of mutual stability amid their lack of combined rigidity? Visualizing isoclinic rotations (rigid and otherwise) allows us to explore such questions of [[W:kinematics|kinematics]], and where dynamic stabilities arise, of [[wikipedia:kinetics (physics)|kinetics]]. In four dimensions, we discover that space has more room in it than we have experienced, which permits previously unimagined motions. Even 3-space is more commodious than we thought; when it is curved and lies embedded in a higher-dimensional space, it permits previously impossible symmetric packings. Sadoc studied double-twisted 3-dimensional molecules, and imagined them embedded in 4-dimensional space as the Hopf fibrations of regular 4-polytopes. He found that these molecules would close-pack on the 3-sphere perfectly without exhibiting any torsion, although their packing in ordinary flat 3-space is imperfect, "frustrated" by their twisted geometry. <blockquote>The frustration, which arises when the molecular orientation is transported along the two [spiral] AB paths of figure 1 [double twist helix], is imposed by the very topological nature of the Euclidean space R³. It would not occur if the molecules were embedded in the non-Euclidean space of the [[W:3-sphere|3-sphere]] S³, or hypersphere. This space with a homogeneous positive curvature can indeed be described by equidistant and uniformly twisted fibers, along which the molecules can be aligned without any conflict between compactness and [[W:torsion of a curve|torsion]].... The fibres of this [[W:Hopf fibration|Hopf fibration]] are great circles of S³, the whole family of which is also called the [[W:Clifford parallel|Clifford parallel]]s.{{Efn|name=Clifford parallels}} Two of these fibers are C_∞ symmetry axes for the whole fibration; each fibre makes one turn around each axis and regularly rotates when moving from one axis to another.{{Efn|name=helical geodesic}} These fibers build a double twist configuration while staying parallel, i.e. without any frustration, in the whole volume of S³.{{Efn|name=Petrie polygon of a honeycomb}} They can therefore be used as models to study the condensation of long molecules in the presence of a double twist constraint.{{Sfn|Sadoc & Charvolin|2009|loc=§1.2 The curved space approach|ps=; studies the helical orientation of molecules in crystal structures and their imperfect packings ("frustrations") in 3-dimensional space.}}</blockquote> Of course we do not find molecules condensing to close-pack the 3-sphere in our experience, and Sadoc does not say that we do. We find 3-spheres in the atomic realm (if atoms are 4-polytopes), and in the cosmic realm (as the surface boundaries of stars, and the concentric surfaces of galaxies). But in between, in the realm of ordinary experience which includes the molecular realm, ourselves and all the objects we can materially handle or observe up close including the planets, we are confined together by gravity as inertia within a curved 3-dimensional space that is no more than one atom thick in the fourth spatial dimension. That is why in the molecular realm we find only objects that occupy 3-spaces which, though infinitesimally curved in the fourth dimension, are tiny patches on whole 3-spheres of galactic size. So Sadoc's exercise is a thought experiment, like Einstein's gedankenexperiments about railroad embankments and trains moving at nearly the speed of light. It is no less illuminating, despite the symmetry it reveals not having a realization as an actual 3-sphere of actual molecules. And might not something very like it have an actual realization in the atomic realm? We know that atoms have their own complex internal structure, which we are unable to model geometrically in ordinary 3-dimensional space. Suppose such a model is impossible because an atom is actually a 4-polytope occupying a tiny spherical region of 4-dimensional space, and so we only find its constituent particles in close-packed helical orbits on the 3-sphere, in the manner of Sadoc's imaginary twisted molecules, but as real 4-dimensional helices of atomic scale. We would expect to find the atomic orbit of a fundamental particle in some discrete Hopf fibration characteristic of a symmetry group, that is, on the maximally symmetric isoclines of a discrete isoclinic rotation characteristic of some regular 4-polytope and the particle. == A theory of the Euclidean atom == <blockquote>Because quantum physics could be tested without being understood, it allowed humans to see how the universe worked without knowing why.<ref>Sebastian Junger, In My Time of Dying</ref></blockquote> ... == Light and Mass are Reflection and Rotation == The phenomena of light and mass are expressions of reflection symmetries and rotation symmetries, respectively. ... Atoms are 4-polytopes, elementary objects with SO(4) rotational symmetry. Light is .... Motion in space is the propagation of the elementary objects of light and matter in Coxeter congruent transformations by kaleidoscopic self-reflections, like the motion of self-reproducing cellular automata in [[Conway's Game of Life|Conway's game of life]]. ... Light is discrete reflections. Mass is discrete rotations. Both are group actions, expressions of intrinsic symmetries. That is all of physics. === Atoms are 4-polytopes === ... == Relativity in real space of four or more orthogonal dimensions == Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions. General relativity is Galilean relativity in a general space of four or more orthogonal dimensions, e.g. in Euclidean 4-space <math>R^4</math>, spherical 4-space <math>S^4</math>, and any orthogonal 4-manifold. Light is a consequence of symmetry group reflections at quantum scale. Gravity and the other fundamental forces are consequences of rotations, which are consequences of quantum reflections. Light is discrete reflections. Gravity and all forces are discrete rotations. Both are group actions, expressions of intrinsic symmetries. That is all of physics. Every observer may properly see themself as stationary and the universe as an ''n''-sphere with themself at the center. The curvature of these spheres is a function of the rate at which causality evolves, and can be measured by the observer as the speed of light. === Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions === ...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here... Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in three spatial dimensions. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (In general relativity, discussed below, the actual rate of physical processes varies from place to place, and those differences are neither reciprocal nor illusory.) None of these Lorentz effects are beyond geometric explanation or paradoxical. The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, successive Euclidean spaces are dimensionally analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature, is an exact expression of intrinsic symmetries: that is Nother's great discovery. === General relativity is Galilean relativity in a general space of four orthogonal dimensions === ... == Dimensional relativity == Coxeter's kinetic law of <math>n</math>-dimensional congruent Euclidean transformations may be called ''dimensional relativity'', since it captures the theories of special and general relativity entire, and has its roots in dimensional analogy. Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessable by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated. By analogy to the surface of the earth, the bounding surface of a spherical region of <math>n</math>-dimensional Euclidean space is an <math>(n-1)</math>-sphere, a spherical space of one fewer dimensions than the <math>n</math>-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean <math>n</math>-spaces of increasing <math>n</math>, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating <math>n</math>-spaces. By the degree of dimensional analogy of which they are capable, some observers see deeper into <math>n</math>-dimensional space than others. == Polycentric spherical relativity == An intelligent observer equipped with the principle of relativity may perceive the universe from any inertial reference frame, not only from their own proper perspective. We see that every observer may properly view themself as stationary and the universe as an ''n''-sphere with themself at the center observing it, perceptually equidistant from all points on its surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything. This ''polycentric model'' of the universe is a further restatement of the principle of relativity. It is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. It should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849: "The universe is a sphere whose center is wherever there is intelligence."{{Sfn|Thoreau|1849|p=349|ps=; "The universe is a sphere whose center is wherever there is intelligence." [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}} == Revolutions == The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity ''c'', with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may, or may not, all have the same origin in space and time. As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment we dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed us that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a sense related to time, at least, it must be 4-dimensional. In this work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space. Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we now observe them, any more than they lie in the three dimensional hyperplane of local space in which we find everything residing in our solar system. When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us only by virtue of how long it takes their light to reach us. We can measure their distribution around us in 4-space, but that is simply how we choose to measure them, not a finding of how they are actually distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean ''n''-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity <math>c</math>, on more or less divergent paths from each other. But only much closer observation will reveal evidence of whether everything we see lies in the same 4-space, or if it is distributed in five or more dimensions, and how it is moving there. To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity <math>c</math>, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw displacements), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw displacement has ''two'' [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity <math>c</math> in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that each galaxy's own distinct 3-sphere is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to lightspeed long ago, in whatever big bang our atoms emerged from, and have never slowed down since. == Origins of the theory == Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of the geometry of Euclidean 4-space relativity, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] contains the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and did not describe our ordinary 3-space embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.<ref>{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}</ref> He invited us to imagine "A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions", but he was careful to disclaim parenthetically that "The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice." Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal of that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.'' The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified spacetime of four dimensions. Anco and Maghadam found that <small><math>SO(4)</math></small> breaks to ... <small><math>S^3</math></small>... if the energy in the Kepler orbit is negative (an elliptical orbit), and to ... <small><math>H^3</math></small> ... Minkowski spacetime if the energy is positive (a hyperbolic orbit). Because the planets orbit on ellipses in our 3-space, Euclidean 4-space is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the truer model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position of centrality as our exclusive conception of our place in space. ...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others. The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; "Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions."}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.<ref>{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}</ref>}} == Boundaries == <blockquote>Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.<ref>{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}</ref></blockquote> Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? ''What is the nature of the boundary which confines us to just three dimensions?'' We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell. Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined motions and objects. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. A boundary is an explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force. <blockquote>The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three .... In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it. We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed "Dimensional Analogy."<ref>{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}</ref></blockquote> I believe, but I cannot prove, that we live in real space, which is Schläfli's and Coxeter's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover in imagination and then explore physically, each an astonishing new enlightenment.<ref>{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}<blockquote> :We shall not cease from exploration :And the end of all our exploring :Will be to arrive where we started :And know the place for the first time. :Through the unknown, remembered gate :When the last of earth left to discover :Is that which was the beginning; :At the source of the longest river :The voice of the hidden waterfall :And the children in the apple-tree :Not known, because not looked for :But heard, half-heard, in the stillness :Between two waves of the sea. </blockquote></ref> Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. This project is forever beginning anew. Coxeter showed us that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether showed us all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions, in which all objects with mass move ceaselessly at the constant velocity <math>c</math>, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages. <blockquote> ::::::BEECH :Where my imaginary line :Bends square in woods, an iron spine :And pile of real rocks have been founded. :And off this corner in the wild, :Where these are driven in and piled, :One tree, by being deeply wounded, :Has been impressed as Witness Tree :And made commit to memory :My proof of being not unbounded. :Thus truth's established and borne out, :Though circumstanced with dark and doubt— :Though by a world of doubt surrounded. :::::::—''The Moodie Forester''<ref>{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}</ref> </blockquote> == Appendix: Sequence of regular 4-polytopes == {{Regular convex 4-polytopes|wiki=W:|columns=7}} == ... == {{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}} {{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}} {{Efn|name=radially equilateral}} {{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as "the convex hull of the neighbouring vertices of a given vertex".{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its "radius" equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}} {{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example: {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0) {{indent|5}}({{spaces|2}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>){{spaces|3}}({{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>) {{indent|5}}(–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>){{spaces|3}}(–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>) {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)<br> is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}} {{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60° rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the "left" is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}} {{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}} {{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; "In mathematics, the path that the (1, 1) knot on the torus traces is also known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two intersecting circles that are the cross-section of a torus by a well-chosen plane cutting it. Picking one such circle and rotating it around the torus axis, the resulting family of circles can be used to rule the torus. By nesting tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the (1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles]."}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}} {{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}} {{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}} {{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}} {{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}} {{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}} {{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}} {{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}} {{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}} {{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90^o bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60^o bend, or as a straight line with one 60^o bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}} {{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; "In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)"}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}} {{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}} {{Efn|Departing from any vertex V₀ in the original great hexagon plane of isoclinic rotation P₀, the first vertex reached V₁ is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P₁. P₁ is inclined to P₀ at a 60° angle.{{Efn|P₀ and P₁ lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V₂ is 120 degrees beyond V₁ along a second {{radic|3}} chord lying in another hexagonal plane P₂ that is Clifford parallel to P₀.{{Efn|P₀ and P₂ are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V₀ and V₂ are ''two'' {{radic|3}} chords apart{{Efn|V₀ and V₂ are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V₀ and V₂ are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P₀ and P₂ are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V₁ lies in both intersecting planes P₁ and P₂, as V₀ lies in both P₀ and P₁. But P₀ and P₂ have ''no'' vertices in common; they do not intersect.) The third vertex reached V₃ is 120 degrees beyond V₂ along a third {{radic|3}} chord lying in another hexagonal plane P₃ that is Clifford parallel to P₁. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V₀ to V₃ is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}} {{Sfn|Mamone, Pileio & Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹₄.}} ==Notes== {{Regular convex 4-polytopes Notelist|wiki=W:}} ==Citations== {{Regular convex 4-polytopes Reflist|wiki=W:}} ==References== {{Refbegin}} * {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}} * {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1}} * {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}} === [[Polyscheme|Polyschemes]] === {{Regular convex 4-polytopes Refs|wiki=W:}} {{Refend}} 8xf8w6dio4nuhtjawye24ro2n0tq1vf 2823731 2823727 2026-08-20T21:08:52Z Dc.samizdat 2856930 /* A theory of the Euclidean cosmos */ 2823731 wikitext text/x-wiki = Real Euclidean four-dimensional space R⁴ = {{align|center|David Brooks Christie}} {{align|center|dc@samizdat.org}} {{align|center|Draft in progress}} {{align|center|June 2023 - August 2026}} <blockquote>'''Abstract:''' The physical universe is properly visualized as a Euclidean space of four orthogonal spatial dimensions. Space itself has a fourth orthogonal dimension, of which we are unaware in ordinary life. Atoms are 4-polytopes, small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. We ourselves and our planet are only 3-dimensional objects, but nonetheless we can see in four dimensions of space. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math>. Light from them reaches us directly, on straight lines through 4-space. This view of the observed universe is compatible with special and general relativity, and with quantum mechanics. It furnishes those theories with an explanatory geometric model.</blockquote> == Summary == We observe that physical space has four perpendicular dimensions, not just three; atoms are [[W:4-polytope|4-polytopes]]; the sun is a 4-ball that is round in four dimensions; everything of intermediate size between an atom and a star, including us and our planet, lies in a 3-dimensional manifold of ordinary space; and our entire 3-space manifold is translating through Euclidean 4-space at the speed of light, in a direction perpendicular to its three interior dimensions. == A theory of the Euclidean cosmos == The physical universe is properly visualized as a [[w:Four-dimensional_space|Euclidean space of four orthogonal spatial dimensions]]. Space itself has a fourth orthogonal dimension, of which we are unaware in ordinary life. Atoms are [[w:4-polytope|4-polytopes]], small round 4-dimensional objects, and stars are 4-balls of atomic plasma, large round 4-dimensional objects. Objects intermediate in size between atoms and stars, including molecules, people, and planets, are so flat as to be essentially 3-dimensional, having only the thickness of an atom in the orthogonal fourth dimension. All objects with mass move inertially through Euclidean 4-space at velocity <math>c</math> as long as they exist, and acceleration only varies their direction. Objects moving in the same direction are in the same inertial reference frame. Their direction of motion through 4-space at velocity <math>c</math> is their proper time dimension, simply because their direction and velocity of motion through time is the same as their direction and velocity of motion through space. A typical spiral galaxy such as ours is a 4-ball of mostly empty space, with stars and other objects distributed non-uniformly within it. The galaxy's orbital center may be nothing: a smaller 4-ball of empty space they surround. The stars in our galaxy appear from our viewpoint to be distributed in a cloud of elliptical spirals occupying a disk-like ellipsoid region of 3-dimensional space, but they are not so confined: they are distributed within a spherical region of 4-dimensional space. The galaxy's actual shape is spherical, not a flattened ellipsoid, but it is rounder than round can be in our ordinary experience: it occupies a hyperspherical region of space. The concentric spirals of stars that we observe lie on concentric [[W:3-sphere|3-sphere]]s (4-dimensional spheres), not on concentric 2-ellipsoids (3-dimensional elliptical spirals). Our sun and solar system lies on one of those concentric 3-spheres. More generally, orbits are circular in 4-space, and elliptical in the 3-space of their elliptic hyperplane. [[File:Hypersphere.png|thumb|[Placeholder image for:]Rotating illustration of the 4-ball galaxy showing its spirals of star clouds on the surface of concentric 3-spheres, obtained by reverse sterographic projection from 3D images of the galaxy.]] The galaxy as a whole, or more properly its orbital center point, is translating through 4-space at velocity <math>c</math>, in a distinct direction orthogonal to all three dimensions of our ordinary proper 3-space. Stars within the galaxy are translating with it at the same velocity <math>c</math> in the same direction, but on spiral trajectories as they pursue their various orbits within the galaxy. The galaxy as a whole occupies a 4-ball within its proper inertial reference frame (that is, in the moving frame of reference in which the galaxy considers itself to be a stationary rotating 4-ball). Over time, the galaxy occupies a 4-dimensional cylinder and progresses along the cylinder's axis at velocity <math>c</math>. In this more universal inertial reference frame, the stars in the galaxy follow helical geodesic paths through the cylinder; their trajectories are screw-displacements, the compound of a simple rotation and a linear translation. The gravitational force and the inertial tendency to follow a geodesic are the same phenomenon, by the equivalence principle. That said, they can be distinguished, and the galaxy is held together primarily by gravity as inertia, not by gravity as attraction to a central mass toward which objects fall in orbit. There is not enough mass in the galaxy to hold it together by attraction, there is just enough to bend the stars' trajectories toward each other, in helical orbits around a barycentric axis. It is the tremendous inertial force of stars in motion at velocity <math>c</math> that holds the cylinder of motion together. The observed universe as a whole appears to be a 3-sphere expanding radially from a central origin point at velocity <math>c</math>, the invariant velocity of mass-carrying objects through 4-space, also the propagation speed of light relative to any moving 3-space manifold, as measured by all observers. For all observers, the conjectured origin point of the universe corresponds not only to a now-distant point in their proper time past, it also corresponds to a distinct now-distant point in 4-dimensional space (the same point in the same Euclidean 4-space for all observers). The big bang had a distinct origin point in real space as well as in real time. More generally, time and Euclidean 4-space can be measured independently, just as time and Euclidean 3-space were measured classically, without the necessity to combine them as spacetime. The same inertial force which holds the galactic cylinder of motion together also confines us physically to an exceedingly thin three-dimensional surface manifold moving through 4-space at velocity <math>c</math>. All objects in our solar system except the sun itself lie within this thinest three-dimensional manifold. That is why we are 3-dimensional objects ourselves, and why we cannot construct more than three perpendiculars through a single point in our local 3-dimensional space. The enclosing surface of a spherical region of 4-space is itself a finite, curved (non-Euclidean) 3-dimensional space called a [[w:3-sphere|3-sphere]]. We live within such a 3-space, in an infinitesimally curved 3-manifold surface embedded in Euclidean 4-space. That surface is the ordinary 3-dimensional space we experience, and it contains the earth, all the planets and the 3-dimensional space between them. Our solar system is only a small patch on the surface of a dimensionally rounder space, although that surface is not infinite. It is curved, and finite, analogous to the way the 2-dimensional surface of the earth -- once thought to be flat -- is curved and finite. Our particular 3-sphere is one of the galaxy's concentric 3-spheres of spiral star-clouds. The solar system occupies a tiny patch of this filmy 4-dimensional soap-bubble of galactic size, that is thicker-skinned than the diameter of an atom only in the interior of stars and supermassive objects. Our entire 3-sphere manifold, as a 3-spherical shell within the moving 4-ball galaxy, is translating through 4-space at velocity <math>c</math> with the galaxy, in a distinct direction that is orthogonal to the manifold's three orthogonal dimensions of interior space. At every material point in the manifold (at every atom), the galaxy's translation through 4-space is following a geometric law of motion discovered by Coxeter, that governs the propagation of rotating objects through Euclidean space by screw translation. The solar system's atoms of mass are 4-polytopes that are simultaneously rotating and translating, and as they advance together they define a moving 3-dimensional manifold by their own collective inertia, also called gravity, the property of matter's ceaseless propagation through 4-space at the constant velocity <math>c</math>, the universal rate of causality at which quantum events occur, all objects move, and the universe evolves. Any moving 3-dimensional manifold that is such an evolving surface boundary is empty in most places, occupied by single atoms in comparatively fewer places, and occupied by bound complexes of multiple atoms (molecules) in still fewer places. In all these places it is no thicker than one atom in the dimension corresponding to its direction of translation, because molecules are 3-dimensional complexes of atoms that add no thickness to the manifold. Every object which we find occurring naturally in the solar system other than the sun itself, even the largest of 3-dimensional objects a planet, is a three-dimensional smear of atoms no thicker than one atom in its fourth dimension, which is the direction of its linear translation through 4-space at velocity <math>c</math>. The moving surface manifold cannot be thicker than one atom at any point unless and until there is enough mass near that point for the force of gravity as attraction to overcome the force of gravity as inertia, allowing atoms to be "heaped up" into larger 4-dimensional objects that form a lump in its moving surface. We have little understanding of such 4-dimensional lumps thicker than one atom, since they occur naturally in our vicinity only in the interior of the sun. In fact the sun is the only such lump occurring naturally in our solar system. We refer to 4-dimensional lumps of matter as plasma, and have little experimental knowledge of their geometry or internal structure. We know that such a lump as the sun burns at its surface 3-sphere and emits radiation, and we know a good deal about those surface processes which are nuclear atomic processes, but we know nothing about its interior 4-ball. Every such moving 3-dimensional surface boundary of matter in the observed universe is evolving in four dimensions at velocity <math>c</math>. Its current location in 4-space corresponds to the present moment in the proper time of its inertial reference frame. Its direction of movement at velocity <math>c</math> corresponds to its proper time dimension, which is a spiral over time, not a Euclidean (straight-line) dimension, since its direction is changing in its orbit. Objects with mass of all sizes, from atoms to the largest objects observed in the cosmos, are perpetually in inertial rotational motion in some orbit, and simultaneously in inertial translational motion propagating themselves through 4-space, two orthogonal inertial motions each at the constant universal rate of transformation <math>c</math>. Every object moves relative to universal 4-coordinate space on its own distinct geodesic spiral, a screw translation trajectory that is the compound of two orthogonal inertial motions, a rotation and a translation. Objects without mass such as photons lie off such moving surface boundaries of matter from which they were emitted, and their motion is of a different nature. They are in translational motion at velocity <math>c</math> in all four dimensions concurrently, without any rotational component of motion, so they move through 4-space on straight lines at a compound velocity. The propagation speed of light measured on a straight line through Euclidean 4-space is <math>c\prime = 2c</math>, so we can see in four dimensions, even though we are physically confined to a 3-dimensional manifold that is moving at velocity <math>c</math>. For example, we can look across the center of our mostly-empty 4-ball galaxy and see stars in the opposite sides of its concentric 3-sphere surfaces. We have been unaware that when we look up at night we see stars and galaxies, themselves large 4-dimensional objects, distributed all around us in 4-dimensional Euclidean space, and moving through it, like us, at the constant velocity <math>c</math> in the 4-space direction corresponding to their proper time, perpendicular to all three dimensions of their proper space. Light from them reaches us directly, propagating on straight lines through 4-space at twice the velocity at which they, and we ourselves, are propagating through 4-space. This physical model of the observed universe is compatible with the theories of special and general relativity, and with the atomic theory of quantum mechanics. It explains those theories geometrically, as expressions of intrinsic symmetries in Euclidean space. == Symmetries == It is common to speak of nature as a web, and so it is, the great web of our physical experiences. Every web must have its root systems somewhere, and nature in this sense must be rooted in the symmetries which underlie physics and geometry, the [[W:Group (mathematics)|mathematics of groups]].{{Sfn|Conway, Burgiel & Goodman-Strauss|2008}} As I understand [[W:Noether's theorem|Noether's theorem]] (which is not mathematically), hers is the deepest meta-theory of nature yet, deeper than [[W:Theory of relativity|Einstein's relativity]] or [[W:Evolution|Darwin's evolution]] or [[W:Euclidean geometry|Euclid's geometry]]. It finds that all fundamental findings in physics are based on conservation laws which can be laid at the doors of distinct [[W:symmetry group |symmetry group]]s. Thus all fundamental systems in physics, as examples [[W:quantum chromodynamics|quantum chromodynamics]] (QCD) the theory of the strong force binding the atomic nucleus and [[W:quantum electrodynamics|quantum electrodynamics]] (QED) the theory of the electromagnetic force, each have a corresponding symmetry [[W:group theory|group theory]] of which they are an expression. [[W:Coxeter group|Coxeter's theory of symmetry groups]] generated by reflections did for geometry what Noether's theorem and Einstein's relativity did for physics. [[W:Coxeter|Coxeter]] showed that Euclidean geometry is based on conservation laws that correspond to distinct symmetry groups, and that their group actions express the principle of relativity. Here is Coxeter's formulation of the motions of objects (their congruent transformations) in an ''n''-dimensional Euclidean space, excerpted:{{Sfn|Coxeter|1973|pp=217-218|loc=§12.2 Congruent transformations}} <blockquote>Let <small><math>\mathrm{Q}</math></small> denote a rotation, <small><math>\mathrm{R}</math></small> a reflection, <small><math>\mathrm{T}</math></small> a translation, and let <small><math>\mathrm{Q}^q \mathrm{R}^r\mathrm{T}</math></small> denote a product of several such transformations, all commutative with one another. Then <small><math>\mathrm{RT}</math></small> is a glide-reflection (in two or three dimensions), <small><math>\mathrm{QR}</math></small> is a rotary-reflection, <small><math>\mathrm{QT}</math></small> is a screw-displacement, and <small><math>\mathrm{Q^2}</math></small> is a double rotation (in four dimensions).<br> Every orthogonal transformation is expressible as:<br> :<small><math>\mathrm{Q}^q \mathrm{R}^r</math></small><br> where <small><math>(2^q + r \le n)</math></small>, the number of dimensions.<br> Transformations involving a translation are expressible as:<br> :<small><math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}</math></small><br> where <small><math>(2^q + r + 1 \le n)</math></small>.<br> For <small><math>(n = 4)</math></small> in particular, every displacement is either a double rotation <small><math>\mathrm{Q}^2</math></small>, or a screw-displacement <small><math>\mathrm{QT}</math></small> [where the rotation component <small><math>\mathrm{Q}</math></small> is a simple rotation, but the <small><math>\mathrm{QT}</math></small> is chiral like a <small><math>\mathrm{Q^2}</math></small>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <small><math>\mathrm{QRT}</math></small>.</blockquote> If we begin with this most elemental [[w:Kinematics|kinematics]] of Coxeter's, and also assume the [[W:Galilean relativity|Galilean principle of relativity]], every displacement in 4-space can be viewed as either a <small><math>\mathrm{Q^2}</math></small> or a <small><math>\mathrm{QT}</math></small>, because we can view any <small><math>\mathrm{QT}</math></small> as a <small><math>\mathrm{Q^2}</math></small> in a linearly moving (translating) reference frame. Therefore any transformation from one inertial reference frame to another is expressable as a <small><math>\mathrm{Q^2}</math></small>. By the same principle, we can view any <small><math>\mathrm{QT}</math></small> or <small><math>\mathrm{Q^2}</math></small> as an isoclinic (equi-angled) <small><math>\mathrm{Q^2}</math></small> by proper choice of reference frame.{{Efn|[[W:Arthur Cayley|Cayley]] showed that any rotation in 4-space can be decomposed into two isoclinic rotations, which intuitively we might see follows from the fact that any transformation from one inertial reference frame to another is expressable as a [[W:SO(4)|rotation in 4-dimensional Euclidean space]].|name=Cayley's rotation factorization into two isoclinic reference frame transformations}} Coxeter's relation is thus a mathematical statement of the principle of relativity, on group-theoretic grounds. It correctly captures the limits to [[W:General relativity|general relativity]], in that we can only exchange the translation (<small><math>\mathrm{T}</math></small>) for ''one'' of the two rotations (<small><math>\mathrm{Q}</math></small>). An observer in any inertial reference frame can always measure the presence, direction and velocity of ''one'' rotation (<small><math>\mathrm{Q}</math></small>) up to uncertainty, and can always distinguish the direction of their own proper time translation (<small><math>\mathrm{T}</math></small>). As I understand Coxeter theory (which is not mathematically), the symmetry groups underlying physics seem to have an expression in a [[W:Euclidean space|Euclidean space]] of four [[W:dimension|dimension]]s, that is, they are [[W:Euclidean geometry#Higher dimensions|four-dimensional Euclidean geometry]]. Therefore as I understand that geometry (which is entirely by synthetic methods rather than by Clifford's algebra), the [[W:Atom|atom]] seems to have a distinct Euclidean geometry, such that atoms and their constituent particles are four-dimensional geometric objects (4-polytopes), and nature can be understood in terms of their [[W:group action|group actions]], including centrally their group <small><math>SO(4)</math></small> [[W:rotations in 4-dimensional Euclidean space|rotations in 4-dimensional Euclidean space]]. The distinct Coxeter symmetry groups have characteristic <small><math>SO(4)</math></small> rotational expressions as the [[W:Regular_4-polytope|regular 4-polytopes]]. Their discrete isoclinic rotations are distinguishing properties of fundamental objects in geometry, relativity and quantum mechanics. For example, stationary atoms exhibit the <small><math>SO(4)</math></small> symmetries of the discrete isoclinic (equi-angled) double rotations (<small><math>\mathrm{Q^2}</math></small>) of a set of regular 4-polytopes that is characteristic of their [[w:Atomic_number|atomic number]]. == Special relativity describes Euclidean 4-space == <blockquote>Our entire model of the universe is built on symmetries. Some, like isotropy (the laws are the same in all directions), homogeneity (same in all places), and time invariance (same at all times) seem natural enough. Even relativity, the Lorentz Invariance that allows everyone to observe a constant speed of light, has an elegance to it that makes it seem natural.<ref>{{Cite book|first=Dave|last=Goldberg|title=The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality|chapter=§10. Hidden Symmetries: Why some symmetries but not others?|year=2013|publisher=Dutton Penguin Group|isbn=978-0-525-95366-1|ref={{SfnRef|Goldberg|2013}}}}</ref></blockquote> Although the Minkowski spacetime of relativity is a non-Euclidean 4-dimensional space,{{Efn|Spacetime is a non-Euclidean (curved) 4-dimensional "space" because it consists of three orthogonal space dimensions and a time dimension. The time dimension is not orthogonal to the three spatial dimensions; the time coordinate has the opposite sign to the three space coordinates so spacetime is hyperbolic, not a flat Euclidean 4-space at all.}} it has been noticed that its 3-dimensional space component could be modeled as a [[W:3-sphere|3-sphere]] embedded in 4-dimensional Euclidean (flat) space. That is, we could imagine that the ordinary 3-dimensional space we perceive is the curved 3-dimensional surface of a 4-dimensional ball (since the surface of a 4-ball is a curved 3-dimensional space called a 3-sphere, just as the surface of a 3-ball like the earth is a curved 2-dimensional space called a 2-sphere). This was first described by Einstein himself in 1921, as a thought experiment in which he carefully described his fourth orthogonal spatial dimension as merely a mathematical abstraction. Subsequently it was noticed by others (not mainstream physicists) that if physical space were really embedded in Euclidean 4-dimensional space (with our 3-dimensional space embedded in 4-space as some 3-manifold, not necessarily a 3-sphere), then the Lorentz transformation effects of special relativity (spatial forshortenings and time dilations and so forth) could all be explained by ordinary perspective geometry in 4-dimensional Euclidean space. Special relativity reduces to classical vector space geometry (based on the 4-dimensional version of the Pythagorean theorem), but if and only if every observer is moving through 4-space at a universal constant velocity ''c'', in some 4-space direction. This counter-intuitive alternative geometric model of relativity, which has usually been called [[W:Formulations of special relativity#Euclidean relativity|Euclidean relativity]], is motivated by the fact that in every kind of relativity, but originally in Einstein's special relativity, each observer moves on a vector through a four-dimensional space consisting of their three proper spatial dimensions and their proper time dimension, and the Pythagorean vector-sum of their motion through this kind of proper 4-space is always ''c'', as measured by all observers from any inertial reference frame. This is the Lorentz invariant, that allows everyone to observe a constant speed of light, regardless of their motion relative to the light source. But no physicists have taken the leap of claiming that therefore, our universe is physically [[W:Euclidean geometry#Higher dimensions|this kind of Euclidean 4-space]], and that observers are actually moving through it at velocity ''c''. In physics as it has been universally understood, observers are not supposed to be able to move at velocity ''c''. Their motion takes place in 3-space and in universal coordinate time (in Minkowski spacetime), and the cosmos is considered to be a non-Euclidean 3-space, generally a closed (finite) expanding 3-space, but with only three spatial dimensions, not four. In the Euclidean relativity alternative view, however, every observer is always moving at velocity ''c'' through the universe, which is real Euclidean 4-dimensional space <small><math>\mathbb{R^4}</math></small>. The direction in which they are moving is called their proper time axis.{{Efn|Time in spacetime is universal coordinate time, but there is another kind of time in relativity, the proper time in each inertial reference frame. Your proper time is the time you experience, and every observer has his own proper time; proper time runs at different rates in different inertial reference frames. It runs slower (compared to universal coordinate time) in a gravitational field (according to general relativity), and observers in motion with respect to each other view each other's clocks as running slower than their own clocks (according to special relativity).}} Their movement in time is not just modelled as movement in an abstract fourth dimension (as it is in Minkowski spacetime), their movement in time is isomorphic to their movement through physical space in a distinct direction at velocity ''c''. Two observers' directions of movement through space may be different (or not, if they happen to be going in the same direction). Your proper time dimension is whichever direction you are moving. The other three directions perpendicular to your proper time axis are the three dimensions of your proper space, which again, will be different directions for you than for other observers moving in a different direction. There are four orthogonal spatial dimensions which we all share, but we share the same orthogonal proper time axis and proper space axes only if we are at rest with respect to each other, actually moving in the same direction at velocity ''c'', in the same inertial reference frame. Your proper 4-space coordinate system is rotated with respect to another observer's proper 4-space coordinate system, precisely as your vectors (directions of motion) are rotated in Euclidean 4-space with respect to each other, but there are no metric distortions (no Lorentz transformations) between your proper 4-space coordinate systems; you are both embedded in the same Euclidean 4-dimensional space <small><math>\mathbb{R^4}</math></small>.{{Efn|The angular divergence between two observer's motion vectors is proportional to their relative velocity: the more they diverge, the greater their relative velocity, up to the maximum divergence possible in the space. In Euclidean relativity all observers are in motion at velocity ''c'' relative to universal 4-coordinate space, so the maximum relative velocity between two observers is 2''c'' when they are moving in exactly opposite directions in 4-space. This is not a contradiction of special relativity, which limits the maximum relative velocity between two observers to ''c'', it is the same measurement in different units. Special relativity measures all velocities in a 3-space of Minkowski spacetime. Euclidean relativity measures all velocities in Euclidean 4-space.}} So in this novel alternate view of relativity, every mass in the universe must be perpetually in motion at velocity ''c'' in Euclidean 4-space, along with all the masses in its vicinity that are going in (nearly) the same direction. The entire solar system, for example, must be translating in the fourth dimension at the "speed of light" ''c'', although we do not notice it, since we are all moving in that same direction together. Acceleration of an object varies its direction of motion through 4-space, but never its velocity, which is invariant for all objects with mass. Two objects which are in motion relative to each other are both actually in motion at the same velocity ''c'', but in at least slightly different directions. In Einstein's relativity, the invariant ''c'' is the speed of light through 3-space. In Euclidean relativity, the invariant ''c'' is the speed of matter through 4-space! The speed of light through 3-space is also perceived as ''c'' by all observers, because they are each living in a moving 3-manifold that is moving through 4-space at velocity ''c''. Despite their extreme differences in viewpoint, Einstein's relativity and Euclidean relativity are equivalent theories in complete agreement with each other, by definition. The two theories make exactly the same predictions about how observers in different reference frames will perceive each other's motions in time and space, and we shall see that they also agree on the predictions of general relativity. They both describe the same geometric relations of space and time, but they describe that geometry as embedded in two very different universal host spaces: Minkowski spacetime versus Euclidean 4-space. ...cite Lewis Epstein's elegant explanation of the Lorentz Invariance as observers moving at constant velocity <math>c</math> through space and proper time ...cite Yamashita{{Sfn|Yamashita|2023}} on the equivalence of special relativity and Euclidean 4-space relativity ...cite Kappraff & Adamson's 2003 paper on The Relationship of the Cotangent Function to Special Relativity Theory, geometry and properties of number,{{Sfn|Kappraff & Adamson|2003|loc=Special Relativity Theory, Geometry and properties of number}} which shows how the Lorentz coefficient is a function of a deep geometric property of number{{Sfn|Kappraff & Adamson|2000|loc=A Fresh Look at Number}} discovered by Steinbach,{{Sfn|Steinbach|1997|loc=Golden Fields: A Case for the Heptagon}} by means of which the root formula of geometry in any Euclidean dimension, the Pythagorean theorem, may be derived solely in terms of the addition of polygon side lengths, without recourse to their products or squares. More generally, Steinbach found that in the relations among regular polytope chords, to add is to multiply; every chord is both the product (quotient) of a pair of chords and the sum (difference) of another pair of chords. Euclidean relativity is not even a fringe theory; no physicists have adopted it. There are many good reasons why the revolutionary leap to a four orthogonal spatial dimensions viewpoint has not been taken, beginning with the universally observed fact that we can only construct three perpendiculars through a point in our immediate space, which appears to be resolutely 3-dimensional, not 4-dimensional. Euclidean relativity offers a nice geometric explanation of the reasons for the Lorentz transformations, but only at the cost of raising other mysteries, which have been difficult for its aficionados to explain. Another mystery is how light signals between observers in relative motion could "catch up" with the receiver moving on a diverging path through 4-space from the emitter. If both observers are already moving at ''c'' (on diverging paths), the propagation speed of light through 4-space between them would have to be greater than ''c''. Euclidean relativity is a revolutionary theory indeed, in which ''c'' cannot possibly be the speed of light! We conclude that, for a theory of Euclidean 4-space to be physically viable (that is, for <math>\mathbb{R^4}</math> to be our real space and not merely an abstract mathematical space), the speed of light through Euclidean 4-space must be <math>c\prime = 2c</math>, with massless photons translating through 4-space at twice the speed of mass-carrying objects. Photons must translate the diagonal distance through 4-space along the long diameter of a unit 4-hypercube, in the same time that massive particles translate linearly along the edge of a unit 4-hypercube. This is conceivable in 4-space (and in no other Euclidean space of any dimensionality) because the long diagonal of the unit 4-hypercube is the natural number <small><math>\sqrt{4}</math></small>. == An object's motion in space is the product of its discrete self-reflections == Coxeter theory describes all the possible motions of an object in space as local functions of the object's discrete geometry (its shape). Coxeter observed that in a Euclidean space of any number of dimensions, any displacement of a geometric object from one place to another, and any rotation of the object from one orientation to another, can be broken down into the product of a small number of discrete self-reflections. Any action of a geometric object that transforms its position and orientation in space may be measured as a distinct group of self-reflections of the object in its own surfaces. Any motion of the object whatsoever may be precisely described as the object propagating itself through space by a discrete set of local self-reflections. Coxeter found that both changes in position (translations) and changes in orientation (rotations) can be broken down into the simplest of all displacements (self-reflections). A translation occurs when an object self-reflects twice, in two distinct surfaces which are parallel to each other. A rotation also occurs when an object self-reflects twice, but in two distinct surfaces which touch (intersect each other). When a object self-reflects once, it turns itself inside out (it reverses its chirality), but in translations and rotations it self-reflects twice, preserving its chirality. Coxeter's laws of motion are a geometric counterpart to Newton's laws of motion in three dimensional Euclidean space. They are helpful because they can be understood as geometric pictures. But they are also a revolutionary advance beyond Newton's laws, because Coxeter formulated them in Euclidean spaces of any number of dimensions. For example, they give us geometric pictures of all the possible motions of objects in four dimensional Euclidean space: <blockquote>Every orthogonal transformation in 4-space is expressible as:<br> :<small><math>\mathrm{Q}^q \mathrm{R}^r \mathrm{T}^t</math></small><br> where <small><math>(2^q + r + t \le 4)</math></small>. Every displacement is either a double rotation <small><math>\mathrm{Q}^2</math></small>, or a screw-displacement <small><math>\mathrm{QT}</math></small> [where the rotation component <small><math>\mathrm{Q}</math></small> is a simple rotation, but the <small><math>\mathrm{QT}</math></small> is chiral like a <small><math>\mathrm{Q^2}</math></small>]. Every enantiomorphous transformation in 4-space (reversing chirality) is a <small><math>\mathrm{QRT}</math></small>.</blockquote> While this description should be understood as simple geometric pictures, some of the pictures may not be easy for us to visualize, since we have no physical experience in 4-dimensional space. Rotation (<small><math>\mathrm{Q}</math></small>), reflection (<small><math>\mathrm{R}</math></small>) and translation (<small><math>\mathrm{T}</math></small>) are just what they are in three-dimensional space, but double rotation (<small><math>\mathrm{Q}^2</math></small>) is something new and unprecedented in our physical experience, because double rotations cannot occur until you have four or more dimensions of space to rotate in. ...to readers who have not studied Coxeter (almost all readers including TAC), the blockquote above is "just math", not visualizable geometry...but I could describe Coxeter's congruent transformations in 4-space here geometrically: I could say clearly what they mean in spatial terms, in language anyone can understand, because they don't require any math to be understood; the "math" here is really just simple pictures (reflections and rotations); even double rotations can be visualized by dimensional analogy, as compounds of simple rotations...since even most physicists are unacquainted with Coxeter geometry, it might be useful to do this here... == Light propagates through 4-space at twice its apparent velocity ''c''== Coxeter's geometric laws of motion apply to all objects with mass in 4-dimensional Euclidean space, but we find there is an additional kind of displacement which applies only to massless particles such as photons. Light quanta (photons) translate through 4-space by 4-dimensional reflection <small><math>\mathrm{R}^4</math></small>, which may be termed a double translation <small><math>\mathrm{T}^2</math></small>, a pure translation via two pairs of parallel reflections, without any rotation component <small><math>\mathrm{Q}</math></small>. Matter (atoms and all particles with mass) are perpetually rotating and translating through 4-space by <small><math>\mathrm{QT}</math></small>, a screw translation of a rotating object, which is relativistically equivalent to a stationary isoclinic <small><math>\mathrm{Q^2}</math></small>, an isoclinically rotating object such as an atom. A simple rotation <small><math>\mathrm{Q}</math></small> or simple translation <small><math>\mathrm{T}</math></small> is a double reflection <small><math>\mathrm{R^2}</math></small>, so a <small><math>\mathrm{QT}</math></small> or <small><math>\mathrm{Q^2}</math></small> is also an <small><math>\mathrm{R^4}</math></small>, but not with the same group of reflection angles as a light signal <small><math>\mathrm{R^4}</math></small>. A translation <small><math>\mathrm{T = R^2}</math></small> is a double reflection in two parallel planes, and a rotation <small><math>\mathrm{Q = R^2}</math></small> is a double reflection in two intersecting planes, as in a <small><math>\mathrm{QT = R^4}</math></small> which is both at once. A double translation <small><math>\mathrm{T^2 = R^4}</math></small> is two double reflections in pairs of parallel planes at once, a reflection in four or more non-intersecting parallel planes; it is all translation and no rotation. In a <small><math>\mathrm{T^2}</math></small> all the motion goes to translation, so the translation goes twice as far as the simple translation <small><math>\mathrm{T}</math></small> in a <small><math>\mathrm{QT}</math></small>. A double translation <small><math>\mathrm{T^2 = R^4}</math></small> is the opposite of a double rotation <small><math>\mathrm{Q^2 = R^4}</math></small>, which is stationary but rotates twice as fast as the simple rotation <small><math>\mathrm{Q}</math></small> in a <small><math>\mathrm{QT}</math></small>. The product of the two translations in a <small><math>\mathrm{T^2}</math></small> is a diagonal 4-space translation over the long diameter of the unit 4-hypercube, exactly twice the distance of a simple <small><math>\mathrm{T}</math></small> over the edge length (or radius) of the unit 4-hypercube. The [[w:Tesseract|4-hypercube (also known as the 8-cell or tesseract)]] is ''radially equilateral'', which means its edge length is equal to its radius, like the hexagon, so its long diameter (twice its radius) is exactly twice its edge length. The photon moves an equal distance in four orthogonal directions. By the four-dimensional Pythagorean theorem, each of those four distances is half the total distance the photon moves: one edge length (one radius) is half the total diagonal distance moved (the long diameter). That total movement is a double-the-distance translation, but without any rotation component, so it cannot carry any mass with it. A <small><math>\mathrm{T^2}</math></small> cannot reposition a 4-polytope the way a <small><math>\mathrm{QT}</math></small> does, it can only reposition a quantum of energy that has no distinguishing rotational symmetry, such as a photon. That is the price light pays to move exactly twice as fast as matter. ...lensing of double translations <small><math>\mathrm{T^2 = R^4}</math></small> in more than two pairs of parallel planes at once...relationship to the frequency of light emitted and the coherence length of the wave packet... == The Kepler problem is framed in Euclidean 4-space == The [[W:Kepler problem|Kepler problem]] is named for [[W:Johannes Kepler|Johannes Kepler]], arguably the greatest geometer since the ancients up to [[w:Ludwig Schläfli|Ludwig Schläfli]], who proposed [[W:Kepler's laws of planetary motion|Kepler's laws of planetary motion]] which solved the problem of the orbits of the planets, and investigated the types of forces that would result in orbits obeying those laws. Those forces were later identified by [[W:Isaac Newton|Isaac Newton]] in his[[W:Philosophiæ Naturalis Principia Mathematica| Principia]], where he proves what today might be called the "inverse Kepler problem": the orbit characteristics require the force to depend on the inverse square of the distance.<ref>{{Cite book|last=Feynman|first=Richard|title=Feynman's Lost Lecture: The Motion of Planets Around the Sun|date=1996|publisher=W. W. Norton & Company|isbn=978-0393039184}}</ref> The inverse square law behind the Kepler problem is the [[W:Central force|central force]] law which governs not only [[W:Newtonian gravity|Newtonian gravity]] and celestial orbits, but also the motion of two charged particles in [[W:Coulomb’s law|Coulomb’s law]] of [[W:Electrostatics|electrostatics]]; it applies to attractive or repulsive forces. Problems in which two bodies interact by a central force that varies as the [[W:Inverse square law|inverse square]] of the distance between them are called Kepler problems. Thus the [[W:Hydrogen atom|hydrogen atom]] is a Kepler problem, since it comprises two charged particles interacting by Coulomb's law, another inverse-square central force. Using classical mechanics, the solution to a Kepler problem can be expressed as a [[W:Kepler orbit|Kepler orbit]] using six kinematical variables or [[W:Orbital elements|orbital elements]]. The solution conserves an orbital element called the [[W:Laplace–Runge–Lenz vector|Laplace–Runge–Lenz (LRL) vector]], a [[W:Constant of motion|constant of motion]], meaning that it is the same no matter where it is calculated on the orbit. The LRL vector was essential in the first quantum mechanical derivation of the [[W:Atomic emission spectrum|spectrum]] of the hydrogen atom, but this approach has rarely been used since the development of the [[W:Schrödinger equation|Schrödinger equation]]. The conservation of the LRL vector corresponds to the <small><math>SO(4)</math></small> symmetry, by Nother's theorem. The LRL vector lies orthogonal to both the orbital plane and the angular momentum vector of the Kepler orbit; we observe that it lies in a fourth orthogonal dimension. Fock in 1935<ref>V. Fock, Zur Theorie des Wasserstoffatoms, Zeitschrift für Physik. 98 (3-4) (1935), 145–154.</ref> and Moser in 1970<ref>J. Moser, Regularization of Kepler’s problem and the averaging method on a manifold, Commun. Pure Appl. 23 (1970), 609–636</ref> observed that the Kepler problem is mathematically equivalent to non-affine geodesic motion (a particle moving freely) on the surface of a 3-sphere, so that the whole problem is symmetric under certain rotations of the four-dimensional space. This higher-dimensional symmetry results in two well-known properties of the Kepler problem: the momentum vector always moves in a perfect circle and, for a given total energy, all such velocity circles intersect each other in the same two points. ... Relativity establishes that an orbit in space is viewed in a different way in each distinct inertial reference frame. Depending on the choice of reference frame, the same Kepler system may be seen to be performing any one of a sequence of relativistically equivalent rotations in 4-space, on a continuum from an isoclinic rotation (Q²) in the orbit's proper reference frame, to a screw transfer (QT) with a simple rotation component (Q) and a translation component (T) at velocity <math>c</math>, in the universal reference frame of 4-coordinate space wherein every object is seen to be translating at velocity <math>c</math>. In reference frames between these two limit cases, the orbit is seen to be performing a double rotation (Q²) at two unequal, completely orthogonal angular rates of rotation: an elliptical double rotation. These include the reference frames of most typical observers, who are moving slowly relative to the observed orbital system's reference frame (their relative motion is a small fraction of the speed of light). ...this is probably misplaced here and should not interrupt the discussion at this point: ...These typical observations agree closely with the predictions of special relativity, because the non-isoclinic elliptical (Q²) resembles a (QT), since one of its two completely orthogonal rotations (Q) has such a long period that it is almost indistinguishable from a straight translation (T). All orbits in 4-space are isoclinic in their own reference frame. Orbiting objects in their own proper Kepler systems follow circular geodesic isoclines through 4-space. Orbits in 4-space are perfectly circular in their own reference frame, as Copernicus assumed the orbits of planets to be. It is the orbit's path through the 3-space of its elliptic hyperplane that is an ellipse, as Kepler found it to be. ...cite Jesper Goransson's very concise paper The geodesic circle that an orbiting object follows through 4-space in the proper reference frame of its own Kepler system is not a simple great circle which turns in two orthogonal dimensions. It is a helical great circle that turns in four orthogonal dimensions at once.{{Efn|Geodesic orbits in 4-space are not simple 2-dimensional great circles; they are helical 4-dimensional great circles that curve in all four dimensions at once. Their circular trajectories are helixes which we call ''isoclines'', since they are the paths taken by points on a rigid object undergoing isoclinic rotation.}} Such circles lie outside our physical experience, since our local space has only three orthogonal dimensions. Nonetheless we can visualize them in imagination, because their helical, circular shape is perfectly well defined by the kinematical variables of the Kepler orbit. The real physical correlates of abstract orthogonal planes and rotation angles are already familiar to us viscerally in our body-language of physical experience, since we are endowed biologically with highly evolved visual signal processing engines. These enable us to see and understand spatial relations and motions, including rotations, without even thinking about angles and orthogonal planes. This physical endowment is an inborn capacity for dimensional analogy which our biologic evolution has provided. All our instinctive spatial reasoning is by dimensional analogy from flat 2-dimensional retinal images to 3-dimensional scenes, using our powerful inborn visualization capacities of reverse stereographic projection and pattern recognition. We humans are thus very well equipped with everything we need to see in four-dimensional space, except experience. ... Recently Anco and Moghadam found that through Noether’s theorem in reverse, the LRL vector gives rise to a corresponding infinitesimal dynamical symmetry on the kinematical variables, which they show to be the semi-direct product of <small><math>SO(3)</math></small> and <small><math>\mathbb{R^3}</math></small>, in contrast to the <small><math>SO(4)</math></small> symmetry group generated by the LRL symmetries and the rotations.{{Sfn|Anco|Moghadam|2026|ps=; The physically relevant part of the LRL vector is its direction ... since its magnitude is just a function of energy and angular momentum.}} This remarkable symmetry breaking is expressive of the ''dimensional relativity'' between ordinary 3-space <small><math>\mathbb{R^3}</math></small>, spherical space <small><math>S^3</math></small> and Euclidean space <small><math>\mathbb{R^4}</math></small>. Consider a hydrogen atom in a Kepler orbit: for example, a hydrogen atom moving freely in space in an orbit around the sun. It is a ''double'' Kepler problem: an electrostatic Kepler problem within itself, and a gravitational Kepler problem in its environment. The ''single'' electrostatic Kepler problem of a hydrogen atom moving freely in space beyond any gravitational influence is a problem in special relativity. In our Euclidean 4-space model, this atom viewed as stationary in its own proper reference frame exhibits an <small><math>SO(4)</math></small> rotation symmetry corresponding to an isoclinic double rotation (<small><math>\mathrm{Q^2}</math></small>). The fourth dimension in this reference frame is the atom's proper time vector; it has constant velocity <math>c</math> and constant direction. From the point of view of our universal 4-coordinate space (which cannot be the proper inertial reference frame of any physical observer, all of whom are moving relative to it at velocity ''c''), the entire Kepler system (the atom) is translating through 4-space via a screw translation (<small><math>\mathrm{QT}</math></small>) at constant velocity <math>c</math>. From this viewpoint the atom has only a simple <small><math>SO(3)</math></small> rotation component (<small><math>\mathrm{Q}</math></small>), breaking its stationary <small><math>SO(4)</math></small> isoclinic rotation symmetry (<small><math>\mathrm{Q^2}</math></small>). Because each discrete part of the rotating atom moves along a helical trajectory through 4-space, the atom is in orbit around a barycentric axis (like a star in a galaxy), but only in a tiny orbit within its own radius, which is its inertial domain of rotation. The straight 4-dimensional cylinder it progresses along at velocity <math>c</math> is very narrow: only the diameter of the rotating atom itself. The gravitational Kepler problem of a hydrogen atom in a Kepler orbit around the sun is a problem in general relativity. In our 4-space model, this atom viewed in its own proper reference frame exhibits the same <small><math>SO(4)</math></small> rotation symmetry as it did in the electrostatic Kepler problem where the atom was translating linearly through space. The Kepler system in this case is not just the atom; it is the entire solar system. The LRL vector of this Kepler system is the proper time vector of the atom's inertial reference frame; once again it has constant velocity ''and constant direction''. Although the momentum vector moves in a perfect circle as the atom orbits the sun, the 4-space LRL vector does not move at all: it is a constant of motion, of linear motion (<small><math>\mathrm{T}</math></small>) of the Kepler system (the entire solar system in this case) in a constant 4-space direction, the proper time direction of the system. The direction of the system's proper time vector would vary under some kinds of acceleration of the atom, but it is constant under this kind of orbital acceleration. It continues to point in the same direction, like a 4-space compass needle, as the atom winds its way along its spiral path around the axis of the sun's straight-line translation through 4-space at velocity <math>c</math>. This compass needle always points in the direction the sun is moving, not the direction the atom is moving at any instant. ...Its Kepler orbit around the sun is its <small><math>SO(3)</math></small> rotation component (<small><math>\mathrm{Q}</math></small>). Although the atom is moving on a geodesic circle in the second problem, by the [[equivalence principle]] the difference in the state of the atomic systems in these two problems cannot be observed by examining the atoms alone. Even from another inertial reference frame, where the atom in the second problem is seen to be translating through 4-space via a wide screw translation (<small><math>\mathrm{QT}</math></small>) around the sun's axis of motion, there is still no difference between the two problems which can be detected by examining only the atoms within their own proper reference frames (even over time), because the LRL vector (<small><math>\mathrm{T}</math></small>) is a constant of motion of the entire system in both cases. ...Anco and Maghadam found that <small><math>SO(4)</math></small>) breaks to ... <small><math>S^3</math></small>)... if the energy in the Kepler orbit is negative (an elliptical orbit), and to ... <small><math>H^3</math></small>) ... Minkowski spacetime if the energy is positive (a hyperbolic orbit). ... Finally we consider a third problem in which a hydrogen atom enters the solar system as a comet, loops around the sun and exits the solar system again. This atom... ... As Hamilton found when he discovered the quaternions, we see that it is necessary to admit a fourth dimension to the system in order to properly model the problem: in Hamilton's case the general problem of ..., and in our case the Kepler problem. These are instances of the same problem in 4-dimensional Euclidean geometry, and indeed a solution to the Kepler problem in quaternions (the four Cartesian coordinates of Euclidean 4-space) is a solution to it in our model of the 4-coordinate Euclidean cosmos. == Distribution of stars in our galaxy == The stars in our own galaxy appear to us to be a rotating spiral cluster in 3-dimensional space. By assuming that light from them reaches us on straight lines through space, by assuming that we can measure their distance from us by its red shift, and by assuming that they are distributed in three dimensions of space, we have plotted their locations in 3-space. If we abandon the last of those three assumptions, we can just as easily reinterpret that dataset to plot their distribution around us in 4-dimensional space, and see how they actually lie. When we perform this experiment on the data for the stars in our galaxy, do we indeed find that they are distributed non-uniformly in various concentric spirals, but the spirals lie on the surface of various 3-spheres, rather than in elliptical orbits as we saw them in 3-space? That would be an expected consequence of the special rotational symmetry group of 4-space <small><math>SO(4)</math></small>, in which circular (isoclinic) orbits are the geodesics (shortest rotational paths) rather than elliptical (non-equi-angled double rotation) orbits. ...have to perform this experiment somehow, at least as a conclusive thought experiment, before I publish this paper... == Rotations == The [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotations]] of the convex [[W:regular 4-polytope|regular 4-polytope]]s are usually described as discrete rotations of a rigid object. For example, the rigid [[24-cell]] can rotate in a [[24-cell#Great hexagons|hexagonal]] (6-vertex) central [[24-cell#Planes of rotation|plane of rotation]]. A 4-dimensional [[24-cell#Isoclinic rotations|''isoclinic'' rotation]] (as distinct from a [[24-cell#Simple rotations|''simple'' rotation]] like the ones that occur in 3-dimensional space) is a ''diagonal'' rotation in multiple [[W:Clifford parallel|Clifford parallel]] [[24-cell#Geodesics|central planes]] of rotation at once. It is diagonal because it is a [[W:SO(4)#Double rotations|double rotation]]: in addition to rotating in parallel (like wheels), the multiple planes of rotation also tilt sideways in the completely orthogonal plane of rotation (like coins flipping) into each other's planes. Consequently, the path taken by each vertex is a [[24-cell#Helical hexagrams and their isoclines|twisted helical circle]], rather than the ordinary flat great circle a vertex follows in a simple rotation. In a rigid 4-polytope rotating isoclinically, ''all'' the vertices lie in one of the parallel planes of rotation, so all the vertices move in parallel along Clifford parallel twisting circular paths. [[24-cell#Clifford parallel polytopes|Clifford parallel planes]] are not parallel in the normal sense of parallel planes in three dimensions; the vertices are all moving in different directions around the [[W:3-sphere|3-sphere]]. In one complete 360° isoclinic revolution, a rigid 4-polytope turns itself inside out. This is sufficiently different from the simple rotations of rigid bodies in our 3-dimensional experience that a [[24-cell#Rotations|detailed description]] enabling the reader to properly visualize its counter-intuitive consequences runs to many pages and illustrations, with many accompanying pages of explanatory notes on surprising phenomena that arise in 4-dimensional space: [[24-cell#Great squares|completely orthogonal planes]], [[24-cell#Clifford parallel polytopes|Clifford parallelism]]{{Efn|name=Clifford parallels}} and [[W:Hopf fibration|Hopf fiber bundles]], [[24-cell#Isoclinic rotations|isoclinic geodesic paths]], and [[24-cell#Double rotations|chiral (mirror image) pairs of rotations]], among other complexities. Moreover, the characteristic rotations of the various regular 4-polytopes are all different; each is a unique surprise. [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|The 6 regular convex 4-polytopes]] have different numbers of vertices (5, 8, 16, 24, 120 and 600 respectively) and those with fewer vertices occur inscribed in those with more vertices (with one exception), with the result that the more complex 4-polytopes subsume the kinds of rotations characteristic of their less complex predecessors, as well as each having a characteristic kind of rotation not found in their predecessors. None of these symmetries is to be found in 3-dimensional space, although their simpler 3-dimensional analogues are all present there. [[W:Euclidean geometry#Higher dimensions|Four dimensional Euclidean space]] is more complicated (and more interesting) than three dimensional space because there is more room in it, in which unprecedented things can happen. It subsumes 3-dimensional space, with all of the symmetries we are accustomed to, and adds astonishing new surprises. These are hard for us to visualize, because the only way we can experience them is in our imagination; we have no body of sensory experience in 4-dimensional space to draw upon, other than our evolution in time. For that reason (our difficulty in visualizing them), descriptions of isoclinic rotations usually begin and end with rigid rotations: [[24-cell#Isoclinic rotations|for example]], all 24 vertices of a single rigid 24-cell rotating in unison, with 6 vertices evenly spaced around each of 4 Clifford parallel twisted circles.{{Efn|name=360 degree geodesic path visiting 3 hexagonal planes}} But that is only the simplest case, which is easiest for us to understand. Compound and [[W:Kinematics|kinematic]] 24-cells (with moving parts) are even more interesting (and more complicated) than the rotation of a single rigid 24-cell. To begin with, when we examine the individual parts of a single rigid 24-cell that are moving in an isoclinic rotation, such as the orbits of individual vertices, we can imagine a case where fewer than 24 point-objects are orbiting on those twisted circular paths at once. [[24-cell#Reflections|For example]], if we imagine just 8 point-objects, evenly spaced around the 24-cell at [[24-cell#Reciprocal constructions from 8-cell and 16-cell|the 8 vertices that lie on the 4 coordinate axes]], and rotate them isoclinically along exactly the same orbits they would take in the above-mentioned rotation of a rigid 24-cell, then in the course of a single 360° rotation the 8 point-objects will trace out the whole 24-cell, with just one point-object reaching each of the 24 vertex positions just once, and no point-object colliding with (or even crossing the path of) any other at any time. This is an example of a discrete Hopf fibration. But it is still an example of a rigid object in a discrete isoclinic rotation: a rigid 8-vertex object (called the 4-[[W:orthoplex|orthoplex]] or [[16-cell]]) performing one half of the characteristic rotation of the 24-cell. We can also imagine ''combining'' distinct isoclinic rotations. What happens when multiple point-objects are orbiting at once, but do ''not'' all follow the Clifford parallel paths characteristic of the ''same'' distinct rigid rotation? What happens when we combine orbits from distinct rotations characteristic of different 4-polytopes, for example when different rigid 4-polytopes are concentric and rotating simultaneously in their characteristic ways? What kinds of such hybrid rotations are possible in the same 3-sphere shell without collisions? In adjacent concentric shells without asymmetric imbalance? What sort of [[Kinematics of the cuboctahedron|kinematic polytopes]] do they trace out, and how do their [[24-cell#Clifford parallel polytopes|component parts]] relate to each other as they move? Is there (sometimes) some kind of mutual stability amid their lack of combined rigidity? Visualizing isoclinic rotations (rigid and otherwise) allows us to explore such questions of [[W:kinematics|kinematics]], and where dynamic stabilities arise, of [[wikipedia:kinetics (physics)|kinetics]]. In four dimensions, we discover that space has more room in it than we have experienced, which permits previously unimagined motions. Even 3-space is more commodious than we thought; when it is curved and lies embedded in a higher-dimensional space, it permits previously impossible symmetric packings. Sadoc studied double-twisted 3-dimensional molecules, and imagined them embedded in 4-dimensional space as the Hopf fibrations of regular 4-polytopes. He found that these molecules would close-pack on the 3-sphere perfectly without exhibiting any torsion, although their packing in ordinary flat 3-space is imperfect, "frustrated" by their twisted geometry. <blockquote>The frustration, which arises when the molecular orientation is transported along the two [spiral] AB paths of figure 1 [double twist helix], is imposed by the very topological nature of the Euclidean space R³. It would not occur if the molecules were embedded in the non-Euclidean space of the [[W:3-sphere|3-sphere]] S³, or hypersphere. This space with a homogeneous positive curvature can indeed be described by equidistant and uniformly twisted fibers, along which the molecules can be aligned without any conflict between compactness and [[W:torsion of a curve|torsion]].... The fibres of this [[W:Hopf fibration|Hopf fibration]] are great circles of S³, the whole family of which is also called the [[W:Clifford parallel|Clifford parallel]]s.{{Efn|name=Clifford parallels}} Two of these fibers are C_∞ symmetry axes for the whole fibration; each fibre makes one turn around each axis and regularly rotates when moving from one axis to another.{{Efn|name=helical geodesic}} These fibers build a double twist configuration while staying parallel, i.e. without any frustration, in the whole volume of S³.{{Efn|name=Petrie polygon of a honeycomb}} They can therefore be used as models to study the condensation of long molecules in the presence of a double twist constraint.{{Sfn|Sadoc & Charvolin|2009|loc=§1.2 The curved space approach|ps=; studies the helical orientation of molecules in crystal structures and their imperfect packings ("frustrations") in 3-dimensional space.}}</blockquote> Of course we do not find molecules condensing to close-pack the 3-sphere in our experience, and Sadoc does not say that we do. We find 3-spheres in the atomic realm (if atoms are 4-polytopes), and in the cosmic realm (as the surface boundaries of stars, and the concentric surfaces of galaxies). But in between, in the realm of ordinary experience which includes the molecular realm, ourselves and all the objects we can materially handle or observe up close including the planets, we are confined together by gravity as inertia within a curved 3-dimensional space that is no more than one atom thick in the fourth spatial dimension. That is why in the molecular realm we find only objects that occupy 3-spaces which, though infinitesimally curved in the fourth dimension, are tiny patches on whole 3-spheres of galactic size. So Sadoc's exercise is a thought experiment, like Einstein's gedankenexperiments about railroad embankments and trains moving at nearly the speed of light. It is no less illuminating, despite the symmetry it reveals not having a realization as an actual 3-sphere of actual molecules. And might not something very like it have an actual realization in the atomic realm? We know that atoms have their own complex internal structure, which we are unable to model geometrically in ordinary 3-dimensional space. Suppose such a model is impossible because an atom is actually a 4-polytope occupying a tiny spherical region of 4-dimensional space, and so we only find its constituent particles in close-packed helical orbits on the 3-sphere, in the manner of Sadoc's imaginary twisted molecules, but as real 4-dimensional helices of atomic scale. We would expect to find the atomic orbit of a fundamental particle in some discrete Hopf fibration characteristic of a symmetry group, that is, on the maximally symmetric isoclines of a discrete isoclinic rotation characteristic of some regular 4-polytope and the particle. == A theory of the Euclidean atom == <blockquote>Because quantum physics could be tested without being understood, it allowed humans to see how the universe worked without knowing why.<ref>Sebastian Junger, In My Time of Dying</ref></blockquote> ... == Light and Mass are Reflection and Rotation == The phenomena of light and mass are expressions of reflection symmetries and rotation symmetries, respectively. ... Atoms are 4-polytopes, elementary objects with SO(4) rotational symmetry. Light is .... Motion in space is the propagation of the elementary objects of light and matter in Coxeter congruent transformations by kaleidoscopic self-reflections, like the motion of self-reproducing cellular automata in [[Conway's Game of Life|Conway's game of life]]. ... Light is discrete reflections. Mass is discrete rotations. Both are group actions, expressions of intrinsic symmetries. That is all of physics. === Atoms are 4-polytopes === ... == Relativity in real space of four or more orthogonal dimensions == Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions. General relativity is Galilean relativity in a general space of four or more orthogonal dimensions, e.g. in Euclidean 4-space <math>R^4</math>, spherical 4-space <math>S^4</math>, and any orthogonal 4-manifold. Light is a consequence of symmetry group reflections at quantum scale. Gravity and the other fundamental forces are consequences of rotations, which are consequences of quantum reflections. Light is discrete reflections. Gravity and all forces are discrete rotations. Both are group actions, expressions of intrinsic symmetries. That is all of physics. Every observer may properly see themself as stationary and the universe as an ''n''-sphere with themself at the center. The curvature of these spheres is a function of the rate at which causality evolves, and can be measured by the observer as the speed of light. === Special relativity is Galilean relativity in a Euclidean space of four orthogonal dimensions === ...TAC suggests this section is needed sooner, i.e. in the preceding Special Relativity section, as it explains how Euclidean relativity reduces special relativity to 4D perspective geometry...it's misplaced (too late) here... Perspective effects known as the Lorentz transformations occur because each observer's proper 3-dimensional space is a moving curved manifold embedded in flat 4-dimensional Euclidean space. The curvature of their 3-space complicates sightline calculations for observers; they sometimes require Lorentz transformations to produce the actual 4-space Cartesian coordinates of objects in the scene being observed. But if all four spatial dimensions are considered, no Lorentz transformations are required (or permitted) in correct scene construction, except when an observer wants to calculate a projection, that is, the shadow of how things will appear to them from a three-dimensional viewpoint (not how they really are).{{Sfn|Yamashita|2023}} Space really has four orthogonal dimensions, and space and time behave there just as they do in a classical vector space, only bigger by one dimension. It is not necessary to combine 4-space with time in a unified spacetime to explain 4-dimensional perspective effects at high relative velocities, because Euclidean 4-space is already 4-dimensional, and those effects fall out naturally from the 4-dimensional Pythagorean theorem, exactly as ordinary visual perspective does in three dimensions from the 3-dimensional Pythagorean theorem. Because one of the four spatial dimensions corresponds to an observer's direction of motion (in both space and proper time), and all observers and all scenes being observed are in motion (at constant velocity) in their respective proper time directions, we observe perspective foreshortenings in time as well as in three spatial dimensions. In special relativity these perspective effects are reciprocal, precisely because they are only apparent, not actual, changes in size and duration. (In general relativity, discussed below, the actual rate of physical processes varies from place to place, and those differences are neither reciprocal nor illusory.) None of these Lorentz effects are beyond geometric explanation or paradoxical. The universe is unexpectedly strange to us in precisely the ways the Euclidean fourth dimension is strange to us; but that does hold many surprises. Euclidean 4-space is much more interesting than Euclidean 3-space, analogous to the way 3-space is much more interesting and deeply explanatory to us than it would be if we experienced it only as a 2-space with many folds and curves, as perhaps an ant does. The emergent properties of 4-space are hard for us to visualize because they lie so wholly beyond our physical experience, just as it was hard for our ancestors to imagine the earth as round like a ball. However, successive Euclidean spaces are dimensionally analogous, and so higher dimensional spaces can be anticipated and explored: that is Schläfli's great discovery. Moreover dimensional analogy itself, like everything else in nature, is an exact expression of intrinsic symmetries: that is Nother's great discovery. === General relativity is Galilean relativity in a general space of four orthogonal dimensions === ... == Dimensional relativity == Coxeter's kinetic law of <math>n</math>-dimensional congruent Euclidean transformations may be called ''dimensional relativity'', since it captures the theories of special and general relativity entire, and has its roots in dimensional analogy. Dimensional analogy is the exploration of [[w:Hermann_Grassmann#Mathematician|Hermann Grassmann's vector space principle]], in which space cannot be limited to any finite number of dimensions. The geometry of higher-dimensional space is accessable by reason of direct analogy, as [[w:Ludwig Schläfli|Ludwig Schläfli]] subsequently demonstrated. By analogy to the surface of the earth, the bounding surface of a spherical region of <math>n</math>-dimensional Euclidean space is an <math>(n-1)</math>-sphere, a spherical space of one fewer dimensions than the <math>n</math>-ball of Euclidean space it surrounds. In dimensional relativity the sky is not a ceiling, but an infinite regress of alternating spherical and Euclidean <math>n</math>-spaces of increasing <math>n</math>, accessible from each observer's point of view. By dimensional analogy, each observer looks up into their own reference frame's regress of concentric alternating <math>n</math>-spaces. By the degree of dimensional analogy of which they are capable, some observers see deeper into <math>n</math>-dimensional space than others. == Polycentric spherical relativity == An intelligent observer equipped with the principle of relativity may perceive the universe from any inertial reference frame, not only from their own proper perspective. We see that every observer may properly view themself as stationary and the universe as an ''n''-sphere with themself at the center observing it, perceptually equidistant from all points on its surface, including their own physical location which is one of those surface points, distinguished to them but moving on the surface, and not the center of anything. This ''polycentric model'' of the universe is a further restatement of the principle of relativity. It is compatible with Galileo's relativity of uniformly moving objects in ordinary space, Einstein's special relativity of inertial reference frames in 4-dimensional spacetime, Einstein's general relativity of all reference frames in non-Euclidean spacetime, and Coxeter's dimensional relativity of orthogonal group actions in Euclidean and spherical spaces of any number of dimensions. It should be known as Thoreau's principle of ''spherical relativity'', since the first precise written statement of it appears in 1849: "The universe is a sphere whose center is wherever there is intelligence."{{Sfn|Thoreau|1849|p=349|ps=; "The universe is a sphere whose center is wherever there is intelligence." [Contemporaneous and independent of [[W:Ludwig Schlafli|Ludwig Schlafli]]'s pioneering work enumerating the complete set of regular polyschemes in any number of dimensions.]}} == Revolutions == The original Copernican revolution in 1543 displaced the center of the universe from the center of the earth to a point farther away, the center of the sun, with the earth performing a ''revolution'' around the sun, and the stars remaining on a fixed 2-sphere around the sun instead of around the earth. But this led inevitably to the recognition that the sun must be a star itself, not equidistant from all the stars, and the center of but one of many spheres, no monotheistic center at all. In such fashion the Euclidean four-dimensional revolution, emerging three to five centuries later, initially lends itself to the big bang theory of a single origin of the whole universe, but leads inevitably to the recognition that all the galaxies need not be equidistant from a single origin in time, any more than all the stars lie in the same galaxy, equidistant from a single center in space. The expanding sphere of matter on the surface of which we find ourselves living is likely to be one of many 3-spheres expanding at velocity ''c'', with their big bang origins occurring at distinct times and places in the ''n''-dimensional universe. The most distant objects we see when we look up at night may, or may not, all have the same origin in space and time. As recently as Copernicus we believed all the stars lay on a single 2-sphere embedded in Euclidean 3-space, with our sun at its center. During the enlightenment we dispersed those stars into an infinite Euclidean 3-space, and relinquished our privileged position at the center. Then Einstein showed us that our 3-space could not be Euclidean, that it must be a 3-manifold curved in every place in obedience to Newton's inverse-square law of gravity; and in a sense related to time, at least, it must be 4-dimensional. In this work we suggest a theory of ''n''-dimensional real space and how light travels in it, a theory which says we can see into four orthogonal dimensions of Euclidean space, and so when we look up at night we see cosmological objects distributed in at least four dimensions of space around us, rather than all located in our own local 3-space. Looking still deeper and farther out, the universe viewed as a 4-sphere might, or might not, be expanding, and the most distant objects we see when we look up at night may, or may not, lie in our 4-dimensional hyperplane. Real space has ''n'' dimensions as [[w:Hermann_Grassmann|Grassmann]] and [[w:Schläfli|Schläfli]] showed, and we do not know how many dimensions the most distant objects we see may be distributed in. They need not all lie within the four spatial dimensions in which we now observe them, any more than they lie in the three dimensional hyperplane of local space in which we find everything residing in our solar system. When we look up at the objects that surround us, we have no way of discerning how many dimensions beyond three the space we are looking into has. We know their distance from us only by virtue of how long it takes their light to reach us. We can measure their distribution around us in 4-space, but that is simply how we choose to measure them, not a finding of how they are actually distributed. Even if it is now evident that they do not all lie in the same 3-space, how many more dimensions than three are needed to contain them? We observe that our 4-ball galaxy is embedded in Euclidean ''n''-space as one of many 4-ball galaxies, each translating in a distinct direction through 4-space at velocity <math>c</math>, on more or less divergent paths from each other. But only much closer observation will reveal evidence of whether everything we see lies in the same 4-space, or if it is distributed in five or more dimensions, and how it is moving there. To remain in agreement with the theory of relativity, the Euclidean four-dimensional viewpoint requires that all mass-carrying objects be in motion in some distinct direction through 4-space at the constant velocity <math>c</math>, although the relative velocity between nearby objects is much smaller since they move on similar vectors, aimed away from a common origin point in the past. It is natural to expect that objects moving at constant velocity away from a common origin will be distributed roughly on the surface of an expanding 3-sphere. Although their paths away from their origin are not straight lines but various helical isoclines (screw displacements), nearby objects must be translating radially at the same velocity, since the objects in a system (such as our solar system or galaxy) do not separate rapidly over time but remain in orbital formation. Each system's screw displacement has ''two'' [[w:Completely_orthogonal|completely orthogonal]] components of motion in 4-space, an orbital rotation (such as the earth's around our sun) and a linear translation of the entire system at velocity <math>c</math> in the direction of the original 3-sphere's radial expansion (along the system's proper time vector). Of course the view from our solar system does not suggest that each galaxy's own distinct 3-sphere is expanding at this great rate from its galactic center. The standard theory has been that the entire observable universe is expanding from a single big bang origin in time, with galaxies forming later. While the Euclidean four-dimensional viewpoint lends itself to that standard theory, it also supports theories which require no single origin point in space and time. These are the voyages of starship Earth, to boldly go where no one has gone before. We made the jump to lightspeed long ago, in whatever big bang our atoms emerged from, and have never slowed down since. == Origins of the theory == Einstein himself may have been the first to imagine the universe as the three-dimensional surface of a four-dimensional Euclidean 3-sphere, in what was narrowly the first written articulation of the geometry of Euclidean 4-space relativity, contemporaneous with the teen-aged Coxeter's (quoted below).{{Efn|[[W:William Rowan Hamilton|Hamilton]]'s algebra '''H''' of [[W:Quaternions|quaternions]] contains the notion of a [[W:Three-dimensional sphere|three-dimensional sphere]] embedded in a four-dimensional space, but Hamilton did not conceive of the quaternions as the Cartesian 4-coordinates of a Euclidean 4-space, and did not describe our ordinary 3-space embedded in Euclidean 4-space.}} Einstein did this as a [[W:Gedankenexperiment|gedankenexperiment]] in the context of investigating whether his equations of general relativity predicted an infinite or a finite universe, in his 1921 Princeton lecture.<ref>{{Cite book|url=http://www.gutenberg.org/ebooks/36276|title=The Meaning of Relativity|last=Einstein|first=Albert|publisher=Princeton University Press|year=1923|isbn=|location=|pages=110-111}}</ref> He invited us to imagine "A spherical manifold of three dimensions, embedded in a Euclidean continuum of four dimensions", but he was careful to disclaim parenthetically that "The aid of a fourth space dimension has naturally no significance except that of a mathematical artifice." Informally, the Euclidean 4-dimensional theory of relativity may be given as a sort of reciprocal of that disclaimer of Einstein's: ''The Minkowski spacetime has naturally no significance except that of a mathematical artifice, as an aid to understanding how things will appear to an observer from their perspective; the foreshortenings, clock desynchronizations and other Lorentz transformations it predicts are proper calculations of actual perspective effects; but real space is a flat, Euclidean continuum of four orthogonal spatial dimensions, and in it the ordinary laws of a flat vector space hold (such as the Pythagorean theorem), and all sightline calculations work classically, so long as you consider all four spatial dimensions.'' The Euclidean theory of relativity differs from the special theory of relativity in ascribing to the physical universe a geometry of four or more orthogonal spatial dimensions, rather than the special theory's [[w:Minkowski spacetime|Minkowski spacetime]] geometry, in which three spatial dimensions and a time dimension comprise a unified spacetime of four dimensions. Anco and Maghadam found that <small><math>SO(4)</math></small> breaks to ... <small><math>S^3</math></small>... if the energy in the Kepler orbit is negative (an elliptical orbit), and to ... <small><math>H^3</math></small> ... Minkowski spacetime if the energy is positive (a hyperbolic orbit). Because the planets orbit on ellipses in our 3-space, Euclidean 4-space is the actual geometry of our physical universe, and Minkowski spacetime is an abstraction; the reciprocal of Einstein's disclaimer is the truer model. Of course spacetime remains a true and useful abstraction, although it must relinquish its privileged position of centrality as our exclusive conception of our place in space. ...origins of the Euclidean 4-space insight in the observations of Fock, Atkinson, Moser and others. The invention of Euclidean geometry of more than three spatial dimensions preceded Einstein's theories by more than fifty years, when it was worked out originally by the Swiss mathematician [[w:Ludwig Schläfli|Ludwig Schläfli]] before 1853.{{Sfn|Coxeter|1973|loc=§7. Ordinary Polytopes in Higher Space; §7.x. Historical remarks|pp=141-144|ps=; "Practically all the ideas in this chapter ... are due to Schläfli, who discovered them before 1853 — a time when Cayley, Grassmann and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions."}} Schläfli extended Euclid's geometry of one, two, and three dimensions in a direct way to four or more dimensions, generalizing the rules and terms of [[w:Euclidean geometry|Euclidean geometry]] to spaces of any number of dimensions. He coined the general term ''[[polyscheme]]'' to mean geometric forms of any number of dimensions, including two-dimensional [[w:polygon|polygons]], three-dimensional [[w:polyhedron|polyhedra]], four dimensional [[w:polychoron|polychora]], and so on, and in the process he found all of the [[w:Regular polytope|regular polyschemes]] that are possible in every dimension, including in particular the [[User:Dc.samizdat/Rotations#Sequence of regular 4-polytopes|six convex regular polychora]] which can be constructed in a Euclidean space of four dimensions (the set analogous to the five [[w:Platonic solid|Platonic solids]] the ancients found in three dimensional space). Thus Schläfli was the first to explore the fourth dimension, reveal its emergent geometric properties, and discover its astonishing regular objects. Because his work was only published posthumously in 1901, and remained almost completely unknown until Coxeter published [[w:Regular_Polytopes_(book)|Regular Polytopes]] in 1947, other researchers had more than fifty years to rediscover the regular polychora, and competing terms were coined; today [[w:Reinhold_Hoppe|Reinhold Hoppe]]'s word ''[[w:Polytope|polytope]]'' is the commonly used term for ''polyscheme.''{{Efn|[[w:Reinhold_Hoppe|Reinhold Hoppe]]'s German word ''polytop'' was introduced into English by [[W:Alicia Boole Stott|Alicia Boole Stott]], who like Hoppe and [[W:Thorold Gosset|Thorold Gosset]] rediscovered Schlafli's six regular convex 4-polytopes, with no knowledge of their prior discovery. Today Schläfli's original ''polyschem'', with its echo of ''schema'' as in the configurations of information structures, seems even more fitting in its generality than ''polytope'' -- perhaps analogously as information software (programming) is even more general than information hardware (computers).}} Because of this century-long lag in the dissemination of a scientific discovery, the regular 4-polytopes appear to have played no role at all, by any name, in the twentieth century discovery and evolution of the theories of relativity and quantum mechanics.{{Efn|One could argue that the higher-dimensional polytopes have barely influenced science or culture at all thus far. The physicist John Edward Huth's comprehensive deep dive through the history of cultural and scientific concepts of physical space, from ancient flatland models of the world through general relativity and quantum mechancs, shows exactly how we got to our present standard model of the universe, although it includes no mention of higher-dimensional Euclidean space.<ref>{{Cite book|last=Huth|first=John Edward|title=A Sense of Space: A local's guide to a flat earth, the edge of the cosmos, and other curious places|year=2025|publisher=University of Chicago Press}}</ref>}} == Boundaries == <blockquote>Ever since we discovered that Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.<ref>{{Cite book|author=Carlo Rovelli|author-link=W:Carlo Rovelli|title=Seven Brief Lessons on Physics|publisher=Riverhead|year=2016|isbn=978-0399184413}}</ref></blockquote> Of course it is strange to consciously contemplate this world we inhabit, our planet, our solar system, our vast galaxy, as the merest film, a boundary no thicker in the places we inhabit than the diameter of an electron (though much thicker in some places we cannot inhabit, such as the interior of stars). But is not our unconscious traditional concept of the boundary of our world even stranger? Since the enlightenment we are accustomed to thinking that there is nothing beyond three dimensional space: no boundary, because there is nothing else to separate us from. But anyone who knows the [[polyscheme]]s Schläfli discovered knows that space can have any number of dimensions, and that there are fundamental objects and motions to be discovered in four dimensions that are even more various and interesting than those we can discover in three. The strange thing, when we think about it that way, is that there ''is'' a boundary between three and four dimensional space. ''Why'' can't we move (or apparently, see) in more than three dimensions? Why is our physical world apparently only three dimensional? Why would it have just ''three'' dimensions, and not four, or five, or the ''n'' dimensions that Schläfli mapped? ''What is the nature of the boundary which confines us to just three dimensions?'' We know that in Euclidean geometry the boundary between three and four dimensions is itself a spherical three dimensional space, so we should suspect that we are materially confined within such a curved boundary surface. Light need not be confined with us within our three dimensional boundary space. We would look directly through four dimensional space in our natural way, by receiving light signals that travelled through it to us on straight lines. In that case the reason we do not observe a fourth spatial dimension in our vicinity is that there are no nearby objects in it, just off our hyperplane in the wild. The nearest four-dimensional object we can see with our eyes is our sun, which lies equatorially in our own hyperplane, though it bulges out of it above and below. But when we look up at the heavens, every pinprick of light we observe is itself a four-dimensional object off our hyperplane, and they are distributed all around us in four-dimensional space through which we gaze. We are four-dimensionally sighted creatures, even though our bodies are three-dimensional objects, thin as an atom in the fourth dimension. But that should not perplex us: we can see into three dimensional space even though our retinas are two dimensional objects, thin as a photoreceptor cell. Our unconscious provincial concept is that there is nothing else outside our three dimensional world: no boundary, because there is nothing else to separate us from. But Schläfli discovered something else: all the astonishing regular objects that exist in higher dimensions, which vastly extend our notions of the beauty and mystery of space itself, and the intrinsic spatial symmetries of our universe which geometry reveals. Space is more commodious than we thought it was, and permits previously unimagined motions and objects. So our provincial conception of our place in it now has the same kind of status as our idea that the sun rises in the east and passes overhead: it is mere appearance, not a true model and no longer a proper explanation. A boundary is an explanation, be it ever so thin. And would a boundary of ''no'' thickness, a mere abstraction with no physical power to separate, be a more suitable explanation? We must look for a physically powerful explanation in the geometry of space itself, which general relativity properly associates with the gravitational or inertial force. <blockquote>The number of dimensions possessed by a figure is the number of straight lines each perpendicular to all the others which can be drawn on it. Thus a point has no dimensions, a straight line one, a plane surface two, and a solid three .... In space as we now know it only three lines can be imagined perpendicular to each other. A fourth line, perpendicular to all the other three would be quite invisible and unimaginable to us. We ourselves and all the material things around us probably possess a fourth dimension, of which we are quite unaware. If not, from a four-dimensional point of view we are mere geometrical abstractions, like geometrical surfaces, lines, and points are to us. But this thickness in the fourth dimension must be exceedingly minute, if it exists at all. That is, we could only draw an exceedingly small line perpendicular to our three perpendicular lines, length, breadth and thickness, so small that no microscope could ever perceive it. We can find out something about the conditions of the fourth and higher dimensions if they exist, without being certain that they do exist, by a process which I have termed "Dimensional Analogy."<ref>{{Citation|title=Dimensional Analogy|last=Coxeter|first=Donald|date=February 1923|publisher=Coxeter Fonds, University of Toronto Archives|authorlink=W:Harold Scott MacDonald Coxeter|series=|postscript=|work=}}</ref></blockquote> I believe, but I cannot prove, that we live in real space, which is Schläfli's and Coxeter's Euclidean space of ''n'' analogous dimensions. As Grassmann showed first, space cannot be limited to any finite number of dimensions. There will always be higher dimensions to discover in imagination and then explore physically, each an astonishing new enlightenment.<ref>{{Cite book|first=T.S.|last=Eliot|title=Little Gidding|volume=Four Quartets|year=1943}}<blockquote> :We shall not cease from exploration :And the end of all our exploring :Will be to arrive where we started :And know the place for the first time. :Through the unknown, remembered gate :When the last of earth left to discover :Is that which was the beginning; :At the source of the longest river :The voice of the hidden waterfall :And the children in the apple-tree :Not known, because not looked for :But heard, half-heard, in the stillness :Between two waves of the sea. </blockquote></ref> Schläfli discovered every regular convex polytope that exists in any dimension, but that was only the beginning of the story of dimensional analogy, not its end or even the end of its beginning. This project is forever beginning anew. Coxeter showed us that Schläfli's Euclidean space is an expression of intrinsic symmetries, as Noether showed us all of physics is. Kappraff and Adamson discovered that even the sequences of humble regular polygons have fractal complexity. Symmetry itself is chaotic, always reachable but forever beyond our complete grasp. We are on a Wilderness Project, just at its beginning, but already we observe a Euclidean space of four or more orthogonal spatial dimensions, in which all objects with mass move ceaselessly at the constant velocity <math>c</math>, the universal rate at which everything moves, quantum events occur, and each of our proper times evolves. I believe these facts explain the experimentally verified theories of relativity and quantum mechanics, by revealing their unified polycentric geometry, the same way the facts about Copernicus's heliocentric solar system explained the observed motions of the planets, by revealing the geometry of gravity. But others will have to do the math, work out the physics, and perform experiments to prove or disprove all of this, because I don't have the mathematics; entirely unlike Coxeter and Einstein, I am illiterate in those languages. <blockquote> ::::::BEECH :Where my imaginary line :Bends square in woods, an iron spine :And pile of real rocks have been founded. :And off this corner in the wild, :Where these are driven in and piled, :One tree, by being deeply wounded, :Has been impressed as Witness Tree :And made commit to memory :My proof of being not unbounded. :Thus truth's established and borne out, :Though circumstanced with dark and doubt— :Though by a world of doubt surrounded. :::::::—''The Moodie Forester''<ref>{{Cite book|title=A Witness Tree|last=Frost|first=Robert|year=1942|series=The Poetry of Robert Frost|publisher=Holt, Rinehart and Winston|edition=1969|}}</ref> </blockquote> == Appendix: Sequence of regular 4-polytopes == {{Regular convex 4-polytopes|wiki=W:|columns=7}} == ... == {{Efn|In a ''[[W:William Kingdon Clifford|Clifford]] displacement'', also known as an [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinic rotation]], all the Clifford parallel{{Efn|name=Clifford parallels}} invariant planes are displaced in four orthogonal directions (two completely orthogonal planes) at once: they are rotated by the same angle, and at the same time they are tilted ''sideways'' by that same angle. A [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]] is [[W:8-cell#Radial equilateral symmetry|4-dimensionally diagonal]].{{Efn|name=isoclinic 4-dimensional diagonal}} Every plane that is Clifford parallel to one of the completely orthogonal planes (including in this case an entire Clifford parallel bundle of 4 hexagons, but not all 16 hexagons) is invariant under the isoclinic rotation: all the points in the plane rotate in circles but remain in the plane, even as the whole plane tilts sideways. All 16 hexagons rotate by the same angle (though only 4 of them do so invariantly). All 16 hexagons are rotated by 60 degrees, and also displaced sideways by 60 degrees to a Clifford parallel hexagon. All of the other central polygons (e.g. squares) are also displaced to a Clifford parallel polygon 60 degrees away.|name=Clifford displacement}} {{Efn|It is not difficult to visualize four hexagonal planes intersecting at 60 degrees to each other, even in three dimensions. Four hexagonal central planes intersect at 60 degrees in the [[W:cuboctahedron|cuboctahedron]]. Four of the 24-cell's 16 hexagonal central planes (lying in the same 3-dimensional hyperplane) intersect at each of the 24-cell's vertices exactly the way they do at the center of a cuboctahedron. But the ''edges'' around the vertex do not meet as the radii do at the center of a cuboctahedron; the 24-cell has 8 edges around each vertex, not 12, so its vertex figure is the cube, not the cuboctahedron. The 8 edges meet exactly the way 8 edges do at the apex of a canonical [[W:cubic pyramid]|cubic pyramid]].{{Efn|name=24-cell vertex figure}}|name=cuboctahedral hexagons}} {{Efn|name=radially equilateral}} {{Efn|Eight {{sqrt|1}} edges converge in curved 3-dimensional space from the corners of the 24-cell's cubical vertex figure{{Efn|The [[W:vertex figure|vertex figure]] is the facet which is made by truncating a vertex; canonically, at the mid-edges incident to the vertex. But one can make similar vertex figures of different radii by truncating at any point along those edges, up to and including truncating at the adjacent vertices to make a ''full size'' vertex figure. Stillwell defines the vertex figure as "the convex hull of the neighbouring vertices of a given vertex".{{Sfn|Stillwell|2001|p=17}} That is what serves the illustrative purpose here.|name=full size vertex figure}} and meet at its center (the vertex), where they form 4 straight lines which cross there. The 8 vertices of the cube are the eight nearest other vertices of the 24-cell. The straight lines are geodesics: two {{sqrt|1}}-length segments of an apparently straight line (in the 3-space of the 24-cell's curved surface) that is bent in the 4th dimension into a great circle hexagon (in 4-space). Imagined from inside this curved 3-space, the bends in the hexagons are invisible. From outside (if we could view the 24-cell in 4-space), the straight lines would be seen to bend in the 4th dimension at the cube centers, because the center is displaced outward in the 4th dimension, out of the hyperplane defined by the cube's vertices. Thus the vertex cube is actually a [[W:cubic pyramid|cubic pyramid]]. Unlike a cube, it seems to be radially equilateral (like the tesseract and the 24-cell itself): its "radius" equals its edge length.{{Efn|The vertex cubic pyramid is not actually radially equilateral,{{Efn|name=radially equilateral}} because the edges radiating from its apex are not actually its radii: the apex of the [[W:cubic pyramid|cubic pyramid]] is not actually its center, just one of its vertices.}}|name=24-cell vertex figure}} {{Efn|The hexagons are inclined (tilted) at 60 degrees with respect to the unit radius coordinate system's orthogonal planes. Each hexagonal plane contains only ''one'' of the 4 coordinate system axes.{{Efn|Each great hexagon of the 24-cell contains one axis (one pair of antipodal vertices) belonging to each of the three inscribed 16-cells. The 24-cell contains three disjoint inscribed 16-cells, rotated 60° isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other (so their corresponding vertices are 120° {{=}} {{radic|3}} apart). A [[16-cell#Coordinates|16-cell is an orthonormal ''basis'']] for a 4-dimensional coordinate system, because its 8 vertices define the four orthogonal axes. In any choice of a vertex-up coordinate system (such as the unit radius coordinates used in this article), one of the three inscribed 16-cells is the basis for the coordinate system, and each hexagon has only ''one'' axis which is a coordinate system axis.|name=three basis 16-cells}} The hexagon consists of 3 pairs of opposite vertices (three 24-cell diameters): one opposite pair of ''integer'' coordinate vertices (one of the four coordinate axes), and two opposite pairs of ''half-integer'' coordinate vertices (not coordinate axes). For example: {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,{{spaces|2}}1,{{spaces|2}}0) {{indent|5}}({{spaces|2}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>){{spaces|3}}({{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>) {{indent|5}}(–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>){{spaces|3}}(–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>,–<small>{{sfrac|1|2}}</small>,{{spaces|2}}<small>{{sfrac|1|2}}</small>) {{indent|17}}({{spaces|2}}0,{{spaces|2}}0,–1,{{spaces|2}}0)<br> is a hexagon on the ''y'' axis. Unlike the {{sqrt|2}} squares, the hexagons are actually made of 24-cell edges, so they are visible features of the 24-cell.|name=non-orthogonal hexagons|group=}} {{Efn|Visualize the three [[16-cell]]s inscribed in the 24-cell (left, right, and middle), and the rotation which takes them to each other. [[24-cell#Reciprocal constructions from 8-cell and 16-cell|The vertices of the middle 16-cell lie on the (w, x, y, z) coordinate axes]];{{Efn|name=six orthogonal planes of the Cartesian basis}} the other two are rotated 60° [[W:Rotations in 4-dimensional Euclidean space#Isoclinic rotations|isoclinically]] to its left and its right. The 24-vertex 24-cell is a compound of three 16-cells, whose three sets of 8 vertices are distributed around the 24-cell symmetrically; each vertex is surrounded by 8 others (in the 3-dimensional space of the 4-dimensional 24-cell's ''surface''), the way the vertices of a cube surround its center.{{Efn|name=24-cell vertex figure}} The 8 surrounding vertices (the cube corners) lie in other 16-cells: 4 in the other 16-cell to the left, and 4 in the other 16-cell to the right. They are the vertices of two tetrahedra inscribed in the cube, one belonging (as a cell) to each 16-cell. If the 16-cell edges are {{radic|2}}, each vertex of the compound of three 16-cells is {{radic|1}} away from its 8 surrounding vertices in other 16-cells. Now visualize those {{radic|1}} distances as the edges of the 24-cell (while continuing to visualize the disjoint 16-cells). The {{radic|1}} edges form great hexagons of 6 vertices which run around the 24-cell in a central plane. ''Four'' hexagons cross at each vertex (and its antipodal vertex), inclined at 60° to each other.{{Efn|name=cuboctahedral hexagons}} The [[24-cell#Hexagons|hexagons]] are not perpendicular to each other, or to the 16-cells' perpendicular [[24-cell#Squares|square central planes]].{{Efn|name=non-orthogonal hexagons}} The left and right 16-cells form a tesseract.{{Efn|Each pair of the three 16-cells inscribed in the 24-cell forms a 4-dimensional [[W:tesseract|hypercube (a tesseract or 8-cell)]], in [[24-cell#Relationships among interior polytopes|dimensional analogy]] to the way two tetrahedra form a cube: the two 8-vertex 16-cells are inscribed in the 16-vertex tesseract, occupying its alternate vertices. The third 16-cell does not lie within the tesseract; its 8 vertices protrude from the sides of the tesseract, forming a cubic pyramid on each of the tesseract's cubic cells. The three pairs of 16-cells form three tesseracts.{{Efn|name=three 8-cells}} The tesseracts share vertices, but the 16-cells are completely disjoint.{{Efn|name=completely disjoint}}|name=three 16-cells form three tesseracts}} Two 16-cells have vertex-pairs which are one {{radic|1}} edge (one hexagon edge) apart. But a [[24-cell#Simple rotations|''simple'' rotation]] of 60° will not take one whole 16-cell to another 16-cell, because their vertices are 60° apart in different directions, and a simple rotation has only one hexagonal plane of rotation. One 16-cell ''can'' be taken to another 16-cell by a 60° [[24-cell#Isoclinic rotations|''isoclinic'' rotation]], because an isoclinic rotation is [[3-sphere]] symmetric: four [[24-cell#Clifford parallel polytopes|Clifford parallel hexagonal planes]] rotate together, but in four different rotational directions,{{Efn|name=Clifford displacement}} taking each 16-cell to another 16-cell. But since an isoclinic 60° rotation is a ''diagonal'' rotation by 60° in ''two'' completely orthogonal directions at once,{{Efn|name=isoclinic geodesic}} the corresponding vertices of the 16-cell and the 16-cell it is taken to are 120° apart: ''two'' {{radic|1}} hexagon edges (or one {{radic|3}} hexagon chord) apart, not one {{radic|1}} edge (60°) apart as in a simple rotation.{{Efn|name=isoclinic 4-dimensional diagonal}} By the [[W:chiral|chiral]] diagonal nature of isoclinic rotations, the 16-cell ''cannot'' reach the adjacent 16-cell by rotating toward it; it can only reach the 16-cell ''beyond'' it. But of course, the 16-cell beyond the 16-cell to its right is the 16-cell to its left. So a 60° isoclinic rotation ''will'' take every 16-cell to another 16-cell: a 60° ''right'' isoclinic rotation will take the middle 16-cell to the 16-cell we may have originally visualized as the ''left'' 16-cell, and a 60° ''left'' isoclinic rotation will take the middle 16-cell to the 16-cell we visualized as the ''right'' 16-cell. (If so, that was our error in visualization; the 16-cell to the "left" is in fact the one reached by the left isoclinic rotation, as that is the only sense in which the two 16-cells are left or right of each other.)|name=three isoclinic 16-cells}} {{Efn|In a double rotation each vertex can be said to move along two completely orthogonal great circles at the same time, but it does not stay within the central plane of either of those original great circles; rather, it moves along a helical geodesic that traverses diagonally between great circles. The two completely orthogonal planes of rotation are said to be ''invariant'' because the points in each stay in the plane ''as the plane moves'', tilting sideways by the same angle that the other plane rotates.|name=helical geodesic}} {{Efn|A point under isoclinic rotation traverses the diagonal{{Efn|name=isoclinic 4-dimensional diagonal}} straight line of a single '''isoclinic geodesic''', reaching its destination directly, instead of the bent line of two successive '''simple geodesics'''. A '''[[W:geodesic|geodesic]]''' is the ''shortest path'' through a space (intuitively, a string pulled taught between two points). Simple geodesics are great circles lying in a central plane (the only kind of geodesics that occur in 3-space on the 2-sphere). Isoclinic geodesics are different: they do ''not'' lie in a single plane; they are 4-dimensional [[W:helix|spirals]] rather than simple 2-dimensional circles.{{Efn|name=helical geodesic}} But they are not like 3-dimensional [[W:screw threads|screw threads]] either, because they form a closed loop like any circle (after ''two'' revolutions). Isoclinic geodesics are ''4-dimensional great circles'', and they are just as circular as 2-dimensional circles: in fact, twice as circular, because they curve in a circle in two completely orthogonal directions at once.{{Efn|Isoclinic geodesics are ''4-dimensional great circles'' in the sense that they are 1-dimensional geodesic ''lines'' that curve in 4-space in two completely orthogonal planes at once. They should not be confused with ''great 2-spheres'',{{Sfn|Stillwell|2001|p=24}} which are the 4-dimensional analogues of 2-dimensional great circles (great 1-spheres).}} These '''isoclines''' are geodesic 1-dimensional lines embedded in a 4-dimensional space. On the 3-sphere{{Efn|All isoclines are geodesics, and isoclines on the 3-sphere are circles (curving equally in each dimension), but not all isoclines on 3-manifolds in 4-space are circles.}} they always occur in [[W:chiral|chiral]] pairs and form a pair of [[W:Villarceau circle|Villarceau circle]]s on the [[W:Clifford torus|Clifford torus]],{{Efn|Isoclines on the 3-sphere occur in non-intersecting chiral pairs. A left and a right isocline form a [[W:Hopf link|Hopf link]] called the {1,1} torus knot{{Sfn|Dorst|2019|loc=§1. Villarceau Circles|p=44|ps=; "In mathematics, the path that the (1, 1) knot on the torus traces is also known as a [[W:Villarceau circle|Villarceau circle]]. Villarceau circles are usually introduced as two intersecting circles that are the cross-section of a torus by a well-chosen plane cutting it. Picking one such circle and rotating it around the torus axis, the resulting family of circles can be used to rule the torus. By nesting tori smartly, the collection of all such circles then form a [[W:Hopf fibration|Hopf fibration]].... we prefer to consider the Villarceau circle as the (1, 1) torus knot [a [[W:Hopf link|Hopf link]]] rather than as a planar cut [two intersecting circles]."}} in which ''each'' of the two linked circles traverses all four dimensions.}} the paths of the left and the right [[W:Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]]. They are [[W:Helix|helices]] bent into a [[W:Möbius strip|Möbius loop]] in the fourth dimension, taking a diagonal [[W:Winding number|winding route]] twice around the 3-sphere through the non-adjacent vertices of a 4-polytope's [[W:Skew polygon#Regular skew polygons in four dimensions|skew polygon]].|name=isoclinic geodesic}} {{Efn|[[File:Hopf band wikipedia.png|thumb|150px|Two [[W:Clifford parallel|Clifford parallel]] great circles spanned by a twisted [[W:Annulus (mathematics)|annulus]].]][[W:Clifford parallel|Clifford parallel]]s are non-intersecting curved lines that are parallel in the sense that the perpendicular (shortest) distance between them is the same at each point. A double helix is an example of Clifford parallelism in ordinary 3-dimensional Euclidean space. In 4-space Clifford parallels occur as geodesic great circles on the [[W:3-sphere|3-sphere]].{{Sfn|Kim|Rote|2016|pp=8-10|loc=Relations to Clifford Parallelism}} Whereas in 3-dimensional space, any two geodesic great circles on the [[W:2-sphere|2-sphere]] will always intersect at two antipodal points, in 4-dimensional space not all great circles intersect. In 4-polytopes various discrete sets of Clifford parallel non-intersecting geodesic great circles can be found on the 3-sphere. They spiral around each other in [[W:Hopf fibration|Hopf fiber bundles]] which visit all the vertices just once. The simplest example is that six mutually orthogonal great circles can be drawn on the 3-sphere, as three pairs of completely orthogonal great circles, intersecting at 8 points defining a [[16-cell]]. Each completely orthogonal pair of circles is Clifford parallel. They cannot intersect at all, because they lie in planes which intersect at only one point: the center of the 16-cell. Because they are perpendicular and share a common center, the two circles are obviously not parallel and separate in the usual way of parallel circles in 3 dimensions; rather they are connected like adjacent links in a chain, each passing through the other without intersecting at any points, forming a [[W:Hopf link|Hopf link]]|name=Clifford parallels}} {{Efn|In the 24-cell each great square plane is completely orthogonal{{Efn|name=completely orthogonal planes}} to another great square plane, and each great hexagon plane is completely orthogonal to a plane which intersects only two vertices: a great [[W:digon|digon]] plane.|name=pairs of completely orthogonal planes}} {{Efn|In an [[24-cell#Isoclinic rotations|isoclinic rotation]], each point anywhere in the 4-polytope moves an equal distance in four orthogonal directions at once, on a [[W:8-cell#Radial equilateral symmetry|4-dimensional diagonal]]. The point is displaced a total [[W:Pythagorean distance]] equal to the square root of four times the square of that distance. For example, when the unit-radius 24-cell rotates isoclinically 60° in a hexagon invariant plane and 60° in its completely orthogonal invariant plane,{{Efn|name=pairs of completely orthogonal planes}} all vertices are displaced to a vertex two edge lengths away. Each vertex is displaced to another vertex {{radic|3}} (120°) away, moving {{radic|3/4}} in four orthogonal coordinate directions.|name=isoclinic 4-dimensional diagonal}} {{Efn|Each square plane is isoclinic (Clifford parallel) to five other square planes but completely orthogonal{{Efn|name=completely orthogonal planes}} to only one of them.{{Efn|name=Clifford parallel squares in the 16-cell and 24-cell}} Every pair of completely orthogonal planes has Clifford parallel great circles, but not all Clifford parallel great circles are orthogonal (e.g., none of the hexagonal geodesics in the 24-cell are mutually orthogonal).|name=only some Clifford parallels are orthogonal}} {{Efn|In the [[16-cell#Rotations|16-cell]] the 6 orthogonal great squares form 3 pairs of completely orthogonal great circles; each pair is Clifford parallel. In the 24-cell, the 3 inscribed 16-cells lie rotated 60 degrees isoclinically{{Efn|name=isoclinic 4-dimensional diagonal}} with respect to each other; consequently their corresponding vertices are 120 degrees apart on a hexagonal great circle. Pairing their vertices which are 90 degrees apart reveals corresponding square great circles which are Clifford parallel. Each of the 18 square great circles is Clifford parallel not only to one other square great circle in the same 16-cell (the completely orthogonal one), but also to two square great circles (which are completely orthogonal to each other) in each of the other two 16-cells. (Completely orthogonal great circles are Clifford parallel, but not all Clifford parallels are orthogonal.{{Efn|name=only some Clifford parallels are orthogonal}}) A 60 degree isoclinic rotation of the 24-cell in hexagonal invariant planes takes each square great circle to a Clifford parallel (but non-orthogonal) square great circle in a different 16-cell.|name=Clifford parallel squares in the 16-cell and 24-cell}} {{Efn|In 4 dimensional space we can construct 4 perpendicular axes and 6 perpendicular planes through a point. Without loss of generality, we may take these to be the axes and orthogonal central planes of a (w, x, y, z) Cartesian coordinate system. In 4 dimensions we have the same 3 orthogonal planes (xy, xz, yz) that we have in 3 dimensions, and also 3 others (wx, wy, wz). Each of the 6 orthogonal planes shares an axis with 4 of the others, and is ''completely orthogonal'' to just one of the others: the only one with which it does not share an axis. Thus there are 3 pairs of completely orthogonal planes: xy and wz intersect only at the origin; xz and wy intersect only at the origin; yz and wx intersect only at the origin.|name=six orthogonal planes of the Cartesian basis}} {{Efn|Two planes in 4-dimensional space can have four possible reciprocal positions: (1) they can coincide (be exactly the same plane); (2) they can be parallel (the only way they can fail to intersect at all); (3) they can intersect in a single line, as two non-parallel planes do in 3-dimensional space; or (4) '''they can intersect in a single point'''{{Efn|To visualize how two planes can intersect in a single point in a four dimensional space, consider the Euclidean space (w, x, y, z) and imagine that the w dimension represents time rather than a spatial dimension. The xy central plane (where w{{=}}0, z{{=}}0) shares no axis with the wz central plane (where x{{=}}0, y{{=}}0). The xy plane exists at only a single instant in time (w{{=}}0); the wz plane (and in particular the w axis) exists all the time. Thus their only moment and place of intersection is at the origin point (0,0,0,0).|name=how planes intersect at a single point}} (and they ''must'', if they are completely orthogonal).{{Efn|Two flat planes A and B of a Euclidean space of four dimensions are called ''completely orthogonal'' if and only if every line in A is orthogonal to every line in B. In that case the planes A and B intersect at a single point O, so that if a line in A intersects with a line in B, they intersect at O.{{Efn|name=six orthogonal planes of the Cartesian basis}}|name=completely orthogonal planes}}|name=how planes intersect}} {{Efn|Polytopes are '''completely disjoint''' if all their ''element sets'' are disjoint: they do not share any vertices, edges, faces or cells. They may still overlap in space, sharing 4-content, volume, area, or lineage.|name=completely disjoint}} {{Efn|If the [[W:Euclidean distance|Pythagorean distance]] between any two vertices is {{sqrt|1}}, their geodesic distance is 1; they may be two adjacent vertices (in the curved 3-space of the surface), or a vertex and the center (in 4-space). If their Pythagorean distance is {{sqrt|2}}, their geodesic distance is 2 (whether via 3-space or 4-space, because the path along the edges is the same straight line with one 90^o bend in it as the path through the center). If their Pythagorean distance is {{sqrt|3}}, their geodesic distance is still 2 (whether on a hexagonal great circle past one 60^o bend, or as a straight line with one 60^o bend in it through the center). Finally, if their Pythagorean distance is {{sqrt|4}}, their geodesic distance is still 2 in 4-space (straight through the center), but it reaches 3 in 3-space (by going halfway around a hexagonal great circle).|name=Geodesic distance}} {{Efn|Two angles are required to fix the relative positions of two planes in 4-space.{{Sfn|Kim|Rote|2016|p=7|loc=§6 Angles between two Planes in 4-Space|ps=; "In four (and higher) dimensions, we need two angles to fix the relative position between two planes. (More generally, ''k'' angles are defined between ''k''-dimensional subspaces.)"}} Since all planes in the same [[W:hyperplane|hyperplane]] are 0 degrees apart in one of the two angles, only one angle is required in 3-space. Great hexagons in different hyperplanes are 60 degrees apart in ''both'' angles. Great squares in different hyperplanes are 90 degrees apart in ''both'' angles (completely orthogonal){{Efn|name=completely orthogonal planes}} or 60 degrees apart in ''both'' angles.{{Efn||name=Clifford parallel squares in the 16-cell and 24-cell}} Planes which are separated by two equal angles are called ''isoclinic''. Planes which are isoclinic have [[W:Clifford parallel|Clifford parallel]] great circles.{{Efn|name=Clifford parallels}} A great square and a great hexagon in different hyperplanes are neither isoclinic nor Clifford parallel; they are separated by a 90 degree angle ''and'' a 60 degree angle.|name=two angles between central planes}} {{Efn|The 24-cell contains 3 distinct 8-cells (tesseracts), rotated 60° isoclinically with respect to each other. The corresponding vertices of two 8-cells are {{radic|3}} (120°) apart. Each 8-cell contains 8 cubical cells, and each cube contains four {{radic|3}} chords (its long diagonals). The 8-cells are not completely disjoint{{Efn|name=completely disjoint}} (they share vertices), but each cube and each {{radic|3}} chord belongs to just one 8-cell. The {{radic|3}} chords joining the corresponding vertices of two 8-cells belong to the third 8-cell.|name=three 8-cells}} {{Efn|Departing from any vertex V₀ in the original great hexagon plane of isoclinic rotation P₀, the first vertex reached V₁ is 120 degrees away along a {{radic|3}} chord lying in a different hexagonal plane P₁. P₁ is inclined to P₀ at a 60° angle.{{Efn|P₀ and P₁ lie in the same hyperplane (the same central cuboctahedron) so their other angle of separation is 0.{{Efn|name=two angles between central planes}}}} The second vertex reached V₂ is 120 degrees beyond V₁ along a second {{radic|3}} chord lying in another hexagonal plane P₂ that is Clifford parallel to P₀.{{Efn|P₀ and P₂ are 60° apart in ''both'' angles of separation.{{Efn|name=two angles between central planes}} Clifford parallel planes are isoclinic (which means they are separated by two equal angles), and their corresponding vertices are all the same distance apart. Although V₀ and V₂ are ''two'' {{radic|3}} chords apart{{Efn|V₀ and V₂ are two {{radic|3}} chords apart on the geodesic path of this rotational isocline, but that is not the shortest geodesic path between them. In the 24-cell, it is impossible for two vertices to be more distant than ''one'' {{radic|3}} chord, unless they are antipodal vertices {{radic|4}} apart.{{Efn|name=Geodesic distance}} V₀ and V₂ are ''one'' {{radic|3}} chord apart on some other isocline. More generally, isoclines are geodesics because the distance between their ''adjacent'' vertices is the shortest distance between those two vertices, but a path between two vertices along a geodesic is not always the shortest distance between them (even on ordinary great circle geodesics).}}, P₀ and P₂ are just one {{radic|1}} edge apart (at every pair of ''nearest'' vertices).}} (Notice that V₁ lies in both intersecting planes P₁ and P₂, as V₀ lies in both P₀ and P₁. But P₀ and P₂ have ''no'' vertices in common; they do not intersect.) The third vertex reached V₃ is 120 degrees beyond V₂ along a third {{radic|3}} chord lying in another hexagonal plane P₃ that is Clifford parallel to P₁. The three {{radic|3}} chords lie in different 8-cells.{{Efn|name=three 8-cells}} V₀ to V₃ is a 360° isoclinic rotation.|name=360 degree geodesic path visiting 3 hexagonal planes}} {{Sfn|Mamone, Pileio & Levitt|2010|loc=§4.5 Regular Convex 4-Polytopes|pp=1438-1439|ps=; the 24-cell has 1152 symmetry operations (rotations and reflections) as enumerated in Table 2, symmetry group 𝐹₄.}} ==Notes== {{Regular convex 4-polytopes Notelist|wiki=W:}} ==Citations== {{Regular convex 4-polytopes Reflist|wiki=W:}} ==References== {{Refbegin}} * {{Cite book|title=A Week on the Concord and Merrimack Rivers|last=Thoreau|first=Henry David|author-link=W:Thoreau|publisher=James Munroe and Company|year=1849|isbn=|location=Boston|ref={{SfnRef|Thoreau|1849}}}} * {{Cite journal|title=Theoretical Evidence for Principles of Special Relativity Based on Isotropic and Uniform Four-Dimensional Space|first=Takuya|last=Yamashita|date=25 May 2023|doi= 10.20944/preprints202305.1785.v1|journal=Preprints|volume=2023|issue=2023051785|url=https://doi.org/10.20944/preprints202305.1785.v1}} * {{Cite_arXiv | arxiv=2512.02903v2 | date=2 January 2026 | title=Symmetry transformation group arising from the Laplace–Runge–Lenz vector | first1=Stephen C. | last1=Anco | first2=Mahdieh Gol Bashmani | last2=Moghadam | class=math-ph}} === [[Polyscheme|Polyschemes]] === {{Regular convex 4-polytopes Refs|wiki=W:}} {{Refend}} j38zodaowq21mlj2pac5sdnke2d928w 0 305659 2823660 2823630 2026-08-20T15:22:16Z Unitfreak 695864 /* Anchoring Bully Timestamps */ 2823660 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the June solstice in 1998. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the invariable plane's galactic ecliptic node—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Sun and the node that are moving. ==== A surrogate for the Sun ==== The path of the invariable node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun as it orbits the Galactic Center. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment, indicating that a travel distance of '''1,007.87 parsecs''' corresponds to timestamp '''{{nowrap|8209 ECC7 C23E}}''', whereas a travel distance of '''1,008.87 parsecs''' corresponds to timestamp '''{{nowrap|8209 EF4D 0949}}'''. The Bully timestamp system was anchored using an intermediate timestamp of '''{{nowrap|8209 ED00 0000}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history:{{Blockquote|text=The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}} Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. In the Bully timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]]. === What about the Earth and Moon? === The motions of the Earth and Moon are not suitable for precise, long-term time measurement. Over deep time, gravitational interactions cause variations in these orbits. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This can vary by up to 20 to 25 minutes from one year to the next due to tugs from neighboring planets, but when these are averaged out, the remaining century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is value in using a divisor of this year as the fundamental unit of the Bully timestamp system. It turns out that 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals exactly '''10,330 Bully timestamps'''. ==== Earth's tropical year ==== The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] There are two different processes at work in '''Figure 5c'''. One process is axial precession—the slow wobble of Earth’s rotational axis. The other process is orbital eccentricity. In 1998, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was four days longer than winter because at that time Earth's aphelion was more aligned with summer and its perihelion was more aligned with winter. During aphelion Earth moves slower in its orbit, so whichever season is aligned with aphelion ends up being the longest. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] == The Bully Mnemonic == <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] 2df1kwlv3wo9juxq3ee5yjck7r3uhay 2823661 2823660 2026-08-20T15:28:06Z Unitfreak 695864 /* A surrogate for the Sun */ 2823661 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the June solstice in 1998. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the invariable plane's galactic ecliptic node—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Sun and the node that are moving. ==== A surrogate for the Sun ==== The path of the invariable node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun as it orbits the Galactic Center. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment, indicating that a travel distance of '''1,007.87 parsecs''' corresponds to timestamp '''{{nowrap|8209 ECC7 C23E}}''', whereas a travel distance of '''1,008.87 parsecs''' corresponds to timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the anchor of the entire system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history:{{Blockquote|text=The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}} Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. In the Bully timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]]. === What about the Earth and Moon? === The motions of the Earth and Moon are not suitable for precise, long-term time measurement. Over deep time, gravitational interactions cause variations in these orbits. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This can vary by up to 20 to 25 minutes from one year to the next due to tugs from neighboring planets, but when these are averaged out, the remaining century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is value in using a divisor of this year as the fundamental unit of the Bully timestamp system. It turns out that 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals exactly '''10,330 Bully timestamps'''. ==== Earth's tropical year ==== The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] There are two different processes at work in '''Figure 5c'''. One process is axial precession—the slow wobble of Earth’s rotational axis. The other process is orbital eccentricity. In 1998, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was four days longer than winter because at that time Earth's aphelion was more aligned with summer and its perihelion was more aligned with winter. During aphelion Earth moves slower in its orbit, so whichever season is aligned with aphelion ends up being the longest. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] == The Bully Mnemonic == <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] 2hissl69xmjtczz2knekaorb81v92qk 2823662 2823661 2026-08-20T15:33:51Z Unitfreak 695864 /* A surrogate for the Sun */ 2823662 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the June solstice in 1998. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the invariable plane's galactic ecliptic node—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Sun and the node that are moving. ==== A surrogate for the Sun ==== The path of the invariable node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun as it orbits the Galactic Center. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment, indicating that a travel distance of '''1,007.87 parsecs''' corresponds to timestamp '''{{nowrap|8209 ECC7 C23E}}''', whereas a travel distance of '''1,008.87 parsecs''' corresponds to timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {{Blockquote|text=Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the anchor of the entire system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun.}} {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history:{{Blockquote|text=The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}} Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. In the Bully timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]]. === What about the Earth and Moon? === The motions of the Earth and Moon are not suitable for precise, long-term time measurement. Over deep time, gravitational interactions cause variations in these orbits. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This can vary by up to 20 to 25 minutes from one year to the next due to tugs from neighboring planets, but when these are averaged out, the remaining century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is value in using a divisor of this year as the fundamental unit of the Bully timestamp system. It turns out that 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals exactly '''10,330 Bully timestamps'''. ==== Earth's tropical year ==== The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] There are two different processes at work in '''Figure 5c'''. One process is axial precession—the slow wobble of Earth’s rotational axis. The other process is orbital eccentricity. In 1998, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was four days longer than winter because at that time Earth's aphelion was more aligned with summer and its perihelion was more aligned with winter. During aphelion Earth moves slower in its orbit, so whichever season is aligned with aphelion ends up being the longest. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] == The Bully Mnemonic == <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] puv5gzbnp80dtqs7zr3d6ol4uly8qgp 2823663 2823662 2026-08-20T15:37:08Z Unitfreak 695864 /* A surrogate for the Sun */ 2823663 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the June solstice in 1998. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the invariable plane's galactic ecliptic node—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Sun and the node that are moving. ==== A surrogate for the Sun ==== The path of the invariable node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun as it orbits the Galactic Center. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment, indicating that a travel distance of '''1,007.87 parsecs''' corresponds to timestamp '''{{nowrap|8209 ECC7 C23E}}''', whereas a travel distance of '''1,008.87 parsecs''' corresponds to timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} {{Blockquote|text=Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the anchor of the entire system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun as shown in '''Figure 5b'''.}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history:{{Blockquote|text=The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}} Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. In the Bully timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]]. === What about the Earth and Moon? === The motions of the Earth and Moon are not suitable for precise, long-term time measurement. Over deep time, gravitational interactions cause variations in these orbits. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This can vary by up to 20 to 25 minutes from one year to the next due to tugs from neighboring planets, but when these are averaged out, the remaining century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is value in using a divisor of this year as the fundamental unit of the Bully timestamp system. It turns out that 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals exactly '''10,330 Bully timestamps'''. ==== Earth's tropical year ==== The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] There are two different processes at work in '''Figure 5c'''. One process is axial precession—the slow wobble of Earth’s rotational axis. The other process is orbital eccentricity. In 1998, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was four days longer than winter because at that time Earth's aphelion was more aligned with summer and its perihelion was more aligned with winter. During aphelion Earth moves slower in its orbit, so whichever season is aligned with aphelion ends up being the longest. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] == The Bully Mnemonic == <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] arpkagbf6l3ybqdghlswxuhw37m2ohm 2823664 2823663 2026-08-20T15:39:05Z Unitfreak 695864 /* A surrogate for the Sun */ 2823664 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the June solstice in 1998. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the invariable plane's galactic ecliptic node—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Sun and the node that are moving. ==== A surrogate for the Sun ==== The path of the invariable node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun as it orbits the Galactic Center. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment, indicating that a travel distance of '''1,007.87 parsecs''' corresponds to timestamp '''{{nowrap|8209 ECC7 C23E}}''', whereas a travel distance of '''1,008.87 parsecs''' corresponds to timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} === The Selected Timestamp === {{Blockquote|text=Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the anchor of the entire system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun as shown in '''Figure 5b'''.}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history:{{Blockquote|text=The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}} Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. In the Bully timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]]. === What about the Earth and Moon? === The motions of the Earth and Moon are not suitable for precise, long-term time measurement. Over deep time, gravitational interactions cause variations in these orbits. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This can vary by up to 20 to 25 minutes from one year to the next due to tugs from neighboring planets, but when these are averaged out, the remaining century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is value in using a divisor of this year as the fundamental unit of the Bully timestamp system. It turns out that 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals exactly '''10,330 Bully timestamps'''. ==== Earth's tropical year ==== The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] There are two different processes at work in '''Figure 5c'''. One process is axial precession—the slow wobble of Earth’s rotational axis. The other process is orbital eccentricity. In 1998, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was four days longer than winter because at that time Earth's aphelion was more aligned with summer and its perihelion was more aligned with winter. During aphelion Earth moves slower in its orbit, so whichever season is aligned with aphelion ends up being the longest. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] == The Bully Mnemonic == <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] migxb5hrz66ro6xmajpjff50ofockkp 2823665 2823664 2026-08-20T15:39:29Z Unitfreak 695864 /* The Selected Timestamp */ 2823665 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the June solstice in 1998. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the invariable plane's galactic ecliptic node—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Sun and the node that are moving. ==== A surrogate for the Sun ==== The path of the invariable node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun as it orbits the Galactic Center. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment, indicating that a travel distance of '''1,007.87 parsecs''' corresponds to timestamp '''{{nowrap|8209 ECC7 C23E}}''', whereas a travel distance of '''1,008.87 parsecs''' corresponds to timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} ==== The Selected Timestamp ==== {{Blockquote|text=Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the anchor of the entire system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun as shown in '''Figure 5b'''.}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history:{{Blockquote|text=The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}} Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. In the Bully timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]]. === What about the Earth and Moon? === The motions of the Earth and Moon are not suitable for precise, long-term time measurement. Over deep time, gravitational interactions cause variations in these orbits. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This can vary by up to 20 to 25 minutes from one year to the next due to tugs from neighboring planets, but when these are averaged out, the remaining century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is value in using a divisor of this year as the fundamental unit of the Bully timestamp system. It turns out that 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals exactly '''10,330 Bully timestamps'''. ==== Earth's tropical year ==== The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] There are two different processes at work in '''Figure 5c'''. One process is axial precession—the slow wobble of Earth’s rotational axis. The other process is orbital eccentricity. In 1998, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was four days longer than winter because at that time Earth's aphelion was more aligned with summer and its perihelion was more aligned with winter. During aphelion Earth moves slower in its orbit, so whichever season is aligned with aphelion ends up being the longest. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] == The Bully Mnemonic == <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] 61mrtxbbvdg645wc563ohg963g3z7sg 2823666 2823665 2026-08-20T15:44:48Z Unitfreak 695864 /* Bullies in the Bully System */ 2823666 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the June solstice in 1998. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the invariable plane's galactic ecliptic node—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Sun and the node that are moving. ==== A surrogate for the Sun ==== The path of the invariable node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun as it orbits the Galactic Center. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment, indicating that a travel distance of '''1,007.87 parsecs''' corresponds to timestamp '''{{nowrap|8209 ECC7 C23E}}''', whereas a travel distance of '''1,008.87 parsecs''' corresponds to timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} ==== The Selected Timestamp ==== {{Blockquote|text=Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the anchor of the entire system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun as shown in '''Figure 5b'''.}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history:{{Blockquote|text=The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}} Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. ==== Naming the Bully System ==== {{Blockquote|text=In the Bully timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === What about the Earth and Moon? === The motions of the Earth and Moon are not suitable for precise, long-term time measurement. Over deep time, gravitational interactions cause variations in these orbits. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This can vary by up to 20 to 25 minutes from one year to the next due to tugs from neighboring planets, but when these are averaged out, the remaining century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is value in using a divisor of this year as the fundamental unit of the Bully timestamp system. It turns out that 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals exactly '''10,330 Bully timestamps'''. ==== Earth's tropical year ==== The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] There are two different processes at work in '''Figure 5c'''. One process is axial precession—the slow wobble of Earth’s rotational axis. The other process is orbital eccentricity. In 1998, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was four days longer than winter because at that time Earth's aphelion was more aligned with summer and its perihelion was more aligned with winter. During aphelion Earth moves slower in its orbit, so whichever season is aligned with aphelion ends up being the longest. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] == The Bully Mnemonic == <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] 54t2y89ax4t6n836k3nks3hlhw1th93 2823667 2823666 2026-08-20T15:46:07Z Unitfreak 695864 /* The Selected Timestamp */ 2823667 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the June solstice in 1998. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the invariable plane's galactic ecliptic node—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Sun and the node that are moving. ==== A surrogate for the Sun ==== The path of the invariable node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun as it orbits the Galactic Center. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment, indicating that a travel distance of '''1,007.87 parsecs''' corresponds to timestamp '''{{nowrap|8209 ECC7 C23E}}''', whereas a travel distance of '''1,008.87 parsecs''' corresponds to timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} ==== Selecting a Timestamp ==== {{Blockquote|text=Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the anchor of the entire system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun as shown in '''Figure 5b'''.}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history:{{Blockquote|text=The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}} Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. ==== Naming the Bully System ==== {{Blockquote|text=In the Bully timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === What about the Earth and Moon? === The motions of the Earth and Moon are not suitable for precise, long-term time measurement. Over deep time, gravitational interactions cause variations in these orbits. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This can vary by up to 20 to 25 minutes from one year to the next due to tugs from neighboring planets, but when these are averaged out, the remaining century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is value in using a divisor of this year as the fundamental unit of the Bully timestamp system. It turns out that 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals exactly '''10,330 Bully timestamps'''. ==== Earth's tropical year ==== The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] There are two different processes at work in '''Figure 5c'''. One process is axial precession—the slow wobble of Earth’s rotational axis. The other process is orbital eccentricity. In 1998, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was four days longer than winter because at that time Earth's aphelion was more aligned with summer and its perihelion was more aligned with winter. During aphelion Earth moves slower in its orbit, so whichever season is aligned with aphelion ends up being the longest. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] == The Bully Mnemonic == <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] i4d9h26duh2mtu75lyvzsjlk6pf4lw1 2823668 2823667 2026-08-20T15:47:33Z Unitfreak 695864 /* Naming the Bully System */ 2823668 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the June solstice in 1998. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the invariable plane's galactic ecliptic node—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Sun and the node that are moving. ==== A surrogate for the Sun ==== The path of the invariable node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun as it orbits the Galactic Center. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment, indicating that a travel distance of '''1,007.87 parsecs''' corresponds to timestamp '''{{nowrap|8209 ECC7 C23E}}''', whereas a travel distance of '''1,008.87 parsecs''' corresponds to timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} ==== Selecting a Timestamp ==== {{Blockquote|text=Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the anchor of the entire system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun as shown in '''Figure 5b'''.}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history:{{Blockquote|text=The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}} Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. ==== Naming the System ==== {{Blockquote|text=In the Bully timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === What about the Earth and Moon? === The motions of the Earth and Moon are not suitable for precise, long-term time measurement. Over deep time, gravitational interactions cause variations in these orbits. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This can vary by up to 20 to 25 minutes from one year to the next due to tugs from neighboring planets, but when these are averaged out, the remaining century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is value in using a divisor of this year as the fundamental unit of the Bully timestamp system. It turns out that 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals exactly '''10,330 Bully timestamps'''. ==== Earth's tropical year ==== The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] There are two different processes at work in '''Figure 5c'''. One process is axial precession—the slow wobble of Earth’s rotational axis. The other process is orbital eccentricity. In 1998, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was four days longer than winter because at that time Earth's aphelion was more aligned with summer and its perihelion was more aligned with winter. During aphelion Earth moves slower in its orbit, so whichever season is aligned with aphelion ends up being the longest. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] == The Bully Mnemonic == <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] 09rzcsr0ogxxqh8j35bq6tms1o4tx91 2823669 2823668 2026-08-20T15:48:22Z Unitfreak 695864 /* Bullies in the Bully System */ 2823669 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the June solstice in 1998. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the invariable plane's galactic ecliptic node—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Sun and the node that are moving. ==== A surrogate for the Sun ==== The path of the invariable node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun as it orbits the Galactic Center. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment, indicating that a travel distance of '''1,007.87 parsecs''' corresponds to timestamp '''{{nowrap|8209 ECC7 C23E}}''', whereas a travel distance of '''1,008.87 parsecs''' corresponds to timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} ==== Selecting a Timestamp ==== {{Blockquote|text=Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the anchor of the entire system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun as shown in '''Figure 5b'''.}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: :The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026. Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. ==== Naming the System ==== {{Blockquote|text=In the Bully timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === What about the Earth and Moon? === The motions of the Earth and Moon are not suitable for precise, long-term time measurement. Over deep time, gravitational interactions cause variations in these orbits. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This can vary by up to 20 to 25 minutes from one year to the next due to tugs from neighboring planets, but when these are averaged out, the remaining century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is value in using a divisor of this year as the fundamental unit of the Bully timestamp system. It turns out that 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals exactly '''10,330 Bully timestamps'''. ==== Earth's tropical year ==== The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] There are two different processes at work in '''Figure 5c'''. One process is axial precession—the slow wobble of Earth’s rotational axis. The other process is orbital eccentricity. In 1998, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was four days longer than winter because at that time Earth's aphelion was more aligned with summer and its perihelion was more aligned with winter. During aphelion Earth moves slower in its orbit, so whichever season is aligned with aphelion ends up being the longest. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] == The Bully Mnemonic == <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] 59sw27u98qxhbs212zritod1049bres 2823670 2823669 2026-08-20T15:53:02Z Unitfreak 695864 /* The Galactic Ecliptic Node near Sagittarius */ 2823670 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the June solstice in 1998. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the invariable node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun as it orbits the Galactic Center. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment, indicating that a travel distance of '''1,007.87 parsecs''' corresponds to timestamp '''{{nowrap|8209 ECC7 C23E}}''', whereas a travel distance of '''1,008.87 parsecs''' corresponds to timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} ==== Selecting a Timestamp ==== {{Blockquote|text=Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the anchor of the entire system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun as shown in '''Figure 5b'''.}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: :The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026. Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. ==== Naming the System ==== {{Blockquote|text=In the Bully timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === What about the Earth and Moon? === The motions of the Earth and Moon are not suitable for precise, long-term time measurement. Over deep time, gravitational interactions cause variations in these orbits. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This can vary by up to 20 to 25 minutes from one year to the next due to tugs from neighboring planets, but when these are averaged out, the remaining century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is value in using a divisor of this year as the fundamental unit of the Bully timestamp system. It turns out that 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals exactly '''10,330 Bully timestamps'''. ==== Earth's tropical year ==== The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] There are two different processes at work in '''Figure 5c'''. One process is axial precession—the slow wobble of Earth’s rotational axis. The other process is orbital eccentricity. In 1998, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was four days longer than winter because at that time Earth's aphelion was more aligned with summer and its perihelion was more aligned with winter. During aphelion Earth moves slower in its orbit, so whichever season is aligned with aphelion ends up being the longest. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] == The Bully Mnemonic == <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] 5nqz5azyqynrlir4eyj6oc34xhm8id4 2823671 2823670 2026-08-20T15:53:45Z Unitfreak 695864 /* Bullies in the Bully System */ 2823671 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the June solstice in 1998. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the invariable node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun as it orbits the Galactic Center. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment, indicating that a travel distance of '''1,007.87 parsecs''' corresponds to timestamp '''{{nowrap|8209 ECC7 C23E}}''', whereas a travel distance of '''1,008.87 parsecs''' corresponds to timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} ==== Selecting a Timestamp ==== {{Blockquote|text=Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the anchor of the entire system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun as shown in '''Figure 5b'''.}} === Bullies in the Bully System === As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: :The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026. Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. ==== Naming the System ==== {{Blockquote|text=In the Bully timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === What about the Earth and Moon? === The motions of the Earth and Moon are not suitable for precise, long-term time measurement. Over deep time, gravitational interactions cause variations in these orbits. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This can vary by up to 20 to 25 minutes from one year to the next due to tugs from neighboring planets, but when these are averaged out, the remaining century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is value in using a divisor of this year as the fundamental unit of the Bully timestamp system. It turns out that 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals exactly '''10,330 Bully timestamps'''. ==== Earth's tropical year ==== The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] There are two different processes at work in '''Figure 5c'''. One process is axial precession—the slow wobble of Earth’s rotational axis. The other process is orbital eccentricity. In 1998, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was four days longer than winter because at that time Earth's aphelion was more aligned with summer and its perihelion was more aligned with winter. During aphelion Earth moves slower in its orbit, so whichever season is aligned with aphelion ends up being the longest. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] == The Bully Mnemonic == <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] oxl7rz7ibvbonzokkvo87pihtc4bz5y 2823672 2823671 2026-08-20T15:58:17Z Unitfreak 695864 /* The Galactic Ecliptic Node near Sagittarius */ 2823672 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the June solstice in 1998. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun as it orbits the Galactic Center. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment, indicating that a travel distance of '''1,007.87 parsecs''' corresponds to timestamp '''{{nowrap|8209 ECC7 C23E}}''', whereas a travel distance of '''1,008.87 parsecs''' corresponds to timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} ==== Selecting a Timestamp ==== {{Blockquote|text=Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the anchor of the entire system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun as shown in '''Figure 5b'''.}} === Bullies in the Bully System === As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: :The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026. Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. ==== Naming the System ==== {{Blockquote|text=In the Bully timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === What about the Earth and Moon? === The motions of the Earth and Moon are not suitable for precise, long-term time measurement. Over deep time, gravitational interactions cause variations in these orbits. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This can vary by up to 20 to 25 minutes from one year to the next due to tugs from neighboring planets, but when these are averaged out, the remaining century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is value in using a divisor of this year as the fundamental unit of the Bully timestamp system. It turns out that 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals exactly '''10,330 Bully timestamps'''. ==== Earth's tropical year ==== The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] There are two different processes at work in '''Figure 5c'''. One process is axial precession—the slow wobble of Earth’s rotational axis. The other process is orbital eccentricity. In 1998, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was four days longer than winter because at that time Earth's aphelion was more aligned with summer and its perihelion was more aligned with winter. During aphelion Earth moves slower in its orbit, so whichever season is aligned with aphelion ends up being the longest. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] == The Bully Mnemonic == <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] paanfuuv61in2sr4kajv27p46hlh3ql 2823673 2823672 2026-08-20T16:01:26Z Unitfreak 695864 /* A surrogate for the Sun */ 2823673 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the June solstice in 1998. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment, indicating that a travel distance of '''1,007.87 parsecs''' corresponds to timestamp '''{{nowrap|8209 ECC7 C23E}}''', whereas a travel distance of '''1,008.87 parsecs''' corresponds to timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} ==== Selecting a Timestamp ==== {{Blockquote|text=Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the anchor of the entire system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun as shown in '''Figure 5b'''.}} === Bullies in the Bully System === As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: :The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026. Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. ==== Naming the System ==== {{Blockquote|text=In the Bully timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === What about the Earth and Moon? === The motions of the Earth and Moon are not suitable for precise, long-term time measurement. Over deep time, gravitational interactions cause variations in these orbits. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This can vary by up to 20 to 25 minutes from one year to the next due to tugs from neighboring planets, but when these are averaged out, the remaining century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is value in using a divisor of this year as the fundamental unit of the Bully timestamp system. It turns out that 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals exactly '''10,330 Bully timestamps'''. ==== Earth's tropical year ==== The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] There are two different processes at work in '''Figure 5c'''. One process is axial precession—the slow wobble of Earth’s rotational axis. The other process is orbital eccentricity. In 1998, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was four days longer than winter because at that time Earth's aphelion was more aligned with summer and its perihelion was more aligned with winter. During aphelion Earth moves slower in its orbit, so whichever season is aligned with aphelion ends up being the longest. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] == The Bully Mnemonic == <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] 2ihtgmwoqkt0cnp6f0bf35ksgq1nak9 2823674 2823673 2026-08-20T16:03:34Z Unitfreak 695864 /* The Galactic Ecliptic Node near Sagittarius */ 2823674 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the June solstice in 1998. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment, indicating that a travel distance of '''1,007.87 parsecs''' corresponds to timestamp '''{{nowrap|8209 ECC7 C23E}}''', whereas a travel distance of '''1,008.87 parsecs''' corresponds to timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} ==== Selecting a Timestamp ==== {{Blockquote|text=Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the anchor of the entire system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun as shown in '''Figure 5b'''.}} === Bullies in the Bully System === As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: :The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026. Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. ==== Naming the System ==== {{Blockquote|text=In the Bully timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === What about the Earth and Moon? === The motions of the Earth and Moon are not suitable for precise, long-term time measurement. Over deep time, gravitational interactions cause variations in these orbits. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This can vary by up to 20 to 25 minutes from one year to the next due to tugs from neighboring planets, but when these are averaged out, the remaining century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is value in using a divisor of this year as the fundamental unit of the Bully timestamp system. It turns out that 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals exactly '''10,330 Bully timestamps'''. ==== Earth's tropical year ==== The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] There are two different processes at work in '''Figure 5c'''. One process is axial precession—the slow wobble of Earth’s rotational axis. The other process is orbital eccentricity. In 1998, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was four days longer than winter because at that time Earth's aphelion was more aligned with summer and its perihelion was more aligned with winter. During aphelion Earth moves slower in its orbit, so whichever season is aligned with aphelion ends up being the longest. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] == The Bully Mnemonic == <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] lljxbvzitug61cc8rhcyh2yca5j8yz2 2823675 2823674 2026-08-20T16:05:48Z Unitfreak 695864 /* Bullies in the Bully System */ 2823675 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the June solstice in 1998. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment, indicating that a travel distance of '''1,007.87 parsecs''' corresponds to timestamp '''{{nowrap|8209 ECC7 C23E}}''', whereas a travel distance of '''1,008.87 parsecs''' corresponds to timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} ==== Selecting a Timestamp ==== {{Blockquote|text=Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the anchor of the entire system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun as shown in '''Figure 5b'''.}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: :The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026. Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. ==== Naming the System ==== {{Blockquote|text=In the Bully timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === What about the Earth and Moon? === The motions of the Earth and Moon are not suitable for precise, long-term time measurement. Over deep time, gravitational interactions cause variations in these orbits. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This can vary by up to 20 to 25 minutes from one year to the next due to tugs from neighboring planets, but when these are averaged out, the remaining century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is value in using a divisor of this year as the fundamental unit of the Bully timestamp system. It turns out that 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals exactly '''10,330 Bully timestamps'''. ==== Earth's tropical year ==== The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] There are two different processes at work in '''Figure 5c'''. One process is axial precession—the slow wobble of Earth’s rotational axis. The other process is orbital eccentricity. In 1998, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was four days longer than winter because at that time Earth's aphelion was more aligned with summer and its perihelion was more aligned with winter. During aphelion Earth moves slower in its orbit, so whichever season is aligned with aphelion ends up being the longest. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] == The Bully Mnemonic == <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] tu1fhbfe3glmewlzu0ocsravxyn07zk 2823676 2823675 2026-08-20T16:12:10Z Unitfreak 695864 /* A surrogate for the Sun */ 2823676 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the June solstice in 1998. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14 parsecs travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} ==== Selecting a Timestamp ==== {{Blockquote|text=Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the anchor of the entire system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun as shown in '''Figure 5b'''.}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: :The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026. Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. ==== Naming the System ==== {{Blockquote|text=In the Bully timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === What about the Earth and Moon? === The motions of the Earth and Moon are not suitable for precise, long-term time measurement. Over deep time, gravitational interactions cause variations in these orbits. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This can vary by up to 20 to 25 minutes from one year to the next due to tugs from neighboring planets, but when these are averaged out, the remaining century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is value in using a divisor of this year as the fundamental unit of the Bully timestamp system. It turns out that 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals exactly '''10,330 Bully timestamps'''. ==== Earth's tropical year ==== The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] There are two different processes at work in '''Figure 5c'''. One process is axial precession—the slow wobble of Earth’s rotational axis. The other process is orbital eccentricity. In 1998, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was four days longer than winter because at that time Earth's aphelion was more aligned with summer and its perihelion was more aligned with winter. During aphelion Earth moves slower in its orbit, so whichever season is aligned with aphelion ends up being the longest. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] == The Bully Mnemonic == <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] d3zen9mg9708fm3ccjrrz4h6jdlq32c 2823677 2823676 2026-08-20T16:13:20Z Unitfreak 695864 /* Selecting a Timestamp */ 2823677 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the June solstice in 1998. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14 parsecs travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} ==== Selecting a Timestamp ==== {{Blockquote|text=Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the time anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun as shown in '''Figure 5b'''.}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: :The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026. Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. ==== Naming the System ==== {{Blockquote|text=In the Bully timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === What about the Earth and Moon? === The motions of the Earth and Moon are not suitable for precise, long-term time measurement. Over deep time, gravitational interactions cause variations in these orbits. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This can vary by up to 20 to 25 minutes from one year to the next due to tugs from neighboring planets, but when these are averaged out, the remaining century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is value in using a divisor of this year as the fundamental unit of the Bully timestamp system. It turns out that 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals exactly '''10,330 Bully timestamps'''. ==== Earth's tropical year ==== The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] There are two different processes at work in '''Figure 5c'''. One process is axial precession—the slow wobble of Earth’s rotational axis. The other process is orbital eccentricity. In 1998, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was four days longer than winter because at that time Earth's aphelion was more aligned with summer and its perihelion was more aligned with winter. During aphelion Earth moves slower in its orbit, so whichever season is aligned with aphelion ends up being the longest. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] == The Bully Mnemonic == <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] jn7k4es2gech72swb80dam1o74fnflp 2823678 2823677 2026-08-20T16:14:44Z Unitfreak 695864 /* Selecting a Timestamp */ 2823678 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the June solstice in 1998. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14 parsecs travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} ==== Selecting a Timestamp ==== {{Blockquote|text=Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the time anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: :The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026. Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. ==== Naming the System ==== {{Blockquote|text=In the Bully timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === What about the Earth and Moon? === The motions of the Earth and Moon are not suitable for precise, long-term time measurement. Over deep time, gravitational interactions cause variations in these orbits. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This can vary by up to 20 to 25 minutes from one year to the next due to tugs from neighboring planets, but when these are averaged out, the remaining century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is value in using a divisor of this year as the fundamental unit of the Bully timestamp system. It turns out that 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals exactly '''10,330 Bully timestamps'''. ==== Earth's tropical year ==== The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] There are two different processes at work in '''Figure 5c'''. One process is axial precession—the slow wobble of Earth’s rotational axis. The other process is orbital eccentricity. In 1998, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was four days longer than winter because at that time Earth's aphelion was more aligned with summer and its perihelion was more aligned with winter. During aphelion Earth moves slower in its orbit, so whichever season is aligned with aphelion ends up being the longest. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] == The Bully Mnemonic == <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] 25zl011qtup9moo40cwo0siji60vm54 2823679 2823678 2026-08-20T16:19:08Z Unitfreak 695864 /* A surrogate for the Sun */ 2823679 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the June solstice in 1998. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} ==== Selecting a Timestamp ==== {{Blockquote|text=Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the time anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: :The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026. Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. ==== Naming the System ==== {{Blockquote|text=In the Bully timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === What about the Earth and Moon? === The motions of the Earth and Moon are not suitable for precise, long-term time measurement. Over deep time, gravitational interactions cause variations in these orbits. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This can vary by up to 20 to 25 minutes from one year to the next due to tugs from neighboring planets, but when these are averaged out, the remaining century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is value in using a divisor of this year as the fundamental unit of the Bully timestamp system. It turns out that 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals exactly '''10,330 Bully timestamps'''. ==== Earth's tropical year ==== The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] There are two different processes at work in '''Figure 5c'''. One process is axial precession—the slow wobble of Earth’s rotational axis. The other process is orbital eccentricity. In 1998, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was four days longer than winter because at that time Earth's aphelion was more aligned with summer and its perihelion was more aligned with winter. During aphelion Earth moves slower in its orbit, so whichever season is aligned with aphelion ends up being the longest. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] == The Bully Mnemonic == <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] d4n18ylad60p3hzvxo1ezaub3vvrt8d 2823680 2823679 2026-08-20T16:25:07Z Unitfreak 695864 /* Anchoring Bully Timestamps */ 2823680 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} ==== Selecting a Timestamp ==== {{Blockquote|text=Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the time anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: :The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026. Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. ==== Naming the System ==== {{Blockquote|text=In the Bully timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === What about the Earth and Moon? === The motions of the Earth and Moon are not suitable for precise, long-term time measurement. Over deep time, gravitational interactions cause variations in these orbits. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This can vary by up to 20 to 25 minutes from one year to the next due to tugs from neighboring planets, but when these are averaged out, the remaining century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is value in using a divisor of this year as the fundamental unit of the Bully timestamp system. It turns out that 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals exactly '''10,330 Bully timestamps'''. ==== Earth's tropical year ==== The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] There are two different processes at work in '''Figure 5c'''. One process is axial precession—the slow wobble of Earth’s rotational axis. The other process is orbital eccentricity. In 1998, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was four days longer than winter because at that time Earth's aphelion was more aligned with summer and its perihelion was more aligned with winter. During aphelion Earth moves slower in its orbit, so whichever season is aligned with aphelion ends up being the longest. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] == The Bully Mnemonic == <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] fi1cd16q6nbs4csf3sr0l0opiytnevh 2823681 2823680 2026-08-20T16:31:47Z Unitfreak 695864 /* Earth's sidereal year */ 2823681 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} ==== Selecting a Timestamp ==== {{Blockquote|text=Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the time anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: :The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026. Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. ==== Naming the System ==== {{Blockquote|text=In the Bully timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === What about the Earth and Moon? === The motions of the Earth and Moon are not suitable for precise, long-term time measurement. Over deep time, gravitational interactions cause variations in these orbits. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This can vary by up to 20 to 25 minutes from one year to the next due to tugs from neighboring planets, but when these are averaged out, the remaining century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. It turns out that 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals exactly '''10,330 Bully timestamps'''. ==== Earth's tropical year ==== The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] There are two different processes at work in '''Figure 5c'''. One process is axial precession—the slow wobble of Earth’s rotational axis. The other process is orbital eccentricity. In 1998, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was four days longer than winter because at that time Earth's aphelion was more aligned with summer and its perihelion was more aligned with winter. During aphelion Earth moves slower in its orbit, so whichever season is aligned with aphelion ends up being the longest. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] == The Bully Mnemonic == <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] jvgf4od3n971vtu5xzhuwxehuxczimw 2823682 2823681 2026-08-20T16:35:37Z Unitfreak 695864 /* The Bully Mnemonic */ 2823682 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} ==== Selecting a Timestamp ==== {{Blockquote|text=Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the time anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: :The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026. Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. ==== Naming the System ==== {{Blockquote|text=In the Bully timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === What about the Earth and Moon? === The motions of the Earth and Moon are not suitable for precise, long-term time measurement. Over deep time, gravitational interactions cause variations in these orbits. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This can vary by up to 20 to 25 minutes from one year to the next due to tugs from neighboring planets, but when these are averaged out, the remaining century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. It turns out that 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals exactly '''10,330 Bully timestamps'''. ==== Earth's tropical year ==== The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] There are two different processes at work in '''Figure 5c'''. One process is axial precession—the slow wobble of Earth’s rotational axis. The other process is orbital eccentricity. In 1998, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was four days longer than winter because at that time Earth's aphelion was more aligned with summer and its perihelion was more aligned with winter. During aphelion Earth moves slower in its orbit, so whichever season is aligned with aphelion ends up being the longest. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] thdo0118pmvy6q5n8z3e6zdv691n5fc 2823683 2823682 2026-08-20T16:36:54Z Unitfreak 695864 /* What about the Earth and Moon? */ 2823683 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} ==== Selecting a Timestamp ==== {{Blockquote|text=Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the time anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: :The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026. Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. ==== Naming the System ==== {{Blockquote|text=In the Bully timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === What about the Earth and Moon? === The motions of the Earth and Moon are not suitable for precise, long-term time measurement. Over deep time, gravitational interactions cause variations in these orbits. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This can vary by up to 20 to 25 minutes from one year to the next due to tugs from neighboring planets, but when these are averaged out, the remaining century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. It turns out that 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals exactly '''10,330 Bully timestamps'''. ==== Earth's tropical year ==== The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] There are two different processes at work in '''Figure 5c'''. One process is axial precession—the slow wobble of Earth’s rotational axis. The other process is orbital eccentricity. In 1998, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was four days longer than winter because at that time Earth's aphelion was more aligned with summer and its perihelion was more aligned with winter. During aphelion Earth moves slower in its orbit, so whichever season is aligned with aphelion ends up being the longest. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] j27yadrvtqacgsmh8i4yycftk5adhjo 2823685 2823683 2026-08-20T17:23:14Z Unitfreak 695864 /* What about the Earth and Moon? */ 2823685 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} ==== Selecting a Timestamp ==== {{Blockquote|text=Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the time anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: :The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026. Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. ==== Naming the System ==== {{Blockquote|text=In the Bully timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === What about the Earth and Moon? === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This can vary by up to 20 to 25 minutes from one year to the next due to tugs from neighboring planets, but when these are averaged out, the remaining century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. It turns out that 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals exactly '''10,330 Bully timestamps'''. ==== Earth's tropical year ==== The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] There are two different processes at work in '''Figure 5c'''. One process is axial precession—the slow wobble of Earth’s rotational axis. The other process is orbital eccentricity. In 1998, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was four days longer than winter because at that time Earth's aphelion was more aligned with summer and its perihelion was more aligned with winter. During aphelion Earth moves slower in its orbit, so whichever season is aligned with aphelion ends up being the longest. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] nkhcivxjncayw4hgx5syhfak2f7pm84 2823686 2823685 2026-08-20T17:23:48Z Unitfreak 695864 /* What about the Earth and Moon? */ 2823686 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} ==== Selecting a Timestamp ==== {{Blockquote|text=Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the time anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: :The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026. Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. ==== Naming the System ==== {{Blockquote|text=In the Bully timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === The Earth and Moon? === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This can vary by up to 20 to 25 minutes from one year to the next due to tugs from neighboring planets, but when these are averaged out, the remaining century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. It turns out that 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals exactly '''10,330 Bully timestamps'''. ==== Earth's tropical year ==== The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] There are two different processes at work in '''Figure 5c'''. One process is axial precession—the slow wobble of Earth’s rotational axis. The other process is orbital eccentricity. In 1998, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was four days longer than winter because at that time Earth's aphelion was more aligned with summer and its perihelion was more aligned with winter. During aphelion Earth moves slower in its orbit, so whichever season is aligned with aphelion ends up being the longest. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] 3ym8wmz6swip4neywxzscdyyt5uui50 2823687 2823686 2026-08-20T17:24:05Z Unitfreak 695864 /* The Earth and Moon? */ 2823687 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} ==== Selecting a Timestamp ==== {{Blockquote|text=Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the time anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: :The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026. Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. ==== Naming the System ==== {{Blockquote|text=In the Bully timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === The Earth and Moon === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This can vary by up to 20 to 25 minutes from one year to the next due to tugs from neighboring planets, but when these are averaged out, the remaining century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. It turns out that 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals exactly '''10,330 Bully timestamps'''. ==== Earth's tropical year ==== The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] There are two different processes at work in '''Figure 5c'''. One process is axial precession—the slow wobble of Earth’s rotational axis. The other process is orbital eccentricity. In 1998, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was four days longer than winter because at that time Earth's aphelion was more aligned with summer and its perihelion was more aligned with winter. During aphelion Earth moves slower in its orbit, so whichever season is aligned with aphelion ends up being the longest. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] 2j71a51rfuzpruz7wv38x6ghl5qccit 2823688 2823687 2026-08-20T17:29:35Z Unitfreak 695864 /* Earth's sidereal year */ 2823688 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} ==== Selecting a Timestamp ==== {{Blockquote|text=Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the time anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: :The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026. Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. ==== Naming the System ==== {{Blockquote|text=In the Bully timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === The Earth and Moon === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This value can vary by 20 to 25 minutes from one year to the next due to gravitational tugs from neighboring planets; however, when these fluctuations are averaged out, the century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. Notably, 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals exactly '''10,330 Bully timestamps'''. ==== Earth's tropical year ==== The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] There are two different processes at work in '''Figure 5c'''. One process is axial precession—the slow wobble of Earth’s rotational axis. The other process is orbital eccentricity. In 1998, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was four days longer than winter because at that time Earth's aphelion was more aligned with summer and its perihelion was more aligned with winter. During aphelion Earth moves slower in its orbit, so whichever season is aligned with aphelion ends up being the longest. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] elb20v7r5pted7yq68jhzcimf2tkukt 2823689 2823688 2026-08-20T17:31:01Z Unitfreak 695864 /* Earth's tropical year */ 2823689 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} ==== Selecting a Timestamp ==== {{Blockquote|text=Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the time anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: :The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026. Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. ==== Naming the System ==== {{Blockquote|text=In the Bully timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === The Earth and Moon === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This value can vary by 20 to 25 minutes from one year to the next due to gravitational tugs from neighboring planets; however, when these fluctuations are averaged out, the century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. Notably, 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals exactly '''10,330 Bully timestamps'''. ==== Earth's tropical year ==== There are two different processes at work in '''Figure 5c'''. One process is axial precession—the slow wobble of Earth’s rotational axis. The other process is orbital eccentricity. In 1998, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was four days longer than winter because at that time Earth's aphelion was more aligned with summer and its perihelion was more aligned with winter. During aphelion Earth moves slower in its orbit, so whichever season is aligned with aphelion ends up being the longest. The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] mwxt4cy0drecw4p96xhp5q7siw6g9r5 2823690 2823689 2026-08-20T19:25:44Z Unitfreak 695864 /* Earth's tropical year */ 2823690 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} ==== Selecting a Timestamp ==== {{Blockquote|text=Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the time anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: :The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026. Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. ==== Naming the System ==== {{Blockquote|text=In the Bully timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === The Earth and Moon === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This value can vary by 20 to 25 minutes from one year to the next due to gravitational tugs from neighboring planets; however, when these fluctuations are averaged out, the century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. Notably, 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals exactly '''10,330 Bully timestamps'''. ==== Earth's tropical year ==== In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy between summer and winter has actually increased since 1998; it will continue to increase for the next fifteen hundred years until summer is a full 94 days long and winter is less than 89 days. There are [[W:Milankovitch_cycles|two different processes at work]] in '''Figure 5c'''. One process is axial precession—the slow wobble of Earth’s rotational axis. The other process is orbital eccentricity. The Earth does not orbit at a constant speed throughout the year. The Earth moves slower during aphelion and faster during perihelion. Therefore, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slower and takes longer to get through that season. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] As shown in '''Figure 5c''', winter was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. After that, it took approximately 5,250 years to cycle to spring being the longest, and another 5,250 years to summer. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over 21,000 years. The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] o7zb6p5w64zfx7ufd2br0ulr0tx313e 2823691 2823690 2026-08-20T19:33:42Z Unitfreak 695864 /* Earth's tropical year */ 2823691 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} ==== Selecting a Timestamp ==== {{Blockquote|text=Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the time anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: :The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026. Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. ==== Naming the System ==== {{Blockquote|text=In the Bully timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === The Earth and Moon === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This value can vary by 20 to 25 minutes from one year to the next due to gravitational tugs from neighboring planets; however, when these fluctuations are averaged out, the century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. Notably, 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals exactly '''10,330 Bully timestamps'''. ==== Earth's tropical year ==== In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy between summer and winter has actually increased since 1998; it will continue to increase for the next fifteen hundred years until summer is a full 94 days long and winter is less than 89 days. The Earth does not orbit at a constant speed throughout the year. The Earth moves slower during [[W:aphelion|aphelion]] and faster during [[W:perihelion|perihelion]]. Therefore, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slower and takes longer to get through that season. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] There are [[W:Milankovitch_cycles|two different processes at work]] in '''Figure 5c'''. One process is axial precession—the slow wobble of Earth’s rotational axis. The other process is orbital eccentricity. As shown in '''Figure 5c''', winter was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. After that, it took approximately 5,250 years to cycle to spring being the longest, and another 5,250 years to summer. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over 21,000 years. The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] ly32c2n97ubqnrqqfn4xd06cjxivvw8 2823692 2823691 2026-08-20T19:34:49Z Unitfreak 695864 /* Earth's sidereal year */ 2823692 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} ==== Selecting a Timestamp ==== {{Blockquote|text=Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the time anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: :The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026. Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. ==== Naming the System ==== {{Blockquote|text=In the Bully timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === The Earth and Moon === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This value can vary by 20 to 25 minutes from one year to the next due to gravitational tugs from neighboring planets; however, when these fluctuations are averaged out, the century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. Surprisingly, 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals exactly '''10,330 Bully timestamps'''. ==== Earth's tropical year ==== In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy between summer and winter has actually increased since 1998; it will continue to increase for the next fifteen hundred years until summer is a full 94 days long and winter is less than 89 days. The Earth does not orbit at a constant speed throughout the year. The Earth moves slower during [[W:aphelion|aphelion]] and faster during [[W:perihelion|perihelion]]. Therefore, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slower and takes longer to get through that season. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] There are [[W:Milankovitch_cycles|two different processes at work]] in '''Figure 5c'''. One process is axial precession—the slow wobble of Earth’s rotational axis. The other process is orbital eccentricity. As shown in '''Figure 5c''', winter was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. After that, it took approximately 5,250 years to cycle to spring being the longest, and another 5,250 years to summer. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over 21,000 years. The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] fckr1rw2u15su5wczbj2st863wg1f6n 2823693 2823692 2026-08-20T19:35:27Z Unitfreak 695864 /* Earth's sidereal year */ 2823693 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} ==== Selecting a Timestamp ==== {{Blockquote|text=Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the time anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: :The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026. Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. ==== Naming the System ==== {{Blockquote|text=In the Bully timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === The Earth and Moon === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This value can vary by 20 to 25 minutes from one year to the next due to gravitational tugs from neighboring planets; however, when these fluctuations are averaged out, the century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. Surprisingly, 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals '''exactly 10,330 Bully timestamps'''. ==== Earth's tropical year ==== In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy between summer and winter has actually increased since 1998; it will continue to increase for the next fifteen hundred years until summer is a full 94 days long and winter is less than 89 days. The Earth does not orbit at a constant speed throughout the year. The Earth moves slower during [[W:aphelion|aphelion]] and faster during [[W:perihelion|perihelion]]. Therefore, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slower and takes longer to get through that season. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] There are [[W:Milankovitch_cycles|two different processes at work]] in '''Figure 5c'''. One process is axial precession—the slow wobble of Earth’s rotational axis. The other process is orbital eccentricity. As shown in '''Figure 5c''', winter was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. After that, it took approximately 5,250 years to cycle to spring being the longest, and another 5,250 years to summer. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over 21,000 years. The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] kfb0oq19ninwhf3zoy99adt0xp2m5oh 2823694 2823693 2026-08-20T19:36:20Z Unitfreak 695864 /* Earth's tropical year */ 2823694 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} ==== Selecting a Timestamp ==== {{Blockquote|text=Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the time anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: :The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026. Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. ==== Naming the System ==== {{Blockquote|text=In the Bully timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === The Earth and Moon === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This value can vary by 20 to 25 minutes from one year to the next due to gravitational tugs from neighboring planets; however, when these fluctuations are averaged out, the century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. Surprisingly, 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals '''exactly 10,330 Bully timestamps'''. ==== Earth's tropical year ==== In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next fifteen hundred years until summer is a full 94 days long and winter is less than 89 days. The Earth does not orbit at a constant speed throughout the year. The Earth moves slower during [[W:aphelion|aphelion]] and faster during [[W:perihelion|perihelion]]. Therefore, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slower and takes longer to get through that season. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] There are [[W:Milankovitch_cycles|two different processes at work]] in '''Figure 5c'''. One process is axial precession—the slow wobble of Earth’s rotational axis. The other process is orbital eccentricity. As shown in '''Figure 5c''', winter was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. After that, it took approximately 5,250 years to cycle to spring being the longest, and another 5,250 years to summer. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over 21,000 years. The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] 6vv224z33ftcqmabprn4la2tz97wggj 2823695 2823694 2026-08-20T19:38:26Z Unitfreak 695864 /* Earth's tropical year */ 2823695 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} ==== Selecting a Timestamp ==== {{Blockquote|text=Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the time anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: :The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026. Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. ==== Naming the System ==== {{Blockquote|text=In the Bully timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === The Earth and Moon === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This value can vary by 20 to 25 minutes from one year to the next due to gravitational tugs from neighboring planets; however, when these fluctuations are averaged out, the century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. Surprisingly, 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals '''exactly 10,330 Bully timestamps'''. ==== Earth's tropical year ==== In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next fifteen hundred years until summer is a full 94 days long and winter is less than 89 days. The Earth does not orbit at a constant speed throughout the year. The Earth moves slower during [[W:aphelion|aphelion]] and faster during [[W:perihelion|perihelion]]. Therefore, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slower and takes longer to get through that season. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] As shown in '''Figure 5c''', winter was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. After that, it took approximately 5,250 years to cycle to spring being the longest, and another 5,250 years to summer. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over 21,000 years. There are [[W:Milankovitch_cycles|two different processes at work]] in '''Figure 5c'''. One process is axial precession—the slow wobble of Earth’s rotational axis. The other process is orbital eccentricity. The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] qxwmxng7d8n4vwjms5zmhu2hhqex2q2 2823696 2823695 2026-08-20T19:39:53Z Unitfreak 695864 /* Earth's tropical year */ 2823696 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} ==== Selecting a Timestamp ==== {{Blockquote|text=Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the time anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: :The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026. Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. ==== Naming the System ==== {{Blockquote|text=In the Bully timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === The Earth and Moon === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This value can vary by 20 to 25 minutes from one year to the next due to gravitational tugs from neighboring planets; however, when these fluctuations are averaged out, the century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. Surprisingly, 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals '''exactly 10,330 Bully timestamps'''. ==== Earth's tropical year ==== In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next fifteen hundred years until summer is a full 94 days long and winter is less than 89 days. The Earth does not orbit at a constant speed throughout the year. The Earth moves slower during [[W:aphelion|aphelion]] and faster during [[W:perihelion|perihelion]]. Therefore, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slower and takes longer to get through that season. As shown in Figure 5c, winter was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. After that, it took approximately 5,250 years to cycle to spring being the longest, and another 5,250 years to summer. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over 21,000 years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] There are [[W:Milankovitch_cycles|two different processes at work]] in '''Figure 5c'''. One process is axial precession—the slow wobble of Earth’s rotational axis. The other process is orbital eccentricity. The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] rrkt1kdeeu6w17tmt0k4blvrgq56b48 2823697 2823696 2026-08-20T20:31:48Z Unitfreak 695864 /* Earth's tropical year */ 2823697 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} ==== Selecting a Timestamp ==== {{Blockquote|text=Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the time anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: :The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026. Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. ==== Naming the System ==== {{Blockquote|text=In the Bully timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === The Earth and Moon === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This value can vary by 20 to 25 minutes from one year to the next due to gravitational tugs from neighboring planets; however, when these fluctuations are averaged out, the century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. Surprisingly, 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals '''exactly 10,330 Bully timestamps'''. ==== Earth's tropical year ==== In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next fifteen hundred years until summer is a full 94 days long and winter is less than 89 days. The Earth's orbital speed is not constant throughout the year. The Earth moves slower during [[W:aphelion|aphelion]] and faster during [[W:perihelion|perihelion]]. Therefore, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slower and takes longer to get through that season. As shown in Figure 5c, winter was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. After that, it took approximately 5,250 years to cycle to spring being the longest season, and another 5,250 years to summer. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over 21,000 years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] Currently, the Milky Way is most visible during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. The transition from spring to summer is correlated with a large green dot and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the galactic equator crossed the solstice points. A large red dot appears in 8329 CE to indicate the approximate crossing from summer to autumn, and a large blue dot, all of the way back in 4496 to 4495 BCE, indicates the crossing from winter to spring. The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] npoe213vgwbowkp4tyiapxf7m5t1mqg 2823698 2823697 2026-08-20T20:33:16Z Unitfreak 695864 /* Naming the System */ 2823698 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} ==== Selecting a Timestamp ==== {{Blockquote|text=Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the time anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: :The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026. Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. ===== Naming the System ===== {{Blockquote|text=In the Bully timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === The Earth and Moon === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This value can vary by 20 to 25 minutes from one year to the next due to gravitational tugs from neighboring planets; however, when these fluctuations are averaged out, the century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. Surprisingly, 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals '''exactly 10,330 Bully timestamps'''. ==== Earth's tropical year ==== In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next fifteen hundred years until summer is a full 94 days long and winter is less than 89 days. The Earth's orbital speed is not constant throughout the year. The Earth moves slower during [[W:aphelion|aphelion]] and faster during [[W:perihelion|perihelion]]. Therefore, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slower and takes longer to get through that season. As shown in Figure 5c, winter was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. After that, it took approximately 5,250 years to cycle to spring being the longest season, and another 5,250 years to summer. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over 21,000 years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] Currently, the Milky Way is most visible during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. The transition from spring to summer is correlated with a large green dot and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the galactic equator crossed the solstice points. A large red dot appears in 8329 CE to indicate the approximate crossing from summer to autumn, and a large blue dot, all of the way back in 4496 to 4495 BCE, indicates the crossing from winter to spring. The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] owsowa4jkmvuejdpmdfsy4rf4m4gaid 2823699 2823698 2026-08-20T20:33:56Z Unitfreak 695864 /* Selecting a Timestamp */ 2823699 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} ===== Selecting a Timestamp ===== {{Blockquote|text=Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the time anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: :The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026. Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. ===== Naming the System ===== {{Blockquote|text=In the Bully timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === The Earth and Moon === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This value can vary by 20 to 25 minutes from one year to the next due to gravitational tugs from neighboring planets; however, when these fluctuations are averaged out, the century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. Surprisingly, 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals '''exactly 10,330 Bully timestamps'''. ==== Earth's tropical year ==== In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next fifteen hundred years until summer is a full 94 days long and winter is less than 89 days. The Earth's orbital speed is not constant throughout the year. The Earth moves slower during [[W:aphelion|aphelion]] and faster during [[W:perihelion|perihelion]]. Therefore, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slower and takes longer to get through that season. As shown in Figure 5c, winter was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. After that, it took approximately 5,250 years to cycle to spring being the longest season, and another 5,250 years to summer. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over 21,000 years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] Currently, the Milky Way is most visible during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. The transition from spring to summer is correlated with a large green dot and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the galactic equator crossed the solstice points. A large red dot appears in 8329 CE to indicate the approximate crossing from summer to autumn, and a large blue dot, all of the way back in 4496 to 4495 BCE, indicates the crossing from winter to spring. The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] j57wzi5bfx4ma3ena1iqt8tslfqos0d 2823700 2823699 2026-08-20T20:34:46Z Unitfreak 695864 /* Naming the System */ 2823700 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} ===== Selecting a Timestamp ===== {{Blockquote|text=Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the time anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: :The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026. Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. ===== Naming the System ===== {{Blockquote|text=In the "Bully" timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === The Earth and Moon === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This value can vary by 20 to 25 minutes from one year to the next due to gravitational tugs from neighboring planets; however, when these fluctuations are averaged out, the century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. Surprisingly, 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals '''exactly 10,330 Bully timestamps'''. ==== Earth's tropical year ==== In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next fifteen hundred years until summer is a full 94 days long and winter is less than 89 days. The Earth's orbital speed is not constant throughout the year. The Earth moves slower during [[W:aphelion|aphelion]] and faster during [[W:perihelion|perihelion]]. Therefore, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slower and takes longer to get through that season. As shown in Figure 5c, winter was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. After that, it took approximately 5,250 years to cycle to spring being the longest season, and another 5,250 years to summer. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over 21,000 years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] Currently, the Milky Way is most visible during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. The transition from spring to summer is correlated with a large green dot and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the galactic equator crossed the solstice points. A large red dot appears in 8329 CE to indicate the approximate crossing from summer to autumn, and a large blue dot, all of the way back in 4496 to 4495 BCE, indicates the crossing from winter to spring. The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] 5dum20np4u490qnxsaq5ejsfadcg5vz 2823702 2823700 2026-08-20T20:37:06Z Unitfreak 695864 /* Earth's tropical year */ 2823702 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} ===== Selecting a Timestamp ===== {{Blockquote|text=Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the time anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: :The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026. Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. ===== Naming the System ===== {{Blockquote|text=In the "Bully" timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === The Earth and Moon === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This value can vary by 20 to 25 minutes from one year to the next due to gravitational tugs from neighboring planets; however, when these fluctuations are averaged out, the century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. Surprisingly, 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals '''exactly 10,330 Bully timestamps'''. ==== Earth's tropical year ==== In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next fifteen hundred years until summer is a full 94 days long and winter is less than 89 days. The Earth's orbital speed is not constant throughout the year. The Earth moves slower during [[W:aphelion|aphelion]] and faster during [[W:perihelion|perihelion]]. Therefore, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slower and takes longer to get through that season. As shown in Figure 5c, winter was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. After that, it took approximately 5,250 years to cycle to spring being the longest season, and another 5,250 years to summer. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over 21,000 years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] Currently, the Milky Way is most visible during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. The transition from spring to summer is correlated with a large green dot and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the galactic equator crossed the solstice points. A large red dot appears in 8329 CE to indicate the approximate crossing from summer to autumn, and a large blue dot, all of the way back in 4496 to 4495 BCE, indicates the crossing from winter to spring. ===== Selecting the Anchor Time ===== {{Blockquote|text=The Bully timestamp system is anchored to }} The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] biqicpr65szub888z3yfxj7erro3okl 2823703 2823702 2026-08-20T20:39:37Z Unitfreak 695864 /* Selecting a Timestamp */ 2823703 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} ===== Selecting a Timestamp ===== {{Cmbox | type = notice | text = 'Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the time anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see Figure 5b). }} {{Blockquote|text=Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the time anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: :The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026. Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. ===== Naming the System ===== {{Blockquote|text=In the "Bully" timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === The Earth and Moon === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This value can vary by 20 to 25 minutes from one year to the next due to gravitational tugs from neighboring planets; however, when these fluctuations are averaged out, the century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. Surprisingly, 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals '''exactly 10,330 Bully timestamps'''. ==== Earth's tropical year ==== In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next fifteen hundred years until summer is a full 94 days long and winter is less than 89 days. The Earth's orbital speed is not constant throughout the year. The Earth moves slower during [[W:aphelion|aphelion]] and faster during [[W:perihelion|perihelion]]. Therefore, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slower and takes longer to get through that season. As shown in Figure 5c, winter was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. After that, it took approximately 5,250 years to cycle to spring being the longest season, and another 5,250 years to summer. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over 21,000 years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] Currently, the Milky Way is most visible during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. The transition from spring to summer is correlated with a large green dot and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the galactic equator crossed the solstice points. A large red dot appears in 8329 CE to indicate the approximate crossing from summer to autumn, and a large blue dot, all of the way back in 4496 to 4495 BCE, indicates the crossing from winter to spring. ===== Selecting the Anchor Time ===== {{Blockquote|text=The Bully timestamp system is anchored to }} The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] 8dwb2ot1v1y4hzf573rkid1h48i9ezj 2823704 2823703 2026-08-20T20:44:23Z Unitfreak 695864 /* Selecting a Timestamp */ 2823704 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} ===== Selecting a Timestamp ===== {{Quote box| align = right| width = 250px| title = Notable Maxim| quote = 'Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the time anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see Figure 5b).| source = — Leonardo da Vinci}} {{Cmbox | type = notice | text = 'Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the time anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see Figure 5b). }} {{Blockquote|text=Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the time anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: :The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026. Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. ===== Naming the System ===== {{Blockquote|text=In the "Bully" timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === The Earth and Moon === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This value can vary by 20 to 25 minutes from one year to the next due to gravitational tugs from neighboring planets; however, when these fluctuations are averaged out, the century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. Surprisingly, 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals '''exactly 10,330 Bully timestamps'''. ==== Earth's tropical year ==== In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next fifteen hundred years until summer is a full 94 days long and winter is less than 89 days. The Earth's orbital speed is not constant throughout the year. The Earth moves slower during [[W:aphelion|aphelion]] and faster during [[W:perihelion|perihelion]]. Therefore, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slower and takes longer to get through that season. As shown in Figure 5c, winter was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. After that, it took approximately 5,250 years to cycle to spring being the longest season, and another 5,250 years to summer. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over 21,000 years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] Currently, the Milky Way is most visible during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. The transition from spring to summer is correlated with a large green dot and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the galactic equator crossed the solstice points. A large red dot appears in 8329 CE to indicate the approximate crossing from summer to autumn, and a large blue dot, all of the way back in 4496 to 4495 BCE, indicates the crossing from winter to spring. ===== Selecting the Anchor Time ===== {{Blockquote|text=The Bully timestamp system is anchored to }} The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] pmc9whfrneck84z6kiffcwv4j0io8ky 2823705 2823704 2026-08-20T20:45:06Z Unitfreak 695864 /* Selecting a Timestamp */ 2823705 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} ===== Selecting a Timestamp ===== {{Quote box| align = center| width = 250px| title = Notable Maxim| quote = 'Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the time anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see Figure 5b).| source = — Leonardo da Vinci}} {{Cmbox | type = notice | text = 'Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the time anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see Figure 5b). }} {{Blockquote|text=Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the time anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: :The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026. Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. ===== Naming the System ===== {{Blockquote|text=In the "Bully" timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === The Earth and Moon === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This value can vary by 20 to 25 minutes from one year to the next due to gravitational tugs from neighboring planets; however, when these fluctuations are averaged out, the century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. Surprisingly, 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals '''exactly 10,330 Bully timestamps'''. ==== Earth's tropical year ==== In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next fifteen hundred years until summer is a full 94 days long and winter is less than 89 days. The Earth's orbital speed is not constant throughout the year. The Earth moves slower during [[W:aphelion|aphelion]] and faster during [[W:perihelion|perihelion]]. Therefore, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slower and takes longer to get through that season. As shown in Figure 5c, winter was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. After that, it took approximately 5,250 years to cycle to spring being the longest season, and another 5,250 years to summer. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over 21,000 years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] Currently, the Milky Way is most visible during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. The transition from spring to summer is correlated with a large green dot and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the galactic equator crossed the solstice points. A large red dot appears in 8329 CE to indicate the approximate crossing from summer to autumn, and a large blue dot, all of the way back in 4496 to 4495 BCE, indicates the crossing from winter to spring. ===== Selecting the Anchor Time ===== {{Blockquote|text=The Bully timestamp system is anchored to }} The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] smwg6k582488sw4bzyztjrdddk9y309 2823707 2823705 2026-08-20T20:45:20Z Unitfreak 695864 /* Selecting a Timestamp */ 2823707 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} ===== Selecting a Timestamp ===== {{Quote box| align = center| width = full| title = Notable Maxim| quote = 'Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the time anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see Figure 5b).| source = — Leonardo da Vinci}} {{Cmbox | type = notice | text = 'Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the time anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see Figure 5b). }} {{Blockquote|text=Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the time anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: :The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026. Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. ===== Naming the System ===== {{Blockquote|text=In the "Bully" timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === The Earth and Moon === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This value can vary by 20 to 25 minutes from one year to the next due to gravitational tugs from neighboring planets; however, when these fluctuations are averaged out, the century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. Surprisingly, 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals '''exactly 10,330 Bully timestamps'''. ==== Earth's tropical year ==== In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next fifteen hundred years until summer is a full 94 days long and winter is less than 89 days. The Earth's orbital speed is not constant throughout the year. The Earth moves slower during [[W:aphelion|aphelion]] and faster during [[W:perihelion|perihelion]]. Therefore, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slower and takes longer to get through that season. As shown in Figure 5c, winter was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. After that, it took approximately 5,250 years to cycle to spring being the longest season, and another 5,250 years to summer. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over 21,000 years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] Currently, the Milky Way is most visible during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. The transition from spring to summer is correlated with a large green dot and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the galactic equator crossed the solstice points. A large red dot appears in 8329 CE to indicate the approximate crossing from summer to autumn, and a large blue dot, all of the way back in 4496 to 4495 BCE, indicates the crossing from winter to spring. ===== Selecting the Anchor Time ===== {{Blockquote|text=The Bully timestamp system is anchored to }} The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] oqyrk7sn9dy2tl8l1u5lfuy8e18lbf2 2823708 2823707 2026-08-20T20:45:48Z Unitfreak 695864 /* Selecting a Timestamp */ 2823708 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} ===== Selecting a Timestamp ===== {{Quote box| align = center| width = full| title = Notable Maxim| quote = 'Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the time anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see Figure 5b).| source = — Leonardo da Vinci}} {{Blockquote|text=Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the time anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: :The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026. Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. ===== Naming the System ===== {{Blockquote|text=In the "Bully" timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === The Earth and Moon === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This value can vary by 20 to 25 minutes from one year to the next due to gravitational tugs from neighboring planets; however, when these fluctuations are averaged out, the century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. Surprisingly, 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals '''exactly 10,330 Bully timestamps'''. ==== Earth's tropical year ==== In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next fifteen hundred years until summer is a full 94 days long and winter is less than 89 days. The Earth's orbital speed is not constant throughout the year. The Earth moves slower during [[W:aphelion|aphelion]] and faster during [[W:perihelion|perihelion]]. Therefore, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slower and takes longer to get through that season. As shown in Figure 5c, winter was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. After that, it took approximately 5,250 years to cycle to spring being the longest season, and another 5,250 years to summer. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over 21,000 years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] Currently, the Milky Way is most visible during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. The transition from spring to summer is correlated with a large green dot and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the galactic equator crossed the solstice points. A large red dot appears in 8329 CE to indicate the approximate crossing from summer to autumn, and a large blue dot, all of the way back in 4496 to 4495 BCE, indicates the crossing from winter to spring. ===== Selecting the Anchor Time ===== {{Blockquote|text=The Bully timestamp system is anchored to }} The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] nq1b0x1bsc9j6f48rysa7faab8muw5m 2823710 2823708 2026-08-20T20:46:32Z Unitfreak 695864 /* Selecting a Timestamp */ 2823710 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} {{Quote box| align = center| width = full| title = Selecting a Timestamp| quote = 'Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the time anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see Figure 5b).| source = — Leonardo da Vinci}} {{Blockquote|text=Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the time anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: :The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026. Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. ===== Naming the System ===== {{Blockquote|text=In the "Bully" timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === The Earth and Moon === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This value can vary by 20 to 25 minutes from one year to the next due to gravitational tugs from neighboring planets; however, when these fluctuations are averaged out, the century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. Surprisingly, 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals '''exactly 10,330 Bully timestamps'''. ==== Earth's tropical year ==== In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next fifteen hundred years until summer is a full 94 days long and winter is less than 89 days. The Earth's orbital speed is not constant throughout the year. The Earth moves slower during [[W:aphelion|aphelion]] and faster during [[W:perihelion|perihelion]]. Therefore, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slower and takes longer to get through that season. As shown in Figure 5c, winter was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. After that, it took approximately 5,250 years to cycle to spring being the longest season, and another 5,250 years to summer. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over 21,000 years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] Currently, the Milky Way is most visible during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. The transition from spring to summer is correlated with a large green dot and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the galactic equator crossed the solstice points. A large red dot appears in 8329 CE to indicate the approximate crossing from summer to autumn, and a large blue dot, all of the way back in 4496 to 4495 BCE, indicates the crossing from winter to spring. ===== Selecting the Anchor Time ===== {{Blockquote|text=The Bully timestamp system is anchored to }} The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] lppuguq54muphwkx06hnl8m86zmr0ax 2823713 2823710 2026-08-20T20:47:57Z Unitfreak 695864 /* A surrogate for the Sun */ 2823713 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} {{Quote box| align = center| width = full| title = Timestamp Anchor| quote = 'Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the time anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see Figure 5b).}} {{Blockquote|text=Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the time anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: :The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026. Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. ===== Naming the System ===== {{Blockquote|text=In the "Bully" timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === The Earth and Moon === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This value can vary by 20 to 25 minutes from one year to the next due to gravitational tugs from neighboring planets; however, when these fluctuations are averaged out, the century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. Surprisingly, 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals '''exactly 10,330 Bully timestamps'''. ==== Earth's tropical year ==== In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next fifteen hundred years until summer is a full 94 days long and winter is less than 89 days. The Earth's orbital speed is not constant throughout the year. The Earth moves slower during [[W:aphelion|aphelion]] and faster during [[W:perihelion|perihelion]]. Therefore, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slower and takes longer to get through that season. As shown in Figure 5c, winter was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. After that, it took approximately 5,250 years to cycle to spring being the longest season, and another 5,250 years to summer. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over 21,000 years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] Currently, the Milky Way is most visible during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. The transition from spring to summer is correlated with a large green dot and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the galactic equator crossed the solstice points. A large red dot appears in 8329 CE to indicate the approximate crossing from summer to autumn, and a large blue dot, all of the way back in 4496 to 4495 BCE, indicates the crossing from winter to spring. ===== Selecting the Anchor Time ===== {{Blockquote|text=The Bully timestamp system is anchored to }} The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] tjiu1ngddqla0gxe23pmh4a8pyweoz7 2823714 2823713 2026-08-20T20:48:40Z Unitfreak 695864 /* A surrogate for the Sun */ 2823714 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} {{Quote box| align = center| width = full| title = Timestamp Anchor| quote = 'Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the time anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: :The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026. Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. ===== Naming the System ===== {{Blockquote|text=In the "Bully" timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === The Earth and Moon === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This value can vary by 20 to 25 minutes from one year to the next due to gravitational tugs from neighboring planets; however, when these fluctuations are averaged out, the century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. Surprisingly, 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals '''exactly 10,330 Bully timestamps'''. ==== Earth's tropical year ==== In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next fifteen hundred years until summer is a full 94 days long and winter is less than 89 days. The Earth's orbital speed is not constant throughout the year. The Earth moves slower during [[W:aphelion|aphelion]] and faster during [[W:perihelion|perihelion]]. Therefore, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slower and takes longer to get through that season. As shown in Figure 5c, winter was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. After that, it took approximately 5,250 years to cycle to spring being the longest season, and another 5,250 years to summer. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over 21,000 years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] Currently, the Milky Way is most visible during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. The transition from spring to summer is correlated with a large green dot and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the galactic equator crossed the solstice points. A large red dot appears in 8329 CE to indicate the approximate crossing from summer to autumn, and a large blue dot, all of the way back in 4496 to 4495 BCE, indicates the crossing from winter to spring. ===== Selecting the Anchor Time ===== {{Blockquote|text=The Bully timestamp system is anchored to }} The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] eeed7sx8j56lq2qpwjsagm2vg144st3 2823716 2823714 2026-08-20T20:50:53Z Unitfreak 695864 /* Bullies in the Bully System */ 2823716 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} {{Quote box| align = center| width = full| title = Timestamp Anchor| quote = 'Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the time anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: {{Blockquote|text=The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}} Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. ===== Naming the System ===== {{Blockquote|text=In the "Bully" timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === The Earth and Moon === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This value can vary by 20 to 25 minutes from one year to the next due to gravitational tugs from neighboring planets; however, when these fluctuations are averaged out, the century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. Surprisingly, 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals '''exactly 10,330 Bully timestamps'''. ==== Earth's tropical year ==== In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next fifteen hundred years until summer is a full 94 days long and winter is less than 89 days. The Earth's orbital speed is not constant throughout the year. The Earth moves slower during [[W:aphelion|aphelion]] and faster during [[W:perihelion|perihelion]]. Therefore, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slower and takes longer to get through that season. As shown in Figure 5c, winter was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. After that, it took approximately 5,250 years to cycle to spring being the longest season, and another 5,250 years to summer. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over 21,000 years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] Currently, the Milky Way is most visible during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. The transition from spring to summer is correlated with a large green dot and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the galactic equator crossed the solstice points. A large red dot appears in 8329 CE to indicate the approximate crossing from summer to autumn, and a large blue dot, all of the way back in 4496 to 4495 BCE, indicates the crossing from winter to spring. ===== Selecting the Anchor Time ===== {{Blockquote|text=The Bully timestamp system is anchored to }} The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] n3ypmpjd4lb7zxgrzagx6myjzkhf9ov 2823717 2823716 2026-08-20T20:51:34Z Unitfreak 695864 /* A surrogate for the Sun */ 2823717 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} {{Quote box| align = center| width = full| title = Timestamp Anchor| quote = 'Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the time anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: {{Blockquote|text=The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}} Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. ===== Naming the System ===== {{Blockquote|text=In the "Bully" timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === The Earth and Moon === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This value can vary by 20 to 25 minutes from one year to the next due to gravitational tugs from neighboring planets; however, when these fluctuations are averaged out, the century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. Surprisingly, 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals '''exactly 10,330 Bully timestamps'''. ==== Earth's tropical year ==== In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next fifteen hundred years until summer is a full 94 days long and winter is less than 89 days. The Earth's orbital speed is not constant throughout the year. The Earth moves slower during [[W:aphelion|aphelion]] and faster during [[W:perihelion|perihelion]]. Therefore, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slower and takes longer to get through that season. As shown in Figure 5c, winter was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. After that, it took approximately 5,250 years to cycle to spring being the longest season, and another 5,250 years to summer. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over 21,000 years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] Currently, the Milky Way is most visible during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. The transition from spring to summer is correlated with a large green dot and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the galactic equator crossed the solstice points. A large red dot appears in 8329 CE to indicate the approximate crossing from summer to autumn, and a large blue dot, all of the way back in 4496 to 4495 BCE, indicates the crossing from winter to spring. ===== Selecting the Anchor Time ===== {{Blockquote|text=The Bully timestamp system is anchored to }} The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] 0lyi5qjeu79tw15elfueu74s9lx2xjn 2823718 2823717 2026-08-20T20:52:55Z Unitfreak 695864 /* Naming the System */ 2823718 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} {{Quote box| align = center| width = full| title = Timestamp Anchor| quote = 'Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the time anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: {{Blockquote|text=The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}} Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. {{Quote box| align = center| width = full| title = The "Bully" Name| quote = In the "Bully" timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === The Earth and Moon === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This value can vary by 20 to 25 minutes from one year to the next due to gravitational tugs from neighboring planets; however, when these fluctuations are averaged out, the century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. Surprisingly, 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals '''exactly 10,330 Bully timestamps'''. ==== Earth's tropical year ==== In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next fifteen hundred years until summer is a full 94 days long and winter is less than 89 days. The Earth's orbital speed is not constant throughout the year. The Earth moves slower during [[W:aphelion|aphelion]] and faster during [[W:perihelion|perihelion]]. Therefore, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slower and takes longer to get through that season. As shown in Figure 5c, winter was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. After that, it took approximately 5,250 years to cycle to spring being the longest season, and another 5,250 years to summer. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over 21,000 years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] Currently, the Milky Way is most visible during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. The transition from spring to summer is correlated with a large green dot and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the galactic equator crossed the solstice points. A large red dot appears in 8329 CE to indicate the approximate crossing from summer to autumn, and a large blue dot, all of the way back in 4496 to 4495 BCE, indicates the crossing from winter to spring. ===== Selecting the Anchor Time ===== {{Blockquote|text=The Bully timestamp system is anchored to }} The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] h6vv3ml79biptc4hg9o92y3y4st30cl 2823720 2823718 2026-08-20T20:55:41Z Unitfreak 695864 /* Selecting the Anchor Time */ 2823720 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} {{Quote box| align = center| width = full| title = Timestamp Anchor| quote = 'Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the time anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: {{Blockquote|text=The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}} Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. {{Quote box| align = center| width = full| title = The "Bully" Name| quote = In the "Bully" timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === The Earth and Moon === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This value can vary by 20 to 25 minutes from one year to the next due to gravitational tugs from neighboring planets; however, when these fluctuations are averaged out, the century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. Surprisingly, 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals '''exactly 10,330 Bully timestamps'''. ==== Earth's tropical year ==== In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next fifteen hundred years until summer is a full 94 days long and winter is less than 89 days. The Earth's orbital speed is not constant throughout the year. The Earth moves slower during [[W:aphelion|aphelion]] and faster during [[W:perihelion|perihelion]]. Therefore, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slower and takes longer to get through that season. As shown in Figure 5c, winter was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. After that, it took approximately 5,250 years to cycle to spring being the longest season, and another 5,250 years to summer. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over 21,000 years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] Currently, the Milky Way is most visible during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. The transition from spring to summer is correlated with a large green dot and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the galactic equator crossed the solstice points. A large red dot appears in 8329 CE to indicate the approximate crossing from summer to autumn, and a large blue dot, all of the way back in 4496 to 4495 BCE, indicates the crossing from winter to spring. {{Quote box| align = center| width = full| title = The "Bully" Anchor Time| quote = TBD.}} The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] 3pji05djbwd0lngptzrwzwnfsbftyw3 2823721 2823720 2026-08-20T20:57:14Z Unitfreak 695864 /* A surrogate for the Sun */ 2823721 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} {{Quote box| align = center| width = full| title = Timestamp Anchor| quote = 'Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: {{Blockquote|text=The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}} Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. {{Quote box| align = center| width = full| title = The "Bully" Name| quote = In the "Bully" timestamp system, the specific "bullies" are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === The Earth and Moon === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This value can vary by 20 to 25 minutes from one year to the next due to gravitational tugs from neighboring planets; however, when these fluctuations are averaged out, the century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. Surprisingly, 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals '''exactly 10,330 Bully timestamps'''. ==== Earth's tropical year ==== In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next fifteen hundred years until summer is a full 94 days long and winter is less than 89 days. The Earth's orbital speed is not constant throughout the year. The Earth moves slower during [[W:aphelion|aphelion]] and faster during [[W:perihelion|perihelion]]. Therefore, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slower and takes longer to get through that season. As shown in Figure 5c, winter was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. After that, it took approximately 5,250 years to cycle to spring being the longest season, and another 5,250 years to summer. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over 21,000 years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] Currently, the Milky Way is most visible during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. The transition from spring to summer is correlated with a large green dot and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the galactic equator crossed the solstice points. A large red dot appears in 8329 CE to indicate the approximate crossing from summer to autumn, and a large blue dot, all of the way back in 4496 to 4495 BCE, indicates the crossing from winter to spring. {{Quote box| align = center| width = full| title = The "Bully" Anchor Time| quote = TBD.}} The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] c5b7r1j0vl0wgw3zrujnueadxubo3oe 2823722 2823721 2026-08-20T20:58:32Z Unitfreak 695864 /* Bullies in the Bully System */ 2823722 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} {{Quote box| align = center| width = full| title = Timestamp Anchor| quote = 'Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: {{Blockquote|text=The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}} Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. {{Quote box| align = center| width = full| title = The "Bully" Name| quote = The specific "bullies" in the "Bully" timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === The Earth and Moon === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This value can vary by 20 to 25 minutes from one year to the next due to gravitational tugs from neighboring planets; however, when these fluctuations are averaged out, the century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. Surprisingly, 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals '''exactly 10,330 Bully timestamps'''. ==== Earth's tropical year ==== In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next fifteen hundred years until summer is a full 94 days long and winter is less than 89 days. The Earth's orbital speed is not constant throughout the year. The Earth moves slower during [[W:aphelion|aphelion]] and faster during [[W:perihelion|perihelion]]. Therefore, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slower and takes longer to get through that season. As shown in Figure 5c, winter was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. After that, it took approximately 5,250 years to cycle to spring being the longest season, and another 5,250 years to summer. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over 21,000 years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] Currently, the Milky Way is most visible during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. The transition from spring to summer is correlated with a large green dot and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the galactic equator crossed the solstice points. A large red dot appears in 8329 CE to indicate the approximate crossing from summer to autumn, and a large blue dot, all of the way back in 4496 to 4495 BCE, indicates the crossing from winter to spring. {{Quote box| align = center| width = full| title = The "Bully" Anchor Time| quote = TBD.}} The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] h827pj9edpc6t4ipg9rvn5e3adqautz 2823723 2823722 2026-08-20T20:59:23Z Unitfreak 695864 /* Earth's tropical year */ 2823723 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The subsequent subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} {{Quote box| align = center| width = full| title = Timestamp Anchor| quote = 'Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: {{Blockquote|text=The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}} Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. {{Quote box| align = center| width = full| title = The "Bully" Name| quote = The specific "bullies" in the "Bully" timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === The Earth and Moon === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This value can vary by 20 to 25 minutes from one year to the next due to gravitational tugs from neighboring planets; however, when these fluctuations are averaged out, the century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. Surprisingly, 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals '''exactly 10,330 Bully timestamps'''. ==== Earth's tropical year ==== In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next fifteen hundred years until summer is a full 94 days long and winter is less than 89 days. The Earth's orbital speed is not constant throughout the year. The Earth moves slower during [[W:aphelion|aphelion]] and faster during [[W:perihelion|perihelion]]. Therefore, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slower and takes longer to get through that season. As shown in Figure 5c, winter was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. After that, it took approximately 5,250 years to cycle to spring being the longest season, and another 5,250 years to summer. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over 21,000 years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] Currently, the Milky Way is most visible during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. The transition from spring to summer is correlated with a large green dot and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the galactic equator crossed the solstice points. A large red dot appears in 8329 CE to indicate the approximate crossing from summer to autumn, and a large blue dot, all of the way back in 4496 to 4495 BCE, indicates the crossing from winter to spring. {{Quote box| align = center| width = full| title = The Time Anchor| quote = TBD.}} The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] 70kshynxmnk3qcawwxysz4f9im77chg 2823725 2823723 2026-08-20T21:01:54Z Unitfreak 695864 /* Anchoring Bully Timestamps */ 2823725 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is the Bully Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} {{Quote box| align = center| width = full| title = Timestamp Anchor| quote = 'Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: {{Blockquote|text=The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}} Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. {{Quote box| align = center| width = full| title = The "Bully" Name| quote = The specific "bullies" in the "Bully" timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === The Earth and Moon === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This value can vary by 20 to 25 minutes from one year to the next due to gravitational tugs from neighboring planets; however, when these fluctuations are averaged out, the century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. Surprisingly, 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals '''exactly 10,330 Bully timestamps'''. ==== Earth's tropical year ==== In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next fifteen hundred years until summer is a full 94 days long and winter is less than 89 days. The Earth's orbital speed is not constant throughout the year. The Earth moves slower during [[W:aphelion|aphelion]] and faster during [[W:perihelion|perihelion]]. Therefore, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slower and takes longer to get through that season. As shown in Figure 5c, winter was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. After that, it took approximately 5,250 years to cycle to spring being the longest season, and another 5,250 years to summer. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over 21,000 years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] Currently, the Milky Way is most visible during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. The transition from spring to summer is correlated with a large green dot and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the galactic equator crossed the solstice points. A large red dot appears in 8329 CE to indicate the approximate crossing from summer to autumn, and a large blue dot, all of the way back in 4496 to 4495 BCE, indicates the crossing from winter to spring. {{Quote box| align = center| width = full| title = The Time Anchor| quote = TBD.}} The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] on4mlaw8ww4mmilwga8xx0bq2ldzthk 2823728 2823725 2026-08-20T21:07:04Z Unitfreak 695864 /* Is the Bully Calendar Realistic? */ 2823728 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is a Galactic Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} {{Quote box| align = center| width = full| title = Timestamp Anchor| quote = 'Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: {{Blockquote|text=The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}} Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. {{Quote box| align = center| width = full| title = The "Bully" Name| quote = The specific "bullies" in the "Bully" timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === The Earth and Moon === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This value can vary by 20 to 25 minutes from one year to the next due to gravitational tugs from neighboring planets; however, when these fluctuations are averaged out, the century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. Surprisingly, 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals '''exactly 10,330 Bully timestamps'''. ==== Earth's tropical year ==== In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next fifteen hundred years until summer is a full 94 days long and winter is less than 89 days. The Earth's orbital speed is not constant throughout the year. The Earth moves slower during [[W:aphelion|aphelion]] and faster during [[W:perihelion|perihelion]]. Therefore, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slower and takes longer to get through that season. As shown in Figure 5c, winter was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. After that, it took approximately 5,250 years to cycle to spring being the longest season, and another 5,250 years to summer. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over 21,000 years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] Currently, the Milky Way is most visible during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. The transition from spring to summer is correlated with a large green dot and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the galactic equator crossed the solstice points. A large red dot appears in 8329 CE to indicate the approximate crossing from summer to autumn, and a large blue dot, all of the way back in 4496 to 4495 BCE, indicates the crossing from winter to spring. {{Quote box| align = center| width = full| title = The Time Anchor| quote = TBD.}} The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] p1td0597kpavy36qy23qcawpbfs0tyc 2823730 2823728 2026-08-20T21:08:32Z Unitfreak 695864 /* Is the system internally consistent? */ 2823730 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is a Galactic Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the Bully system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is not exactly the same. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} {{Quote box| align = center| width = full| title = Timestamp Anchor| quote = 'Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: {{Blockquote|text=The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}} Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. {{Quote box| align = center| width = full| title = The "Bully" Name| quote = The specific "bullies" in the "Bully" timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === The Earth and Moon === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This value can vary by 20 to 25 minutes from one year to the next due to gravitational tugs from neighboring planets; however, when these fluctuations are averaged out, the century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. Surprisingly, 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals '''exactly 10,330 Bully timestamps'''. ==== Earth's tropical year ==== In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next fifteen hundred years until summer is a full 94 days long and winter is less than 89 days. The Earth's orbital speed is not constant throughout the year. The Earth moves slower during [[W:aphelion|aphelion]] and faster during [[W:perihelion|perihelion]]. Therefore, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slower and takes longer to get through that season. As shown in Figure 5c, winter was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. After that, it took approximately 5,250 years to cycle to spring being the longest season, and another 5,250 years to summer. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over 21,000 years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] Currently, the Milky Way is most visible during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. The transition from spring to summer is correlated with a large green dot and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the galactic equator crossed the solstice points. A large red dot appears in 8329 CE to indicate the approximate crossing from summer to autumn, and a large blue dot, all of the way back in 4496 to 4495 BCE, indicates the crossing from winter to spring. {{Quote box| align = center| width = full| title = The Time Anchor| quote = TBD.}} The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] l2nsp1xoqmt02kksno6tk2i5bynff67 2823732 2823730 2026-08-20T21:09:27Z Unitfreak 695864 /* Is the Bully system internally consistent? */ 2823732 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is a Galactic Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the Bully system internally consistent? ==== Earlier in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is a different orbital velocity. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} {{Quote box| align = center| width = full| title = Timestamp Anchor| quote = 'Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: {{Blockquote|text=The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}} Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. {{Quote box| align = center| width = full| title = The "Bully" Name| quote = The specific "bullies" in the "Bully" timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === The Earth and Moon === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This value can vary by 20 to 25 minutes from one year to the next due to gravitational tugs from neighboring planets; however, when these fluctuations are averaged out, the century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. Surprisingly, 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals '''exactly 10,330 Bully timestamps'''. ==== Earth's tropical year ==== In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next fifteen hundred years until summer is a full 94 days long and winter is less than 89 days. The Earth's orbital speed is not constant throughout the year. The Earth moves slower during [[W:aphelion|aphelion]] and faster during [[W:perihelion|perihelion]]. Therefore, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slower and takes longer to get through that season. As shown in Figure 5c, winter was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. After that, it took approximately 5,250 years to cycle to spring being the longest season, and another 5,250 years to summer. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over 21,000 years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] Currently, the Milky Way is most visible during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. The transition from spring to summer is correlated with a large green dot and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the galactic equator crossed the solstice points. A large red dot appears in 8329 CE to indicate the approximate crossing from summer to autumn, and a large blue dot, all of the way back in 4496 to 4495 BCE, indicates the crossing from winter to spring. {{Quote box| align = center| width = full| title = The Time Anchor| quote = TBD.}} The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] j2qg271unz0m3rg3a9yayxxiju32cn5 2823733 2823732 2026-08-20T21:09:53Z Unitfreak 695864 /* Is the Bully system internally consistent? */ 2823733 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is a Galactic Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the Bully system internally consistent? ==== Initially in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second orbital timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is a different orbital velocity. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} {{Quote box| align = center| width = full| title = Timestamp Anchor| quote = 'Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: {{Blockquote|text=The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}} Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. {{Quote box| align = center| width = full| title = The "Bully" Name| quote = The specific "bullies" in the "Bully" timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === The Earth and Moon === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This value can vary by 20 to 25 minutes from one year to the next due to gravitational tugs from neighboring planets; however, when these fluctuations are averaged out, the century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. Surprisingly, 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals '''exactly 10,330 Bully timestamps'''. ==== Earth's tropical year ==== In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next fifteen hundred years until summer is a full 94 days long and winter is less than 89 days. The Earth's orbital speed is not constant throughout the year. The Earth moves slower during [[W:aphelion|aphelion]] and faster during [[W:perihelion|perihelion]]. Therefore, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slower and takes longer to get through that season. As shown in Figure 5c, winter was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. After that, it took approximately 5,250 years to cycle to spring being the longest season, and another 5,250 years to summer. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over 21,000 years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] Currently, the Milky Way is most visible during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. The transition from spring to summer is correlated with a large green dot and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the galactic equator crossed the solstice points. A large red dot appears in 8329 CE to indicate the approximate crossing from summer to autumn, and a large blue dot, all of the way back in 4496 to 4495 BCE, indicates the crossing from winter to spring. {{Quote box| align = center| width = full| title = The Time Anchor| quote = TBD.}} The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] oyq19a60l1jcs2vrai6h1q7e4ercerq 2823734 2823733 2026-08-20T21:10:31Z Unitfreak 695864 /* Is the Bully system internally consistent? */ 2823734 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is a Galactic Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the Bully system internally consistent? ==== Initially in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per '''2 × 16¹⁰ Bully timestamps''', which is a different orbital velocity. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} {{Quote box| align = center| width = full| title = Timestamp Anchor| quote = 'Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: {{Blockquote|text=The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}} Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. {{Quote box| align = center| width = full| title = The "Bully" Name| quote = The specific "bullies" in the "Bully" timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === The Earth and Moon === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This value can vary by 20 to 25 minutes from one year to the next due to gravitational tugs from neighboring planets; however, when these fluctuations are averaged out, the century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. Surprisingly, 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals '''exactly 10,330 Bully timestamps'''. ==== Earth's tropical year ==== In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next fifteen hundred years until summer is a full 94 days long and winter is less than 89 days. The Earth's orbital speed is not constant throughout the year. The Earth moves slower during [[W:aphelion|aphelion]] and faster during [[W:perihelion|perihelion]]. Therefore, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slower and takes longer to get through that season. As shown in Figure 5c, winter was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. After that, it took approximately 5,250 years to cycle to spring being the longest season, and another 5,250 years to summer. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over 21,000 years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] Currently, the Milky Way is most visible during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. The transition from spring to summer is correlated with a large green dot and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the galactic equator crossed the solstice points. A large red dot appears in 8329 CE to indicate the approximate crossing from summer to autumn, and a large blue dot, all of the way back in 4496 to 4495 BCE, indicates the crossing from winter to spring. {{Quote box| align = center| width = full| title = The Time Anchor| quote = TBD.}} The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] 4sc3yw3kd5kn5vxvsmym7ej6hndbo4a 2823735 2823734 2026-08-20T21:11:13Z Unitfreak 695864 /* Is the Bully system internally consistent? */ 2823735 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is a Galactic Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the Bully system internally consistent? ==== Initially in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per 2 × 16¹⁰ Bully timestamps, which is a different orbital velocity. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to '''1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits''' with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} {{Quote box| align = center| width = full| title = Timestamp Anchor| quote = 'Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: {{Blockquote|text=The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}} Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. {{Quote box| align = center| width = full| title = The "Bully" Name| quote = The specific "bullies" in the "Bully" timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === The Earth and Moon === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This value can vary by 20 to 25 minutes from one year to the next due to gravitational tugs from neighboring planets; however, when these fluctuations are averaged out, the century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. Surprisingly, 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals '''exactly 10,330 Bully timestamps'''. ==== Earth's tropical year ==== In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next fifteen hundred years until summer is a full 94 days long and winter is less than 89 days. The Earth's orbital speed is not constant throughout the year. The Earth moves slower during [[W:aphelion|aphelion]] and faster during [[W:perihelion|perihelion]]. Therefore, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slower and takes longer to get through that season. As shown in Figure 5c, winter was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. After that, it took approximately 5,250 years to cycle to spring being the longest season, and another 5,250 years to summer. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over 21,000 years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] Currently, the Milky Way is most visible during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. The transition from spring to summer is correlated with a large green dot and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the galactic equator crossed the solstice points. A large red dot appears in 8329 CE to indicate the approximate crossing from summer to autumn, and a large blue dot, all of the way back in 4496 to 4495 BCE, indicates the crossing from winter to spring. {{Quote box| align = center| width = full| title = The Time Anchor| quote = TBD.}} The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] 42fg5g428hrucyok5ieektfvtd9opl5 2823736 2823735 2026-08-20T21:12:35Z Unitfreak 695864 /* Is the Bully system internally consistent? */ 2823736 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is a Galactic Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the Bully system internally consistent? ==== Initially in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per 2 × 16¹⁰ Bully timestamps, which is a different orbital velocity. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to 1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} {{Quote box| align = center| width = full| title = Timestamp Anchor| quote = 'Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: {{Blockquote|text=The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}} Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. {{Quote box| align = center| width = full| title = The "Bully" Name| quote = The specific "bullies" in the "Bully" timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === The Earth and Moon === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This value can vary by 20 to 25 minutes from one year to the next due to gravitational tugs from neighboring planets; however, when these fluctuations are averaged out, the century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. Surprisingly, 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals '''exactly 10,330 Bully timestamps'''. ==== Earth's tropical year ==== In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next fifteen hundred years until summer is a full 94 days long and winter is less than 89 days. The Earth's orbital speed is not constant throughout the year. The Earth moves slower during [[W:aphelion|aphelion]] and faster during [[W:perihelion|perihelion]]. Therefore, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slower and takes longer to get through that season. As shown in Figure 5c, winter was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. After that, it took approximately 5,250 years to cycle to spring being the longest season, and another 5,250 years to summer. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over 21,000 years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] Currently, the Milky Way is most visible during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. The transition from spring to summer is correlated with a large green dot and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the galactic equator crossed the solstice points. A large red dot appears in 8329 CE to indicate the approximate crossing from summer to autumn, and a large blue dot, all of the way back in 4496 to 4495 BCE, indicates the crossing from winter to spring. {{Quote box| align = center| width = full| title = The Time Anchor| quote = TBD.}} The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] 90wjyojuuyzlszu7a3gdjb38khr9lna 2823737 2823736 2026-08-20T21:16:23Z Unitfreak 695864 /* A surrogate for the Sun */ 2823737 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is a Galactic Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the Bully system internally consistent? ==== Initially in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per 2 × 16¹⁰ Bully timestamps, which is a different orbital velocity. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to 1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} {{Quote box| align = center| width = full| title = Timestamp Anchor| quote = Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: {{Blockquote|text=The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}} Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. {{Quote box| align = center| width = full| title = The "Bully" Name| quote = The specific "bullies" in the "Bully" timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === The Earth and Moon === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This value can vary by 20 to 25 minutes from one year to the next due to gravitational tugs from neighboring planets; however, when these fluctuations are averaged out, the century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. Surprisingly, 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals '''exactly 10,330 Bully timestamps'''. ==== Earth's tropical year ==== In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next fifteen hundred years until summer is a full 94 days long and winter is less than 89 days. The Earth's orbital speed is not constant throughout the year. The Earth moves slower during [[W:aphelion|aphelion]] and faster during [[W:perihelion|perihelion]]. Therefore, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slower and takes longer to get through that season. As shown in Figure 5c, winter was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. After that, it took approximately 5,250 years to cycle to spring being the longest season, and another 5,250 years to summer. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over 21,000 years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] Currently, the Milky Way is most visible during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. The transition from spring to summer is correlated with a large green dot and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the galactic equator crossed the solstice points. A large red dot appears in 8329 CE to indicate the approximate crossing from summer to autumn, and a large blue dot, all of the way back in 4496 to 4495 BCE, indicates the crossing from winter to spring. {{Quote box| align = center| width = full| title = The Time Anchor| quote = TBD.}} The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] q7so8n3dvt89l3f3d0u3b6khruhzs3h 2823738 2823737 2026-08-20T21:25:00Z Unitfreak 695864 /* Earth's sidereal year */ 2823738 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is a Galactic Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the Bully system internally consistent? ==== Initially in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per 2 × 16¹⁰ Bully timestamps, which is a different orbital velocity. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to 1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} {{Quote box| align = center| width = full| title = Timestamp Anchor| quote = Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: {{Blockquote|text=The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}} Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. {{Quote box| align = center| width = full| title = The "Bully" Name| quote = The specific "bullies" in the "Bully" timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === The Earth and Moon === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This value can vary by 20 to 25 minutes from one year to the next due to gravitational tugs from neighboring planets; however, when these fluctuations are averaged out, the century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. Surprisingly, 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals '''exactly 10,330 Bully timestamps'''. {{Quote box| align = center| width = full| title = Timestamp Duration| quote = * Sun orbits one Solar Radius per Bully timestamp. * Bully timestamp exact divisor of rounded Sidereal Year. }} ==== Earth's tropical year ==== In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next fifteen hundred years until summer is a full 94 days long and winter is less than 89 days. The Earth's orbital speed is not constant throughout the year. The Earth moves slower during [[W:aphelion|aphelion]] and faster during [[W:perihelion|perihelion]]. Therefore, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slower and takes longer to get through that season. As shown in Figure 5c, winter was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. After that, it took approximately 5,250 years to cycle to spring being the longest season, and another 5,250 years to summer. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over 21,000 years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] Currently, the Milky Way is most visible during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. The transition from spring to summer is correlated with a large green dot and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the galactic equator crossed the solstice points. A large red dot appears in 8329 CE to indicate the approximate crossing from summer to autumn, and a large blue dot, all of the way back in 4496 to 4495 BCE, indicates the crossing from winter to spring. {{Quote box| align = center| width = full| title = The Time Anchor| quote = TBD.}} The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] p2hu4874a2t4j6u99sqw42c82gipymp 2823739 2823738 2026-08-20T21:25:33Z Unitfreak 695864 /* Earth's sidereal year */ 2823739 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is a Galactic Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the Bully system internally consistent? ==== Initially in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per 2 × 16¹⁰ Bully timestamps, which is a different orbital velocity. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to 1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} {{Quote box| align = center| width = full| title = Timestamp Anchor| quote = Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: {{Blockquote|text=The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}} Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. {{Quote box| align = center| width = full| title = The "Bully" Name| quote = The specific "bullies" in the "Bully" timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === The Earth and Moon === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This value can vary by 20 to 25 minutes from one year to the next due to gravitational tugs from neighboring planets; however, when these fluctuations are averaged out, the century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. Surprisingly, 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals '''exactly 10,330 Bully timestamps'''. {{Quote box| align = center| width = full| title = Bully Timestamp Duration| quote = * Sun orbits one Solar Radius per Bully timestamp. * Bully timestamp exact divisor of rounded Sidereal Year. }} ==== Earth's tropical year ==== In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next fifteen hundred years until summer is a full 94 days long and winter is less than 89 days. The Earth's orbital speed is not constant throughout the year. The Earth moves slower during [[W:aphelion|aphelion]] and faster during [[W:perihelion|perihelion]]. Therefore, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slower and takes longer to get through that season. As shown in Figure 5c, winter was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. After that, it took approximately 5,250 years to cycle to spring being the longest season, and another 5,250 years to summer. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over 21,000 years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] Currently, the Milky Way is most visible during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. The transition from spring to summer is correlated with a large green dot and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the galactic equator crossed the solstice points. A large red dot appears in 8329 CE to indicate the approximate crossing from summer to autumn, and a large blue dot, all of the way back in 4496 to 4495 BCE, indicates the crossing from winter to spring. {{Quote box| align = center| width = full| title = The Time Anchor| quote = TBD.}} The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] br16qpyrn11on7b9rsoqxuohjoe83c6 2823740 2823739 2026-08-20T21:25:49Z Unitfreak 695864 /* Earth's sidereal year */ 2823740 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is a Galactic Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the Bully system internally consistent? ==== Initially in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per 2 × 16¹⁰ Bully timestamps, which is a different orbital velocity. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to 1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} {{Quote box| align = center| width = full| title = Timestamp Anchor| quote = Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: {{Blockquote|text=The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}} Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. {{Quote box| align = center| width = full| title = The "Bully" Name| quote = The specific "bullies" in the "Bully" timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === The Earth and Moon === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This value can vary by 20 to 25 minutes from one year to the next due to gravitational tugs from neighboring planets; however, when these fluctuations are averaged out, the century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. Surprisingly, 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals '''exactly 10,330 Bully timestamps'''. {{Quote box| align = center| width = full| title = Bully Timestamp Duration| quote = * Sun orbits one Solar Radius per Bully timestamp. * Bully timestamp exact divisor of rounded Sidereal Year. }} ==== Earth's tropical year ==== In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next fifteen hundred years until summer is a full 94 days long and winter is less than 89 days. The Earth's orbital speed is not constant throughout the year. The Earth moves slower during [[W:aphelion|aphelion]] and faster during [[W:perihelion|perihelion]]. Therefore, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slower and takes longer to get through that season. As shown in Figure 5c, winter was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. After that, it took approximately 5,250 years to cycle to spring being the longest season, and another 5,250 years to summer. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over 21,000 years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] Currently, the Milky Way is most visible during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. The transition from spring to summer is correlated with a large green dot and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the galactic equator crossed the solstice points. A large red dot appears in 8329 CE to indicate the approximate crossing from summer to autumn, and a large blue dot, all of the way back in 4496 to 4495 BCE, indicates the crossing from winter to spring. {{Quote box| align = center| width = full| title = The Time Anchor| quote = TBD.}} The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] hj7vnawk6es93wbn8mnphufccpd1mpu 2823741 2823740 2026-08-20T21:26:17Z Unitfreak 695864 /* Earth's sidereal year */ 2823741 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is a Galactic Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the Bully system internally consistent? ==== Initially in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per 2 × 16¹⁰ Bully timestamps, which is a different orbital velocity. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to 1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} {{Quote box| align = center| width = full| title = Timestamp Anchor| quote = Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: {{Blockquote|text=The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}} Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. {{Quote box| align = center| width = full| title = The "Bully" Name| quote = The specific "bullies" in the "Bully" timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === The Earth and Moon === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This value can vary by 20 to 25 minutes from one year to the next due to gravitational tugs from neighboring planets; however, when these fluctuations are averaged out, the century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. Surprisingly, 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals '''exactly 10,330 Bully timestamps'''. {{Quote box| align = center| width = full| title = Bully Timestamp Duration| quote =* Sun orbits one Solar Radius per Bully timestamp. * Bully timestamp exact divisor of rounded Sidereal Year. }} ==== Earth's tropical year ==== In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next fifteen hundred years until summer is a full 94 days long and winter is less than 89 days. The Earth's orbital speed is not constant throughout the year. The Earth moves slower during [[W:aphelion|aphelion]] and faster during [[W:perihelion|perihelion]]. Therefore, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slower and takes longer to get through that season. As shown in Figure 5c, winter was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. After that, it took approximately 5,250 years to cycle to spring being the longest season, and another 5,250 years to summer. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over 21,000 years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] Currently, the Milky Way is most visible during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. The transition from spring to summer is correlated with a large green dot and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the galactic equator crossed the solstice points. A large red dot appears in 8329 CE to indicate the approximate crossing from summer to autumn, and a large blue dot, all of the way back in 4496 to 4495 BCE, indicates the crossing from winter to spring. {{Quote box| align = center| width = full| title = The Time Anchor| quote = TBD.}} The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] 1ydv550jfjp420uph1t26wv8xno013b 2823742 2823741 2026-08-20T21:27:14Z Unitfreak 695864 /* Earth's sidereal year */ 2823742 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is a Galactic Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the Bully system internally consistent? ==== Initially in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per 2 × 16¹⁰ Bully timestamps, which is a different orbital velocity. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to 1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} {{Quote box| align = center| width = full| title = Timestamp Anchor| quote = Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: {{Blockquote|text=The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}} Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. {{Quote box| align = center| width = full| title = The "Bully" Name| quote = The specific "bullies" in the "Bully" timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === The Earth and Moon === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This value can vary by 20 to 25 minutes from one year to the next due to gravitational tugs from neighboring planets; however, when these fluctuations are averaged out, the century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. Surprisingly, 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals '''exactly 10,330 Bully timestamps'''. {{Quote box| align = center| width = full| title = Bully Timestamp Duration| quote = 1. The Sun orbits one Solar Radius per Bully timestamp. 2. The Bully timestamp is an exact divisor of rounded Sidereal Year. }} ==== Earth's tropical year ==== In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next fifteen hundred years until summer is a full 94 days long and winter is less than 89 days. The Earth's orbital speed is not constant throughout the year. The Earth moves slower during [[W:aphelion|aphelion]] and faster during [[W:perihelion|perihelion]]. Therefore, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slower and takes longer to get through that season. As shown in Figure 5c, winter was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. After that, it took approximately 5,250 years to cycle to spring being the longest season, and another 5,250 years to summer. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over 21,000 years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] Currently, the Milky Way is most visible during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. The transition from spring to summer is correlated with a large green dot and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the galactic equator crossed the solstice points. A large red dot appears in 8329 CE to indicate the approximate crossing from summer to autumn, and a large blue dot, all of the way back in 4496 to 4495 BCE, indicates the crossing from winter to spring. {{Quote box| align = center| width = full| title = The Time Anchor| quote = TBD.}} The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] k42mjiruv37bdgzoqhrwl8ur2sknu61 2823743 2823742 2026-08-20T21:27:30Z Unitfreak 695864 /* Earth's sidereal year */ 2823743 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is a Galactic Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the Bully system internally consistent? ==== Initially in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per 2 × 16¹⁰ Bully timestamps, which is a different orbital velocity. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to 1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} {{Quote box| align = center| width = full| title = Timestamp Anchor| quote = Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: {{Blockquote|text=The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}} Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. {{Quote box| align = center| width = full| title = The "Bully" Name| quote = The specific "bullies" in the "Bully" timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === The Earth and Moon === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This value can vary by 20 to 25 minutes from one year to the next due to gravitational tugs from neighboring planets; however, when these fluctuations are averaged out, the century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. Surprisingly, 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals '''exactly 10,330 Bully timestamps'''. {{Quote box| align = center| width = full| title = Bully Timestamp Duration| quote = 1. The Sun orbits one Solar Radius per Bully timestamp. 2. The Bully timestamp is an exact divisor of rounded Sidereal Year. }} ==== Earth's tropical year ==== In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next fifteen hundred years until summer is a full 94 days long and winter is less than 89 days. The Earth's orbital speed is not constant throughout the year. The Earth moves slower during [[W:aphelion|aphelion]] and faster during [[W:perihelion|perihelion]]. Therefore, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slower and takes longer to get through that season. As shown in Figure 5c, winter was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. After that, it took approximately 5,250 years to cycle to spring being the longest season, and another 5,250 years to summer. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over 21,000 years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] Currently, the Milky Way is most visible during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. The transition from spring to summer is correlated with a large green dot and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the galactic equator crossed the solstice points. A large red dot appears in 8329 CE to indicate the approximate crossing from summer to autumn, and a large blue dot, all of the way back in 4496 to 4495 BCE, indicates the crossing from winter to spring. {{Quote box| align = center| width = full| title = The Time Anchor| quote = TBD.}} The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] 0qzjy1dmc273wwtwn21jnz5v0ffyh62 2823744 2823743 2026-08-20T21:27:43Z Unitfreak 695864 /* Earth's sidereal year */ 2823744 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is a Galactic Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the Bully system internally consistent? ==== Initially in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per 2 × 16¹⁰ Bully timestamps, which is a different orbital velocity. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to 1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} {{Quote box| align = center| width = full| title = Timestamp Anchor| quote = Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: {{Blockquote|text=The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}} Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. {{Quote box| align = center| width = full| title = The "Bully" Name| quote = The specific "bullies" in the "Bully" timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === The Earth and Moon === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This value can vary by 20 to 25 minutes from one year to the next due to gravitational tugs from neighboring planets; however, when these fluctuations are averaged out, the century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. Surprisingly, 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals '''exactly 10,330 Bully timestamps'''. {{Quote box| align = center| width = full| title = Bully Timestamp Duration| quote = 1. The Sun orbits one Solar Radius per Bully timestamp. 2. The Bully timestamp is an exact divisor of rounded Sidereal Year. }} ==== Earth's tropical year ==== In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next fifteen hundred years until summer is a full 94 days long and winter is less than 89 days. The Earth's orbital speed is not constant throughout the year. The Earth moves slower during [[W:aphelion|aphelion]] and faster during [[W:perihelion|perihelion]]. Therefore, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slower and takes longer to get through that season. As shown in Figure 5c, winter was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. After that, it took approximately 5,250 years to cycle to spring being the longest season, and another 5,250 years to summer. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over 21,000 years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] Currently, the Milky Way is most visible during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. The transition from spring to summer is correlated with a large green dot and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the galactic equator crossed the solstice points. A large red dot appears in 8329 CE to indicate the approximate crossing from summer to autumn, and a large blue dot, all of the way back in 4496 to 4495 BCE, indicates the crossing from winter to spring. {{Quote box| align = center| width = full| title = The Time Anchor| quote = TBD.}} The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] mpuzx3dwa8xo0cl21ezpjex3s9twp6s 2823745 2823744 2026-08-20T21:30:14Z Unitfreak 695864 /* Earth's sidereal year */ 2823745 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is a Galactic Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the Bully system internally consistent? ==== Initially in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per 2 × 16¹⁰ Bully timestamps, which is a different orbital velocity. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to 1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} {{Quote box| align = center| width = full| title = Timestamp Anchor| quote = Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: {{Blockquote|text=The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}} Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. {{Quote box| align = center| width = full| title = The "Bully" Name| quote = The specific "bullies" in the "Bully" timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === The Earth and Moon === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This value can vary by 20 to 25 minutes from one year to the next due to gravitational tugs from neighboring planets; however, when these fluctuations are averaged out, the century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. Surprisingly, 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals '''exactly 10,330 Bully timestamps'''. {{Quote box| align = center| width = 100%| title = Bully Timestamp Duration | quote = {{ordered list | The Sun orbits one Solar Radius per Bully timestamp. | The Bully timestamp is an exact divisor of rounded Sidereal Year. }} }} ==== Earth's tropical year ==== In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next fifteen hundred years until summer is a full 94 days long and winter is less than 89 days. The Earth's orbital speed is not constant throughout the year. The Earth moves slower during [[W:aphelion|aphelion]] and faster during [[W:perihelion|perihelion]]. Therefore, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slower and takes longer to get through that season. As shown in Figure 5c, winter was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. After that, it took approximately 5,250 years to cycle to spring being the longest season, and another 5,250 years to summer. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over 21,000 years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] Currently, the Milky Way is most visible during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. The transition from spring to summer is correlated with a large green dot and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the galactic equator crossed the solstice points. A large red dot appears in 8329 CE to indicate the approximate crossing from summer to autumn, and a large blue dot, all of the way back in 4496 to 4495 BCE, indicates the crossing from winter to spring. {{Quote box| align = center| width = full| title = The Time Anchor| quote = TBD.}} The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] ii2o9xx0a6ehvlxg0aajl3pm5le8omb 2823746 2823745 2026-08-20T21:30:39Z Unitfreak 695864 /* Earth's sidereal year */ 2823746 wikitext text/x-wiki <small>[[Bully_Metric|Bully Metric Main Page]]<br /> [[Bully_Metric_Timestamps|Bully Metric Timestamps Main Page]]<br /> [https://unitfreak.github.io/Bully-Row-Timestamps/Java_Bully.html Current Bully Timestamp (GitHub)]<br /> </small> The '''Bully Metric Timestamp''' system is an alternative timekeeping framework that utilizes the orbit of the Sun around the Milky Way Galaxy to mark the passage of time. A new successive Bully timestamp is realized each time the Sun advances by approximately one solar radius along its path through the Cosmos. Using '''12-digit''' [[w:hexadecimal|hexadecimal]] timestamps, the Bully system has enough unique identifiers to span the entire history of the universe—from the Big Bang into the far-distant future. The total capacity of the system is: &thinsp; :<math>16^{12} \times 3,055 \text{ sec} \approx 27.25 \text{ billion years}</math> == One Solar Radius == [[File:Bully_Metric_Galactic_Orbit_1_Timestamp.png|thumb|right|450px|alt=Diagram showing the Sun advancing a distance equal to its own radius along its galactic trajectory over a period of 3055 seconds.|'''Figure 1:''' Motion of the Sun between two successive Bully timestamps.]] The Sun orbits the center of the Milky Way galaxy at a very fast speed, roughly 227.7 kilometers per second (km/s), which equals approximately 0.076% of the speed of light. Even though the Sun is moving very quickly, it is also physically immense. The radius of the Sun (<math>R_\odot</math>) is 695,700 kilometers. Dividing the solar radius by the galactic orbital velocity, we find that it takes approximately 3,055 seconds (about five-sixths of an hour) for the Sun to travel a distance equal to its own radius: &thinsp; :<math>\Delta t = \frac{695,700 \text{ km}}{227.7 \text{ km/s}} \approx 3055 \text{ seconds}</math> &thinsp; '''Figure 1''' illustrates the physical movement of the Sun between two successive Bully timestamps. Timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI (International Atomic Time) on June 21, 1998'''. The sequential timestamp, '''8209 ED00 0001''', occurred exactly 3,055 seconds later at '''12:50:55 TAI on June 21, 1998'''. As shown in Figure 1, the Sun orbited a distance of roughly one solar radius during this 3,055-second period. === The Heliosphere === The heliosphere, it turns out, is not actually a sphere. As shown in '''Figure 2''', the heliosphere is a vast, oblong, tailed, bubble-like region that extends from the Sun into the surrounding space. The heliosphere is somewhat analogous to Earth's atmosphere, except that Earth's atmosphere is a comparatively thin layer of gas that remains near the Earth's surface. By comparison, the heliosphere is a plasma that is constantly blasted out into space due to the extreme heat and energy of the Sun. [[File:Bully_Metric_Galactic_Orbit_65536_Timestamps.png|thumb|right|450px|alt=Diagram showing the Sun traveling through the oblong shape of the heliosphere over a span of 16 to the 4th power timestamps.|'''Figure 2:''' Motion of the Sun during the passage of 16⁴ Bully timestamps.]] The heliosphere is very large. It is so vast that if it were truly spherical, its diameter would be on an order of magnitude similar to '''16⁴ (65,536) solar radii'''. The digit in the '''fifth position''' in a Bully timestamp represents the time required for the Sun to orbit for '''6.344 years''', which covers a distance of approximately '''65,536 solar radii''', or roughly the diameter of one spherical heliosphere. Figure 2 illustrates the orbit of the Sun (Sun not drawn to scale) over a period of 6.344 years. As explained previously, timestamp '''8209 ED00 0000''' is defined to have occurred at exactly '''12:00:00 TAI on June 21, 1998'''. Timestamp '''8209 ED01 0000''' therefore occurred roughly 6.344 years later at '''18:34:40 TAI on October 24, 2004'''. Incidentally, the Voyager 1 spacecraft crossed into the heliosheath, as shown in Figure 2, on December 16th 2004. Both Voyager spacecraft (Voyager 1 and Voyager 2) have since crossed entirely out of the heliosphere and entered the surrounding interstellar space. === Naked Eye Stars === '''Figure 3a''' illustrates the physical movement of the Sun (Sun not drawn to scale) between 16⁸ successive Bully timestamps. It is estimated that timestamp '''8209 0000 0000''' would have occurred roughly 383,000 B.C., and timestamp '''820A 0000 0000''' is estimated to occur around 33,000 A.D., for a total time lapse of '''416,000 years'''. The stacked histogram in Figure 3a has a red dashed line marking 96.83 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy and 96.83 parsecs is the distance the sun travels in 16⁸ Bully timestamps. As indicated in the histogram, a large percentage of naked-eye stars are nearer to the sun than 96.83 parsecs, meaning that the appearance of the night sky completely changes over this timeframe. [[File:Bully_Metric_Galactic_Orbit_4294967296_Timestamps.png|thumb|center|600px|alt=Diagram showing a stacked histogram of "Naked Eye" stars binned according to brightness and distance from the sun. A large percentage of these stars are closer to the sun than 16^8 R_☉, which is the distance that the sun travels in 16^8 Bully timestamps.|'''Figure 3a:''' Motion of the Sun during the passage of 16⁸ Bully timestamps. The included stacked histogram shows that a large percentage of "Naked Eye" stars are within this travel distance of the sun, 96.83 parsecs or 16⁸ ''R''_☉.]] [[Bully_Metric_Naked-Eye_Stars|Learn More About the Meaning of Naked-Eye Stars]] == The Galactic Calendar == [[W:Andrea Ghez|Andrea Ghez]] and [[W:Reinhard Genzel|Reinhard Genzel]] were jointly awarded one-half of the 2020 Nobel Prize in Physics for their discovery of a supermassive compact object—now universally known as the black hole Sagittarius A*—at the center of the Milky Way. Using the world’s largest telescopes, both teams observed stars whipping around an invisible, incredibly heavy mass at extreme speeds. One star, called S2, completes an orbit in just 16 years. Their calculations revealed that an entity of roughly 4 million solar masses is packed into an area no larger than our solar system, offering definitive evidence of a supermassive black hole. By meticulously mapping the complete 3D elliptical orbits of stars over decades, Reinhard Genzel's research team calculated the exact distance to the Galactic Center to an unprecedented degree of accuracy. They narrowed the measurement down to an extremely precise [https://www.mpe.mpg.de/6588951/The-black-hole 8,275 parsecs] (or 26,990 light-years), with a margin of error of less than 1%. If the Sun were assumed to follow a perfectly circular orbit around Sagittarius A*, with a constant radial distance of 8,275 parsecs, the total circumference of that ideal orbit would be determined by multiplying the radius by 2π: :<math>\begin{align} {\text{Circumference}} &= 2\pi \times 8,275{\text{ parsecs}} \\ &\approx 51,993{\text{ parsecs}} \end{align}</math> If we divide this '''roughly 52,000-parsec''' idealized orbit into "Galactic Weeks", where each week represents 1,000 parsecs of orbital travel, then a full Galactic Year would consist of 52 weeks. This beautifully mirrors the structure of an Earth year, which is also composed of roughly 52 weeks. === Idealized Galactic Years === Within the context of Bully timekeeping, an idealized '''Bully Galactic Year''' is defined to have a duration of exactly '''2 × 16¹⁰ Bully timestamps''' (approximately 213 million years), and the Sun is assumed to follow an orbital path of exactly 52,000 parsecs. The table in '''Figure 4a''' illustrates the division of an idealized Galactic Year into 52 equal portions. The table shows the Bully timestamp at which each 1,000 parsecs of travel distance would be achieved in this idealized orbit. {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; width:100%; max-width:800px;" |+ '''Figure 4a:''' The 66th Bully Galactic Calendar |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|1st Quarter}} || {{nowrap|2nd Quarter}} || {{nowrap|3rd Quarter}} || {{nowrap|4th Quarter}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 0}} || {{color|blue|''0 parsecs''}} <br/>'''{{nowrap|8200 0000 0000}}''' || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|8280 0000 0000}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|8300 0000 0000}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|8380 0000 0000}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 1}} || {{color|blue|''1000 parsecs''}} <br/> '''{{nowrap|8209 D89D 89D8}}''' || {{color|blue|''14,000 parsecs''}} <br/> '''{{nowrap|8289 D89D 89D8}}''' || {{color|blue|''27,000 parsecs''}} <br/> '''{{nowrap|8309 D89D 89D8}}''' || {{color|blue|''40,000 parsecs''}} <br/> '''{{nowrap|8389 D89D 89D8}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 2}} || {{color|blue|''2,000 parsecs''}} <br/> '''{{nowrap|8213 B13B 13B1}}''' || {{color|blue|''15,000 parsecs''}} <br/> '''{{nowrap|8293 B13B 13B1}}''' || {{color|blue|''28,000 parsecs''}} <br/> '''{{nowrap|8313 B13B 13B1}}''' || {{color|blue|''41,000 parsecs''}} <br/> '''{{nowrap|8393 B13B 13B1}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 3}} || {{color|blue|''3,000 parsecs''}} <br/> '''{{nowrap|821D 89D8 9D89}}''' || {{color|blue|''16,000 parsecs''}} <br/> '''{{nowrap|829D 89D8 9D89}}''' || {{color|blue|''29,000 parsecs''}} <br/> '''{{nowrap|831D 89D8 9D89}}''' || {{color|blue|''42,000 parsecs''}} <br/> '''{{nowrap|839D 89D8 9D89}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 4}} || {{color|blue|''4,000 parsecs''}} <br/> '''{{nowrap|8227 6276 2762}}''' || {{color|blue|''17,000 parsecs''}} <br/> '''{{nowrap|82A7 6276 2762}}''' || {{color|blue|''30,000 parsecs''}} <br/> '''{{nowrap|8327 6276 2762}}''' || {{color|blue|''43,000 parsecs''}} <br/> '''{{nowrap|83A7 6276 2762}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 5}} || {{color|blue|''5,000 parsecs''}} <br/> '''{{nowrap|8231 3B13 B13B}}''' || {{color|blue|''18,000 parsecs''}} <br/> '''{{nowrap|82B1 3B13 B13B}}''' || {{color|blue|''31,000 parsecs''}} <br/> '''{{nowrap|8331 3B13 B13B}}''' || {{color|blue|''44,000 parsecs''}} <br/> '''{{nowrap|83B1 3B13 B13B}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 6}} || {{color|blue|''6,000 parsecs''}} <br/> '''{{nowrap|823B 13B1 3B13}}''' || {{color|blue|''19,000 parsecs''}} <br/> '''{{nowrap|82BB 13B1 3B13}}''' || {{color|blue|''32,000 parsecs''}} <br/> '''{{nowrap|833B 13B1 3B13}}''' || {{color|blue|''45,000 parsecs''}} <br/> '''{{nowrap|83BB 13B1 3B13}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 7}} || {{color|blue|''7,000 parsecs''}} <br/> '''{{nowrap|8244 EC4E C4EC}}''' || {{color|blue|''20,000 parsecs''}} <br/> '''{{nowrap|82C4 EC4E C4EC}}''' || {{color|blue|''33,000 parsecs''}} <br/> '''{{nowrap|8344 EC4E C4EC}}''' || {{color|blue|''46,000 parsecs''}} <br/> '''{{nowrap|83C4 EC4E C4EC}}''' |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 8}} || {{color|blue|''8,000 parsecs''}} <br/> '''{{nowrap|824E C4EC 4EC4}}''' || {{color|blue|''21,000 parsecs''}} <br/> '''{{nowrap|82CE C4EC 4EC4}}''' || {{color|blue|''34,000 parsecs''}} <br/> '''{{nowrap|834E C4EC 4EC4}}''' || {{color|blue|''47,000 parsecs''}} <br/> '''{{nowrap|83CE C4EC 4EC4}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 9}} || {{color|blue|''9,000 parsecs''}} <br/> '''{{nowrap|8258 9D89 D89D}}''' || {{color|blue|''22,000 parsecs''}} <br/> '''{{nowrap|82D8 9D89 D89D}}''' || {{color|blue|''35,000 parsecs''}} <br/> '''{{nowrap|8358 9D89 D89D}}''' || {{color|blue|''48,000 parsecs''}} <br/> '''{{nowrap|83D8 9D89 D89D}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 10}} || {{color|blue|''10,000 parsecs''}} <br/> '''{{nowrap|8262 7627 6276}}''' || {{color|blue|''23,000 parsecs''}} <br/> '''{{nowrap|82E2 7627 6276}}''' || {{color|blue|''36,000 parsecs''}} <br/> '''{{nowrap|8362 7627 6276}}''' || {{color|blue|''49,000 parsecs''}} <br/> '''{{nowrap|83E2 7627 6276}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 11}} || {{color|blue|''11,000 parsecs''}} <br/> '''{{nowrap|826C 4EC4 EC4E}}''' || {{color|blue|''24,000 parsecs''}} <br/> '''{{nowrap|82EC 4EC4 EC4E}}''' || {{color|blue|''37,000 parsecs''}} <br/> '''{{nowrap|836C 4EC4 EC4E}}''' || {{color|blue|''50,000 parsecs''}} <br/> '''{{nowrap|83EC 4EC4 EC4E}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|Week 12}} || {{color|blue|''12,000 parsecs''}} <br/> '''{{nowrap|8276 2762 7627}}''' || {{color|blue|''25,000 parsecs''}} <br/> '''{{nowrap|82F6 2762 7627}}''' || {{color|blue|''38,000 parsecs''}} <br/> '''{{nowrap|8376 2762 7627}}''' || {{color|blue|''51,000 parsecs''}} <br/> '''{{nowrap|83F6 2762 7627}}''' |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | End of Quarter || {{color|blue|''13,000 parsecs''}} <br/> '''{{nowrap|827F FFFF FFFF}}''' || {{color|blue|''26,000 parsecs''}} <br/> '''{{nowrap|82FF FFFF FFFF}}''' || {{color|blue|''39,000 parsecs''}} <br/> '''{{nowrap|837F FFFF FFFF}}''' || {{color|blue|''52,000 parsecs''}} <br/> '''{{nowrap|83FF FFFF FFFF}}''' |} Timestamps in the range '''8200 0000 0000''' through '''83FF FFFF FFFF''' indicate that the system is recording time within the '''66th Bully Galactic Year''' of the Universe. However, the Sun (and our solar system) did not come into existence until the 45th Bully Galactic Year, meaning our solar system is only '''21 Bully Galactic Years old'''. ==== Is a Galactic Calendar Realistic? ==== [[File:Sun_in_orbit_around_Galactic_Centre.gif|thumb|right|300px|alt=Diagram showing multiple stars moving along their respective orbital paths around the Galactic Center over a span of 250 million years.|'''Figure 4b:''' Stars orbiting around the Galactic Center during a 250 million-year time period.]] The duration of time required for the Sun (or any other star) to orbit once around the center of the Milky Way Galaxy is not a fixed constant, but rather depends on the path a particular star follows as it orbits (see Figure 4b). Stars closer to the center orbit much more quickly than those on the outer edges. The stars shown in '''Figure 4b''' all eventually localize near the Sun despite having vastly different orbital trajectories, visually illustrating the long-term subtlety of galactic orbits. Because the Sun’s deep-time trajectory is slightly chaotic and unpredictable, an operational offset will always exist between the passage of Bully time and physical observations of the Sun's galactic displacement. Therefore, while the table in '''Figure 4a''' states that one week ('''{{nowrap|8209 D89D 89D8}}''') corresponds to 1,000 parsecs of displacement, this relationship must be understood as an estimate. In practice, even if the system were calibrated so that timestamp '''{{nowrap|8209 D89D 89D8}}''' perfectly aligned with the exact moment the Sun traveled 1,000 parsecs, this precise alignment would immediately begin to decay. The subsequent milestone at timestamp '''{{nowrap|8213 B13B 13B1}}''' would almost certainly not occur at the exact instant the Sun reached the 2,000-parsec mark. ==== Is the Bully system internally consistent? ==== Initially in this resource, the Sun was assumed to travel roughly one solar radius per 3,055-second timestamp. However, the Bully Galactic Calendar assumes exactly 52,000 parsecs of orbital travel per 2 × 16¹⁰ Bully timestamps, which is a different orbital velocity. Since the long-term orbital dynamics of the Sun are subject to gravitational perturbations, standard stellar movement is not perfectly uniform or predictive. The Sun's true orbital velocity will always be a topic of ongoing discovery and refinement. The previous conjectured value of '''1 ''R''_☉ per Bully timestamp was just a useful assumption''' and not a reflection of a long-term stable physical reality. Similarly, the idealized Bully Calendar velocity of 52,000 parsecs per 2 × 16¹⁰ Bully timestamps is a useful assumption to help visualize and conceptualize the Sun's orbit. The table in '''Figure 4c''' illustrates how scaling the assumed baseline velocity from 1 ''R''_☉ per Bully timestamp up to 1.0488227 ''R''_☉ per Bully timestamp aligns the highest digits with rounded integer multiples of the parsec length. {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4c: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1 ''R''_☉ per Bully timestamp </small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance in parsecs assuming 1.0488227 ''R''_☉ per Bully timestamp </small> |- | 8 | style="text-align: left; padding: 8px;" | '''16¹¹''' | 396,635 | 416,000 |- | 1 / 2 | style="text-align: left; padding: 8px;" | '''16¹⁰''' | 24,789.7 | 26,000.0 |- | 1 / 32 | style="text-align: left; padding: 8px;" | '''16⁹''' | 1,549.36 | 1,625.00 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | 1 | style="text-align: left; padding: 8px;" | '''2 × 16¹⁰''' | style="color: #888;" | N/A | 52,000 |- | 1 / 52 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26''' | style="color: #888;" | N/A | 1,000 |- | 1 / 52,000 | style="text-align: left; padding: 8px;" | '''16¹⁰ / 26,000''' | style="color: #888;" | N/A | 1 |} == Anchoring Bully Timestamps == To establish a rigid temporal framework, the Bully system is anchored by selecting timestamp '''{{nowrap|8209 ED00 0000}}''' to coincide precisely with '''12:00:00 TAI on June 21, 1998'''. Following this initial anchoring, the progression of all subsequent Bully timestamps is maintained uniformly via terrestrial atomic clocks, advancing by exactly one unit every '''3,055 TAI seconds'''. The following subsections will explain why timestamp '''{{nowrap|8209 ED00 0000}}''' was selected and anchored to the '''June solstice in 1998'''. === The Galactic Ecliptic Node near Sagittarius === '''Figure 5a''' depicts the 6.98-degree angular separation that exists between Sagittarius A* (the supermassive black hole at the center of the Milky Way) and the descending node of our Solar System’s [[W:Invariable_plane|Laplace invariable plane]] where it intersects the Galactic equator. [[File:Sagittarius_A*_and_adjacent_Galactic_Ecliptic_Node.png|thumb|center|600px|alt=An educational image illustrating the 6.98-degree separation between Sagittarius A* and the adjacent Galactic Ecliptic Node. The Node, moving in concert with the Sun, shifts away from Sagittarius A* at a rate of 2.70 mas per year in right ascension and 5.60 mas per year in declination.|'''Figure 5a:''' A diagram showing the 6.98-degree angular separation between Sagittarius A* and the descending node of the Solar System's Laplace invariable plane.]] As the Sun orbits the Galactic Center, the galactic ecliptic node of the Solar System's invariable plane—moving in concert with the Sun—shifts away from Sagittarius A* at a rate of 2.70 mas (milliarcseconds) per year in right ascension and 5.60 mas per year in declination. From the perspective of the Sun, the node appears to be stationary, and the supermassive black hole appears to be moving in the opposite direction. In reality, it is the Solar System and the node that are moving. ==== A surrogate for the Sun ==== The path of the Solar System's galactic ecliptic node as it shifts away from Sagittarius A* can be used as a surrogate to track the motion of the Sun. The node is currently located 6.9803° away from Sagittarius A*. The Sun's orbital travel distance is calculated by multiplying 6.9803° by the orbital radius (8,275 parsecs) and the ratio of radians to degrees (2π / 360°): <math> \begin{aligned} d &= 8,275 \text{ pc} \times 6.9803^\circ \times \left(\frac{2\pi}{360^\circ}\right) \\ &\approx 1,008.14 \text{ pc} \end{aligned} </math> Based on this calculation, the galactic ecliptic node—and by extension, the Sun—has traveled 1,008.14 parsecs in its orbit around the Galactic Center. According to the reference table in '''Figure 4a''', this 1,008.14-parsec distance falls beyond the 1,000-parsec milestone associated with timestamp '''{{nowrap|8209 D89D 89D8}}''', indicating that we have completed the zeroth week of the 66th Bully Galactic Year. To pinpoint a more exact location, the table in '''Figure 5b''' provides a finer-grained increment. Our Sun's 1,008.14-parsec travel distance is larger than the '''1,007.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 ECC7 C23E}}''', but it is smaller than the '''1,008.87 parsecs''' corresponding with timestamp '''{{nowrap|8209 EF4D 0949}}'''. (Note: Figure 4a assumes an idealized travel distance of 52,000 parsecs per Bully Galactic Year, whereas Figure 5b uses the calculated distance of 51,993 parsecs per Bully Galactic Year.) {| class="wikitable" style="margin: 20px auto 40px auto; text-align:center; max-width:300px;" |+ '''Figure 5b:''' Week one, 66th Galactic Year |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Year 66 <br /> Galactic || {{nowrap|Bully timestamp}} || Solar Distance Traveled |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|One Week}} ||'''{{nowrap|8209 D89D 89D8}}''' || {{nowrap|{{color|blue|''999.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.007 Weeks}} ||'''{{nowrap|8209 EA42 7B31}}''' || {{nowrap|{{color|blue|''1006.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.008 Weeks}} ||'''{{nowrap|8209 ECC7 C23E}}''' || {{nowrap|{{color|blue|''1007.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.009 Weeks}} ||'''{{nowrap|8209 EF4D 0949}}''' || {{nowrap|{{color|blue|''1008.87 parsecs''}}}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|1.010 Weeks}} ||'''{{nowrap|8209 F1D2 5056}}''' || {{nowrap|{{color|blue|''1009.87 parsecs''}}}} |} {{Quote box| align = center| width = full| title = Timestamp Anchor| quote = Bully timestamp '''{{nowrap|8209 ED00 0000}}''' was selected to be the timestamp anchor of the entire Bully system because it closely aligns with the 1,008.14-parsec orbital travel distance of the Sun (see table in Figure 5b).}} === Bullies in the Bully System === A planetary system's Laplace invariable plane passes through its barycenter (center of mass) and is strictly perpendicular to its total angular momentum vector. In our Solar System, the four giant planets account for 98% of this total angular momentum: Jupiter contributes the bulk at 60.3%, followed by Saturn (24.5%), Neptune (7.9%), and Uranus (5.3%). The individual descending nodes of each giant planet's ecliptic where they intersect the galactic equator are shown in '''Figure 5a''': * '''Invariable Plane Node (+)''': Marked with a large plus sign. * '''Jupiter (♃)''': Positioned slightly to the right of the invariable plane's node. * '''Uranus (⛢)''': Positioned to the right of Jupiter. * '''Saturn (♄)''': Positioned on the inner left. * '''Neptune (♆)''': Positioned on the far left. As noted in the Merriam-Webster dictionary, the word "bully" had a positive connotation through much of history: {{Blockquote|text=The earliest meaning of English bully was 'sweetheart'. The word was probably borrowed from Dutch boel, 'lover'. Later bully was used for anyone who seemed a good fellow, then for a blustering daredevil. Today, a bully is usually one whose claims to strength and courage are based on the intimidation of those who are weaker.“Bully.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/bully. Accessed 19 Aug. 2026.}} Large astronomical objects—such as Sagittarius A*, the Sun, and giant planets like Jupiter and Saturn—can be thought of as bullies, both in the historical meaning of "excellent" or "beautiful" and in the modern meaning of being intimidating and threatening. {{Quote box| align = center| width = full| title = The "Bully" Name| quote = The specific "bullies" in the "Bully" timestamp system are [[w:Sagittarius A*|Sagittarius A*]], the [[w:Sun|Sun]], and the Solar System's [[w:Giant planet|giant planets]].}} === The Earth and Moon === The motions of the Earth and Moon are not suitable for precise, long-term time measurement due to deep time gravitational interactions. For example, tidal friction gradually slows the Earth's rotation and causes the Moon to drift farther away, making legacy day and month units unstable over millions of years. While the Bully timestamp system is not directly anchored to the motions of the Earth and Moon, it was developed with these motions in mind and incorporates a few of their unique characteristics. ==== Earth's sidereal year ==== The exact length of Earth's sidereal year is currently calculated to be '''31,558,149.76 seconds'''. This value can vary by 20 to 25 minutes from one year to the next due to gravitational tugs from neighboring planets; however, when these fluctuations are averaged out, the century-over-century lengthening is a mere 9.6 milliseconds. Given the relative stability and significance of Earth's sidereal year, there is utility in using a divisor of this year as the fundamental unit of the Bully timestamp system. Surprisingly, 3,055 seconds is an exact divisor of 31,558,150 seconds. Hence, Earth's sidereal year, rounded to the nearest second, equals '''exactly 10,330 Bully timestamps'''. {{Quote box| align = center| width = 100%| title = Bully Timestamp Duration | quote = {{ordered list | The Sun orbits one Solar Radius per Bully timestamp. | The Bully timestamp is an exact divisor of a rounded Sidereal Year. }} }} ==== Earth's tropical year ==== In 1998 in the Northern Hemisphere, winter lasted 89 days, spring lasted 92 days and 18 hours, summer lasted 93 days and 15 hours, and autumn lasted 89 days and 21 hours. Summer was nearly five days longer than winter that year. As shown in '''Figure 5c''', this duration discrepancy will continue to increase for the next fifteen hundred years until summer is a full 94 days long and winter is less than 89 days. The Earth's orbital speed is not constant throughout the year. The Earth moves slower during [[W:aphelion|aphelion]] and faster during [[W:perihelion|perihelion]]. Therefore, whichever season is aligned with aphelion ends up being the longest because the Earth is moving slower and takes longer to get through that season. As shown in Figure 5c, winter was the longest season in the Northern Hemisphere (aligned with aphelion) back before 5,000 BCE. After that, it took approximately 5,250 years to cycle to spring being the longest season, and another 5,250 years to summer. While it is just beyond the range of the graph, it is clear that all four seasons will complete a full cycle once in a little over 21,000 years. [[File:TBD_Place_Holder.png|thumb|center|600px|alt=TBD.|'''Figure 5c: '''How the lengths of Earth's seasons, and the season with best Milky Way visibility, shifts over time.]] Currently, the Milky Way is most visible during Northern Hemisphere summer months (which are winter months in the Southern Hemisphere). Going back in time prior to 1998, there was an era when the Milky Way would have been more visible during spring months in the north. Going even further back, the Milky Way would have been best viewed in northern winter (or southern summer). These seasonal shifts in Milky Way visibility are correlated with large dots in Figure 5c. The transition from spring to summer is correlated with a large green dot and a green banner indicating that astronomer Jean Meeus identified May 1998 CE as the precise moment when the galactic equator crossed the solstice points. A large red dot appears in 8329 CE to indicate the approximate crossing from summer to autumn, and a large blue dot, all of the way back in 4496 to 4495 BCE, indicates the crossing from winter to spring. {{Quote box| align = center| width = full| title = The Time Anchor| quote = TBD.}} The Earth's tropical year, which measures the complete cycle of the seasons from one vernal equinox to the next, lasts '''31,556,925.2 seconds'''. Due to axial precession the tropical year is roughly 1,224 seconds shorter than the sidereal year. The difference between the sidereal and tropical year lengths is roughly 2/5 of a Bully timestamp. So the time required for 25,825 tropical years is roughly equivalent to 25,824 sidereal years. ==== The Metonic cycle ==== The '''Metonic cycle''' is a period of approximately 19 solar years, after which the moon's phases recur on the same days of the year. For example, a New Moon occurred on July 23 in 1998, and nineteen years later, in 2017, a New Moon again occurred on July 23. The last four hex digits of the Bully timestamp cycle approximately three times per Metonic cycle as illustrated in the following list: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> July 23 New Moon Metonic Cycles * July 23, 1998 on 8209 ED0'''0 038B''' * July 23, 2017 on 8209 ED0'''3 0238''' * July 23, 2036 on 8209 ED0'''6 00EA''' </div> [[Bully_Metric_Metonic_cycle|Learn More About the Metonic Cycle in Bully Timestamps]] ==== The Bully Mnemonic ==== <math display="block"> {1 \, Sidereal \, Year} = {31,558,150 \, Seconds} </math> <math display="block"> {1 \, Tropical \, Year} = {31,556,926 \, Seconds} </math> <math display="block"> 1 \, Great \, Year \approx 25,824 \, Sidereal \, Years \approx 25,825 \, Tropical \, Years </math> <math display="block">{1 \, Galactic \, Year} \approx 8264 \, Great \, Year \approx 213,417,800 \, Tropical \, Years </math> The '''Bully Mnemonic''' is a technique for remembering the exact number of seconds that occur in Earth's [https://en.wikipedia.org/wiki/Sidereal_year sidereal year] and [https://en.wikipedia.org/wiki/Tropical_year tropical year], a good approximation of the Earth's [https://en.wikipedia.org/wiki/Great_Year Great Year], and a rough approximation of the Solar System's [https://en.wikipedia.org/wiki/Galactic_year galactic year]. Click on the following link to learn more about the Bully Mnemonic and the role it plays in the mathematical foundation of Bully timestamps. * [[Bully Mnemonic |Learn More About The Bully Mnemonic]] * [[Bully Mnemonic Extension |Learn More About The Bully Mnemonic Extension]] ==== The power of two ==== {| class="wikitable" style="margin: 20px auto 40px auto; border-collapse: collapse; font-family: sans-serif;" |+ style="font-weight: bold; margin-bottom: 8px;" | Figure 4f: Distance Conversions to Parsecs ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Time Duration</span> ! colspan="2" style="background-color: #f2f2f2;{{Text color default}}; text-align: center; padding: 10px;" | <span style="font-size: larger;">Orbital Distance (Parsecs)</span> |- ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Galactic Years</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small>Bully Timestamps</small> ! style="background-color: #f2f2f2;{{Text color default}}; text-align: left; padding: 10px;" | <small> Distance assuming 1.048682 ''R''_☉ per Bully timestamp </small> |- | '''2³''' = 8 | style="text-align: left; padding: 8px;" | '''2⁴⁴''' | '''2^18.666''' ≈ 415,935 |- | '''2^-1''' = <math>\frac{1}{2}</math> | style="text-align: left; padding: 8px;" | '''2⁴⁰''' | '''2^14.666''' ≈ 25,996 |- | '''2^-5''' = <math>\frac{1}{32}</math> | style="text-align: left; padding: 8px;" | '''2³⁶''' | '''2^10.666''' ≈ 1,624.74 |- style="background-color: #e6f2ff;{{Text color default}}; font-weight: bold;" ! colspan="4" style="text-align: left; padding: 8px;" | Off Nominal Values |- | '''2⁰''' = 1 | style="text-align: left; padding: 8px;" | '''2⁴¹''' | '''2^15.666''' = 51,991 |- | '''2^-15.666''' | style="text-align: left; padding: 8px;" | '''2^25.334''' | '''2⁰''' = 1 |} The '''first''', '''fifth''', and '''ninth''' digits in a Bully timestamp respectively represent 3,055 seconds, roughly 6.344 years, and approximately 416,000 years of orbit around the Milky Way galaxy. It is worth noting that the length 16⁸ ''R''_☉ is remarkably close to 10¹⁰ light-seconds. In fact, these distances are so similar (differing by less than 0.35%) that one can estimate the ratio of the sun's orbital speed to the speed of light by dividing: &thinsp; :<math>\frac{10^{10}}{16^8 \times 3055} \approx 0.076\%</math> &thinsp; Furthermore, these values (16⁸ ''R''_☉ and 10¹⁰ light-seconds) are of the same order of magnitude as 100 parsecs, where a parsec (roughly 3.26 light-years) is a common length unit used in astronomy. To be precise, '''16⁸ ''R''_☉ is approximately 96.83 parsecs'''. == Bully Timestamp Realization == Each Bully timestamp is '''realized''' exactly 3055 seconds TAI after the previous one. However, since atomic clocks did not exist prior to the 1950's, any assignment of Bully timestamps prior to 1958 should be viewed as an '''estimate''' of how time might have transpired in the past, rather than an actual realization of Bully time. Similarly, any assignment of future timestamps should be viewed as an estimate of what may occur, rather than a realization. Bully timestamps should only be considered "realized" when time is measured with an accuracy of 10^-10. There have been over 700,000 realized Bully timestamps during the era of modern atomic time keeping (1958 AD ... present). [[Bully_Metric_Realized_Timestamps|Learn More About Realized Bully Timestamps]] === Time Estimation Divisions === [[File:History-of-the-Universe With Bully Timestamps.jpg|frame|center|text-bottom|Figure 1: History of the Universe with a few example Bully timestamps shown in red.]] For the purpose of time estimation, the Bully system's time range is divided into three distinct sets: ==== First Set ==== * ''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'': Used to estimate time during the universe's formative period ('''Figure 1'''), spanning roughly 3 billion years beginning with the Big Bang. The following list highlights key events from selected timestamps during this formative era: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * First timestamp: ''{{mono|0000 0000 0000}}'' ** [[w:Cosmic_inflation|Cosmic Inflation]] ** [[w:Baryogenesis|Baryogenesis]] ** [[w:Big_Bang_nucleosynthesis|Nucleosynthesis]] * Approximately: ''{{mono|0000 EA00 0000}}'' ** [[w:Decoupling_(cosmology)|Decoupling]] ** [[w:Recombination_(cosmology)|Recombination]] * Approximately: ''{{mono|0100 0000 0000}}'' ** [[w:Star_formation|First Star Formation]] * Approximately: ''{{mono|0297 0000 0000}}'' ** [[w:MoM-z14|Oldest Observed Galaxy]] </div> ==== Second Set ==== * ''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'': Used to estimate cosmic look-back time ('''Figure 2'''), spanning from approximately 10.4 billion years ago to exactly 12:00:00 TAI on June 21, 1998. Key milestones from the presolar through geological eras include: <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|3B00 0000 0000}}'' ** [[w:Murchison_meteorite|Oldest Presolar Grains]] * Approximately: ''{{mono|5720 9000 0000}}'' ** [[w:Hadean|Hadean Eon Begins]] * Approximately: ''{{mono|5C2A 0000 0000}}'' ** [[w:Archean|Archean Eon Begins]] * Approximately: ''{{mono|6A8C 0000 0000}}'' ** [[w:Proterozoic|Proterozoic Eon Begins]] * Approximately: ''{{mono|7D56 0000 0000}}'' ** [[w:Phanerozoic|Phanerozoic Eon Begins]] </div> [[File:Geologic time scale - spiral - ICS colours (light) - path text.svg|frame|center|text-bottom|alt=Geologic time scale proportionally represented as a log-spiral. The image also shows some notable events in Earth's history and the general evolution of life.|thumb|Figure 2: The geologic time scale, proportionally represented as a [[w:Logarithmic_spiral|log-spiral]] with some major events in Earth's history. A [[w:megaannum|megaannum]] (Ma) represents one million (10⁶) years.]] ==== Third Set ==== * ''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'': Used to estimate (and realize) future events. This set begins at precisely 12:00:00 TAI on June 21, 1998, and progresses forward for approximately 13.4 billion years. <div style="background-color: #f0f4f7;{{Text color default}}; padding: 15px; border-left: 5px solid #009688;"> * Approximately: ''{{mono|B000 0000 0000}}'' ** [[w:Sun#Life_phases|Death of Sun (main-sequence)]] </div> === Time Estimation Using Cosmic Redshift === In [[w:physics|physics]], a '''redshift''' is an increase in [[w:wavelength|wavelength]] (or a decrease in [[w:frequency|frequency]]) of [[w:electromagnetic radiation|electromagnetic radiation]]. Cosmological redshifts are driven directly by the [[w:expansion of the universe|expansion of the universe]]. The redshift value is denoted by {{math|''z''}}, where the ratio of observed to emitted wavelength is {{math|1 + ''z''}}. If the original wavelength of a radiation source is known, its cosmological redshift can reveal the light travel time. However, mapping redshift precisely to elapsed time requires an exact cosmological model. Ongoing measurement tension surrounding the [[w:Hubble constant|Hubble constant]] introduces uncertainty into calculations of the exact [[w:Age of the universe|age of the universe]] and distant stars. This cosmological uncertainty directly affects the accuracy of assigning Bully timestamps. The table in Figure 3 contrasts two estimation tracks based on competing cosmological datasets. One column applies the local distance ladder framework from the '''SH0ES Team''' (corresponding to a younger universe estimate of 12.7 Gyr). The other utilizes cosmic microwave background data from the '''Planck Collaboration''' (yielding an older universe estimate of approximately 13.8 Gyr). Larger z values correspond with the more distant past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 3: Bully Timestamps for Selected Redshift Values Given Different Universe Age Estimates |- style="background-color: #eaecf0; font-size: medium; font-weight: bold;{{Text color default}};" ! style="padding: 10px; font-size: large;" | Redshift z <br /> (z = ∞ to 2) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};”" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = ∞ || {{nowrap|0000 0000 0000}} || {{nowrap|0000 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 18.0 || {{nowrap|01CC 0000 0000}} || {{nowrap|01F4 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 15.0 || {{nowrap|0253 0000 0000}} || {{nowrap|0287 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 12.0 || {{nowrap|032D 0000 0000}} || {{nowrap|0374 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 9.0 || {{nowrap|04B5 0000 0000}} || {{nowrap|051E 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 6.0 || {{nowrap|0809 0000 0000}} || {{nowrap|08BB 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | z = 3.0 || {{nowrap|1285 0000 0000}} || {{nowrap|1420 0000 0000}} |- style="font-size:small:small;background-color:#ffffff;;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;;{{Text color default}};" | z = 2.0 || {{nowrap|1C4D 0000 0000}} || {{nowrap|1EC2 0000 0000}} |} The forward-progressing timestamps ''{{mono|0000 0000 0000}}'' through ''{{mono|1FFF FFFF FFFF}}'' are illustrated in Figure 4 (bottom of figure). By convention, these timestamps are assumed to begin at the Big Bang and progress forward for approximately three billion years. [[File:Redshift-by-universe-age-H0-comparison.png|frame|center|alt=Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.|Figure 4: Age of the Universe plot showing Bully timestamps mapped to cosmic redshift.]] Timestamps ''{{mono|2000 0000 0000}}'' through ''{{mono|8200 0000 0000}}'' (top of Figure 4) measure "lookback" time anchored at timestamp ''8209 ED00 0000''. Because the total age of the universe is unfixed, the precise mathematical relationship between universal age and lookback time remains indefinite. Two different possible universe ages are shown with the Planck Collaboration shown in red and the SH0ES Team shown in blue. The data illustrated in Figure 5 is the same as is shown in Figure 4, but Figure 5 plots against lookback time on the x-axis, so in this plot the universe age is unfixed with the Planck Collaboration shown in red and the SH0ES Team shown in blue. [[File:Redshift-by-lookback-time-H0-comparison.png|frame|center|alt=A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.|Figure 5: A cosmic lookback plot showing Bully timestamps mapped to cosmic redshift.]] The table in Figure 6 is similar to the table in Figure 3, in that it contrasts two estimation tracks based on competing cosmological datasets. However, whereas the data in Figure 3 was for large z values, Figure 6 shows small z values. Smaller z values correspond with the recent past. {| class="wikitable" style="text-align:center; width:100%; max-width:800px; font-size: small; font-family: monospace, monospace;" |+ Figure 6: Redshift Values for Selected Bully Timestamps Given Different Universe Age Estimates |- style="background-color: #eaecf0;{{Text color default}}; font-size: medium; font-weight: bold;" ! style="padding: 10px; font-size: large;" | Bully Timestamp <br /> (z = 1 to 0) || SHOES Team <br /> (12.7 Gyr) || Planck Collaboration <br /> (13.8 Gyr) |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|4000 0000 0000}} || z = 0.925134 || z = 0.796535 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|6000 0000 0000}} || z = 0.342787 || z = 0.308619 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8000 0000 0000}} || z = 0.016418 || z = 0.015093 |- style="font-size:small:small;background-color:#ffffff;{{Text color default}};" | style="font-weight: bold; background-color: #eaecf0;{{Text color default}};" | {{nowrap|8209 ED00 0000}} || z ≈ 0.000000 || z ≈ 0.000000 |} === Time Estimation Relativistic and Cosmological Considerations === What does it mean when cosmologists state that the universe is approximately 13.8 billion years old? According to Einstein's theories of special and general relativity, time passes differently for each observer depending on their path through spacetime and the gravitational forces in their vicinity. How, then, can the universe have a single age? Shouldn't its age depend entirely on the observer's frame of reference? The "age of the universe" cited by cosmologists is actually its maximum possible age. Among all paths an observer could take through spacetime, one specific trajectory maximizes elapsed time. This privileged frame of reference belongs to an observer who remains at rest relative to the Cosmic Microwave Background (CMB) and resides in a region of space with negligible matter. We will refer to this as the "CMB rest frame." Importantly, Bully timestamps are divided into three distinct sets, with only the first set (''{{mono|0000 0000 0000}}'' — ''{{mono|1FFF FFFF FFFF}}'') utilizing the CMB rest frame. Timestamps in the third set (''{{mono|8209 ED00 0000}}'' — ''{{mono|FFFF FFFF FFFF}}'') are realized using atomic clocks at sea level on Earth. Due to relativistic time dilation, these terrestrial clocks run slower than identically constructed clocks placed at rest in empty space. All "realized" Bully timestamps from 1958 to the present conform to Earth's sea-level frame of reference. Furthermore, the "estimated" Bully timestamps in the second set (''{{mono|2000 0000 0000}}'' — ''{{mono|8209 ED00 0000}}'') are typically derived from the radioactive decay of samples found on or within the Earth; thus, these samples decay at a rate comparable to Earth's sea-level frame. The oldest timestamps in this second set come from presolar grains, which formed in different star systems prior to the emergence of our solar system. Because some of these samples may have traveled through space in frames of reference drastically different from Earth's current sea-level frame, the accuracy of these cosmic estimates is inherently limited. [[Bully_Metric_CMB_Stabilized_Timestamps| Learn More About Relativistic and Cosmological Considerations]] == Contextualized vs. Decontextualized Time == Local clocks and calendars reflect '''contextualized time''', which uses region-specific offsets from Coordinated Universal Time (UTC) to align with physical reality. This time is "contextual" because it provides an intuitive sense of conditions at some specific geographic location; for instance, a traveler arriving in London at 4:00 a.m. can instinctively expect darkness and quiet streets. To maintain this alignment with Earth's natural cycles, UTC requires periodic "leaps" (seconds and years). In '''Figure 10''', the light blue line represents Earth's irregular rotation ('''UT1'''), while the dark blue line shows '''UTC''', which is manually adjusted with leap seconds to track UT1. In contrast, standards such as International Atomic Time ('''TAI'''), Terrestrial Time ('''TT'''), and '''GPS time''' are '''decontextualized'''. They are independent of Earth's rotation, meaning they do not correspond to "true time" at any specific geographical location. Represented by the black lines in '''Figure 10''', these standards track a continuous, uniform interval measured by atomic clocks. This uninterrupted linearity is vital for scientific and technical systems, where the discontinuities introduced by leap seconds could lead to critical errors or system failures. [[File:Bully Timestamps in relation to modern time keeping.png|frame|center|text-bottom|Figure 10: Modern Time Keeping]] The various decontextualized standards currently in use are effectively "frozen" in the astronomical conditions present at the time of their deployment. Because long-term changes in Earth's motion are unpredictable, each system launched with a different initial offset. For example, when GPS was launched in 1980, the '''Delta T''' adjustment (TT-UTC) exceeded 51 seconds. In contrast, the 1972 LORAN-C upgrade began with an adjustment closer to 42 seconds. This historical discrepancy results in a permanent nine-second offset between GPS and LORAN-C. Similarly, LORAN-C remains offset from TAI (deployed in 1958) by exactly ten seconds. The Bully timestamp system, shown on the far-right axis of '''Figure 10''', follows the same uniform, decontextualized logic as TAI and TT but avoids this "legacy offset" confusion. Unlike existing standards, Bully timestamps are not linked to others by a constant, arbitrary time offset. This independence ensures they are uniquely recognizable and impossible to misinterpret. [[Bully_Metric_Timestamp_units|Learn More About Contextualized vs Decontextualized time]] == Why do we need Bully timestamps? == All the timestamps in '''Figure 11''' refer to one single, simultaneous moment in time. The left frame illustrates the fragmentation of Coordinated Universal Time (UTC) through time zones. For instance, on June 21, 1998, a UTC time of 11:59:29 a.m. in Accra, Ghana, was simultaneously 8:59:29 p.m. in Tokyo. These time zone offsets are not based on science, but on '''political mandates''' that have resulted in [https://en.wikipedia.org/wiki/List_of_UTC_offsets 38 distinct UTC offsets], including confusing half- and quarter-hour increments. {| class="wikitable" style="margin-right: 0; margin-left: 1em; text-align: center;" |+ Figure 11: UTC Time Zones vs. Bully Timestamps. |- ! Selected UTC Time Zones !! [https://gssc.esa.int/navipedia/index.php/Transformations_between_Time_Systems Decontextualized timestamps] |- | rowspan = 3 | [[File:Timezone-boundary-builder_release_2023d.png|thumb|upright=1.0| June 21, 1998 at 8:59:29 pm (JST)</br> June 21, 1998 at 7:59:29 pm (CST)</br> June 21, 1998 at 2:59:29 pm (EEST)</br> June 21, 1998 at 12:59:29 pm (IST)</br> June 21, 1998 at 11:59:29 am (GMT)</br> June 21, 1998 at 8:59:29 am (BRT)</br> June 21, 1998 at 4:59:29 am (PDT)</br> June 21, 1998 at 1:59:29 am (HST)</br> ]] || [[File:WorldMap-Blank-Noborders.svg|thumb|<br/> 06/21/1998 12:00:32.184 (TT)<br/> 06/21/1998 12:00:00 (TAI)<br/> 06/21/1998 11:59:42 (GPS) ]] |- ! Bully Timestamp |- || [[File:WorldMap-Blank-Noborders.svg|thumb|8209 ED00 0000 (+ 0.000 sec)]] |} ==== Legacy Decontextualized Timestamps ==== The decontextualized timestamps (TAI, TT, GPS) in the upper-right frame of '''Figure 11''' attempt to solve the UTC geographic fragmentation problem, yet they remain "cluttered" by Gregorian formatting. Applying a Gregorian date—which is built to track the Sun—to an atomic standard is a '''category error'''. Seeing three different timestamps share the same date while differing by several "leap" seconds is intellectually disorienting because the date has been stripped of its astronomical meaning. In these technical contexts, the Gregorian format is an artificial mask applied for convenience, hiding the true linear nature of time. For scientific and technical applications, TAI and TT are often expressed via '''Modified Julian Date (MJD)'''—a continuous count of SI days since a fixed epoch. While MJD avoids Gregorian irregularities, it remains "tethered" to the 86,400-second day, a unit that is astronomically meaningless when decontextualized. Similarly, '''GPS time''' relies on a week-based count (since January 6, 1980), forcing a technical system to conform to an arbitrary seven-day cycle. Both systems are cumbersome "hybrids" that attempt to measure linear time using units designed for Earth’s rotation. ==== Decontextualized Bully Timestamps ==== The '''Bully Timestamp''', shown in the lower-right frame of '''Figure 11''', breaks the Gregorian formatting tether. It is a single, unique identifier that applies simultaneously to all locations on Earth because it is never adjusted for geography or orbital drift. For example, Bully timestamp {{mono|8209 ED00 0000}} was realized at the exact moment the UTC based clock read 11:59:29 a.m. in Accra and 8:59:29 p.m. in Tokyo. By discarding the baggage of weeks, days, and hours, the Bully timestamp emerges as the least ambiguous format for representing universal, decontextualized time. Click on the below links for a comparison of current time in six time standards (local, UTC, GPS, Loran, and TAI), all displayed using traditional Gregorian format: [http://www.leapsecond.com/m/gps.htm LeapSecond.com] [https://www.ipses.com/eng/in-depth-analysis/standard-of-time-definition ipses.com] [http://www.csgnetwork.com/multitimedisp.html csgnetwork.com] == The Foundations of Bully Metric == The Bully Timestamp System was derived from the orbital periods of major Solar System bodies. Specifically, the duration of Earth's '''sidereal year''' (~31,558,150 seconds) is roughly equal to <math>10,330 \times 3,055</math> SI seconds. This foundational constant—3,055 seconds—serves as the building block for the Bully timestamp system. The name "Bully" is a dual-reference to the massive astronomical objects that define our local spacetime. In an archaic sense, "bully" means '''"beautiful" or "excellent,"''' describing the celestial harmony of the cosmos. In the modern sense, it refers to the '''dominance and gravitational influence''' of "bullies" like [https://en.wikipedia.org/wiki/Sagittarius_A* Sagittarius A*], the [https://en.wikipedia.org/wiki/Sun Sun], and giant planets like Jupiter and Saturn. These massive bodies dictate the motion of everything around them, serving as the physical anchors for the Bully Metric system. * [[Bully_Metric_Foundations|Learn More About The Foundations of Bully Metric]] * [[Bully_Metric_Astronomical_Coordinates|Learn More About The Bully Metric Coordinate System]] hu8j2zprtzp1kkw3hcgt9r7tm031px7 0 321584 2823774 2819302 2026-08-21T01:12:37Z Howie2024 2995240 /* Subpages */ start the standalone paper of PDT/Normalized Probability Dilation Paper. 2823774 wikitext text/x-wiki {{Research project}} {{Original research}} {{To be peer reviewed}} {{subst:proofread}} == Research abstract == '''Probability Dilation Theory (PDT)''' is a measure-theoretic research framework for studying how probability measures transform under '''positive reweighting (dilation)''' while preserving normalization and producing controlled changes in expectation values. The theory is an exploratory framework for iterative probability-measure evolution under positive dilation fields. The framework studies how repeated probabilistic reweighting transformations may generate emergent statistical structure, entropy flow, and multiscale probability dynamics. At its core, PDT studies how repeated positive probability reweighting transformations alter the long-term structure of probability distributions. PDT treats a probability measure as the primary mathematical object and investigates: * invariant identities induced by reweighting, * composition and iteration of dilations, * fixed points and near-fixed behavior, * whether iterative measure updates can generate testable multiscale statistical structure (to be evaluated via explicit models and simulations). PDT is presented as a mathematical framework. Any proposed application to physics or cosmology must be expressed as a concrete model (space, baseline measure, dilation field) and tested against falsifiable predictions. == Overview == PDT is motivated by the observation that some structural information can be recovered from sampling statistics (e.g., [[w:Buffon's needle problem|Buffon’s needle]]). PDT abstracts this idea by focusing on measure transformation itself: a dilation field modifies a baseline probability measure in a way that is: * mathematically well-defined (positivity and normalization), * composable under iteration, * analyzable for invariants and fixed points. === Conceptual interpretation === A simplified conceptual flow of the PDT framework is: <pre> Baseline probability measure P ↓ Positive dilation field D(x) ↓ Reweighted probability measure P~ ↓ Observable statistical changes </pre> Repeated dilation may qualitatively behave as: <pre> Broad initial distribution ↓ Localized reweighting ↓ Probability concentration ↓ Emergent multiscale structure </pre> Different classes of dilation fields may therefore generate qualitatively different long-term probability dynamics. In this interpretation, PDT does not alter the underlying sample space directly. Instead, it modifies how probability mass is distributed across that space through a positive reweighting field. Regions with larger values of the dilation field contribute more strongly to the transformed measure, while normalization preserves total probability. Earlier exploratory formulations of Probability Dilation Theory (PDT) were informally referred to as the Einstein Buffon Process (EBP), reflecting initial probabilistic-geometric interpretations inspired by Buffon-type constructions and Einstein-style scaling analogies. The framework has since evolved toward a broader iterative theory of probability-measure dynamics under positive dilation fields. A simple iterative interpretation may also be visualized as: <pre> P₀ ↓ D₁ P₁ ↓ D₂ P₂ ↓ D₃ P₃ ↓ ⋯ </pre> where each dilation field reweights the probability structure generated by the previous step. Different classes of dilation fields may therefore generate qualitatively different long-term probability dynamics. = Mathematical framework = == Definitions and notation == Let <math>(\Omega,\Sigma)</math> be a measurable space. * <math>P</math> denotes a probability measure on <math>(\Omega,\Sigma)</math>. * If <math>P</math> has a density <math>p</math> with respect to a reference measure <math>\mu</math>, then <math>dP=p\,d\mu</math>. * <math>D:\Omega\to(0,\infty)</math> is a measurable '''dilation field''' (a positive weight function). * <math>Z(P,D)</math> is the normalization constant: .<math> Z(P,D)=\int_\Omega D\,dP </math> * For an observable <math>f:\Omega\to\mathbb{R}</math> integrable under the relevant measure, <math> \mathbb{E}_P[f] = \int_\Omega f\,dP </math>. == PDT transformation (probability reweighting) == Given <math>P</math> and <math>D</math> with <math>0<Z(P,D)<\infty</math>, define the '''PDT transform''' <math>\widetilde{P}=\mathrm{PDT}(P;D)</math> by: <math> \widetilde{P}(A) = \frac{ \int_A D\,dP }{ \int_\Omega D\,dP } \quad\text{for all }A\in\Sigma </math> If <math>dP=p\,d\mu</math>, then <math>d\widetilde{P}=\widetilde{p}\,d\mu</math>, where <math> \widetilde{p}(x) = \frac{D(x)\,p(x)}{Z} </math> and <math> Z = \int_\Omega D(x)\,p(x)\,d\mu </math> '''Interpretation:''' the dilation field <math>D</math> shifts probability mass toward regions where <math>D</math> is larger, while renormalization keeps total probability equal to 1. PDT is mathematically related to importance sampling, Gibbs-style reweighting, and Radon–Nikodym measure transformations, although the framework emphasizes compositional and geometric interpretations of probability reweighting rather than only numerical estimation procedures. Unlike conventional importance sampling, however, PDT emphasizes the compositional and potentially dynamical behavior of repeated probability reweighting transformations. A familiar physical example of a strictly positive factor is the Lorentz factor: <math> \gamma(v) = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} </math> for <math> |v|<c </math> Lorentz contraction for a rod of rest length <math>L_0</math> moving at speed <math>v</math> is: <math> L(v)=\frac{L_0}{\gamma(v)} </math> To connect this idea to PDT (as an illustration only), one may define a positive dilation field based on <math>\gamma</math>. == Worked finite example == Consider a finite probability space: <math> \Omega=\{a,b,c\} </math> with baseline probabilities: <math> P(a)=0.2,\quad P(b)=0.3,\quad P(c)=0.5 </math> Define a positive dilation field: <math> D(a)=1,\quad D(b)=2,\quad D(c)=4 </math> The normalization constant is: <math> Z=\sum_x D(x)P(x) </math> giving: <math> Z=(1)(0.2)+(2)(0.3)+(4)(0.5)=2.8 </math> The PDT-transformed probabilities become: <math> \widetilde{P}(a)=\frac{0.2}{2.8}\approx0.071 </math> <math> \widetilde{P}(b)=\frac{0.6}{2.8}\approx0.214 </math> <math> \widetilde{P}(c)=\frac{2.0}{2.8}\approx0.714 </math> This illustrates how PDT shifts probability mass toward regions with larger dilation weights while preserving normalization. == Composition of dilations == An important structural property of sequential PDT transformations is that compose multiplicatively. Suppose two positive dilation fields: <math> D_1(x)>0 </math> and <math> D_2(x)>0 </math> are applied successively to a baseline probability measure <math>P</math>. The first dilation produces: <math> \widetilde{P}_1(A) = \frac{\int_A D_1\,dP} {\int_\Omega D_1\,dP} </math> Applying the second dilation field to <math>\widetilde{P}_1</math> gives: <math> \widetilde{P}_2(A) = \frac{\int_A D_2\,d\widetilde{P}_1} {\int_\Omega D_2\,d\widetilde{P}_1} </math> Substituting the first transformation into the second yields: <math> \widetilde{P}_2(A) = \frac{ \int_A D_2D_1\,dP }{ \int_\Omega D_2D_1\,dP } </math> This shows that sequential PDT transformations compose through multiplication of the dilation fields. This compositional structure allows iterative probability reweighting to be studied using products of positive fields, potentially generating multiscale or hierarchical probability structures under repeated application. == Fixed points and iterative dynamics == An important question in PDT concerns the long-term behavior of repeated PDT transformations. Given an initial probability measure: <math> P_0 </math> and a sequence of positive dilation fields: <math> D_1,D_2,D_3,\dots </math> successive PDT transformations generate a sequence of measures: <math> P_0 \rightarrow P_1 \rightarrow P_2 \rightarrow P_3 \rightarrow \cdots </math> where each transformed measure is obtained by reweighting the previous one. A measure <math>P</math> is called a fixed point of a dilation field <math>D</math> if: <math> \widetilde{P}=P </math> under the PDT transformation. In the simplest case, this requires the dilation field to be constant almost everywhere with respect to <math>P</math>. More general fixed-point behavior may arise when iterative compositions balance probability amplification against normalization. More generally, repeated compositions of nontrivial dilation fields may generate: * hierarchical probability structure; * multiscale statistical behavior; * attractor-like distributions; * approximately stable transformed measures. These questions connect PDT to broader areas of: * dynamical systems; * stochastic processes; * iterative renormalization methods; * probabilistic geometry. At present these iterative properties remain largely unexplored within the PDT framework. == Entropy and iterative probability flow == Repeated PDT transformations may alter the entropy structure of a probability measure. For a discrete probability distribution: <math> P=\{p_i\} </math> the Shannon entropy is: <math> H(P) = -\sum_i p_i \log p_i </math> Under iterative PDT transformation, successive transformed measures: <math> P_0 \rightarrow P_1 \rightarrow P_2 \rightarrow \cdots </math> may exhibit changing entropy behavior depending on the structure of the dilation fields. For example: * strongly localized dilation fields may concentrate probability mass and reduce entropy; * broader or smoothing dilation fields may distribute probability more evenly and increase entropy; * iterative compositions may generate approximately stable entropy profiles. These questions connect PDT to: * information theory, * statistical mechanics, * stochastic dynamics, * and renormalization-style iterative systems. At present the entropy behavior of iterative PDT transformations remains an open area for investigation. == Toy experiment: entropy under repeated dilation == A simple finite-state experiment illustrates how repeated PDT transformations can change the entropy of a probability distribution. Let the initial probability distribution be: <math> P_0=(0.2,0.2,0.2,0.2,0.2) </math> and define a positive dilation field: <math> D=(1,1,2,4,8) </math> At each step, apply the PDT update: <math> P_{n+1}(i) = \frac{D(i)P_n(i)} {\sum_j D(j)P_n(j)} </math> The Shannon entropy is: <math> H(P_n) = -\sum_i P_n(i)\log P_n(i) </math> In this toy model, repeated dilation shifts probability mass toward the highest-weight state. Over ten iterations, the entropy decreases from approximately: <math> H(P_0)\approx1.6094 </math> to: <math> H(P_{10})\approx0.00775 </math> The final distribution is approximately: <math> P_{10} \approx (0.000000001,\;0.000000001,\;0.000000953,\;0.000975609,\;0.999023437) </math> This example demonstrates probability concentration under repeated positive dilation. It is a finite-state toy model and should not be interpreted as physical evidence; its purpose is to illustrate iterative PDT behavior. == Mathematical context == PDT transformations may be viewed as exploratory probability-measure reweighting procedures related conceptually to conditioning behavior, stochastic transformations, entropy evolution, and probabilistic dilation phenomena studied in imprecise probability theory and dynamical systems literature. In PDT, the term ''dilation'' refers to probabilistic reweighting and transformation behavior under localized weighting fields rather than the formal operator-theoretic notion of dilation used in functional analysis. The iterative entropy-flow experiments explored in PDT resemble finite-state dynamical systems in which repeated transformations generate convergence, concentration, and emergent probabilistic structure over successive iterations. === Example entropy evolution === {| class="wikitable" ! Iteration !! Shannon entropy |- | 0 || 1.6094 |- | 1 || 1.2990 |- | 2 || 0.7790 |- | 3 || 0.4399 |- | 5 || 0.1500 |- | 10 || 0.0078 |} Entropy evolution under repeated localized PDT transformation showing entropy reduction and probability concentration under iterative probabilistic reweighting. Programmatically generated using Python in a ChatGPT-assisted workflow. The entropy decreases under repeated application of the dilation field as probability mass becomes increasingly concentrated in the highest-weight states. === Localized dilation fields === A useful class of PDT transformations is generated by localized positive dilation fields. Consider a one-dimensional finite configuration space with states indexed by: <math> x=0,1,2,\dots,N </math> and define a localized dilation field centered at <math>x_0</math>: <math> D(x) = \exp\!\left( \lambda \exp\!\left( -\frac{(x-x_0)^2}{2\sigma^2} \right) \right) </math> where: * <math>\lambda>0</math> controls the strength of the dilation; * <math>\sigma</math> controls the spatial width of the localized field. Narrow values of <math>\sigma</math> produce sharply localized amplification, while broader values produce smoother probability reweighting across the configuration space. Under iterative PDT dynamics: <math> P_{n+1}(x) = \frac{ D(x)P_n(x) }{ \sum_y D(y)P_n(y) } </math> the probability distribution may progressively concentrate near the center of the dilation field. === Example entropy evolution for localized fields === Using an initially uniform distribution over 21 states and iterating the PDT transformation 10 times produces the following representative entropy behavior: {| class="wikitable" ! Field width <math>\sigma</math> ! Final entropy after 10 iterations ! Maximum probability after 10 iterations |- | 1.5 || 0.0352 || 0.9950 |- | 3.0 || 0.8162 || 0.7141 |- | 6.0 || 1.5367 || 0.3595 |} [[File:PDT entropy evolution localized field.png|thumb|center|600px|Entropy evolution under repeated localized PDT transformation showing entropy reduction and probability concentration under iterative probabilistic reweighting.]] [[File:Epd_entropy_evolution.png|thumb|center|600px|Entropy evolution under repeated localized PDT dilation. Narrow localized dilation fields produce rapid entropy reduction and probability concentration under iterative reweighting.]] These results indicate that narrower localized dilation fields generate stronger probability concentration and more rapid entropy reduction. == Comparative entropy-flow experiments == The following finite-state computational experiments illustrate comparative entropy evolution under several classes of PDT dilation fields. Each experiment begins with the same initially uniform probability distribution and applies repeated PDT transformations under different field structures. The experiments are exploratory and intended to illustrate qualitative differences in iterative probabilistic behavior rather than empirical physical predictions. {| class="wikitable" |+ Comparative entropy-flow behavior under PDT field classes ! Field class ! Final entropy ! Entropy decrease ! Final max probability ! Qualitative behavior |- | Localized | 0.3104 | 3.4032 | 0.9275 | Strong probability concentration |- | Oscillatory | 1.5779 | 2.1357 | 0.3418 | Distributed oscillatory structure |- | Multi-peak | 0.2851 | 3.4284 | 0.9425 | Multiple concentration regions |- | Stochastic | 0.7744 | 2.9392 | 0.7413 | Fluctuating concentration behavior |} These experiments suggest that different classes of dilation fields may generate qualitatively distinct entropy-flow and concentration behavior under iterative PDT dynamics. Localized and multi-peak fields produce strong entropy reduction and probability concentration, while oscillatory fields preserve more distributed probabilistic structure. Stochastic fields exhibit fluctuating but still partially concentrating behavior in this finite-state example. In this toy model, repeated localized dilation behaves qualitatively like an attractor centered on the highest-weight region of the configuration space. [[File:Pdt comparative entropy flow.png|thumb|Comparative entropy evolution under localized, oscillatory, multi-peak, and stochastic PDT dilation fields.]] The experiment is intended only as a finite-state demonstration of iterative PDT dynamics and should not be interpreted as physical evidence. === Oscillatory dilation fields === Another useful class of PDT transformations is generated by oscillatory positive dilation fields. One example is: <math> D(x) = \exp(\lambda\sin(kx)) </math> where: * <math>\lambda>0</math> controls the strength of the oscillatory amplification; * <math>k</math> controls the spatial frequency of the oscillation. Because the exponential is always positive, the dilation field remains strictly positive for all states. Unlike localized dilation fields, oscillatory fields may generate multiple competing high-weight regions across the configuration space. Under repeated PDT transformation: <math> P_{n+1}(x) = \frac{ D(x)P_n(x) }{ \sum_y D(y)P_n(y) } </math> probability mass may evolve toward several distributed concentration regions rather than a single dominant attractor. === Example oscillatory-field experiment === A finite-state experiment was performed using: * 41 discrete states; * an initially uniform probability distribution; * a positive oscillatory dilation field with three spatial oscillation cycles; * 10 successive PDT iterations. Representative entropy behavior was: {| class="wikitable" ! Iteration ! Shannon entropy |- | 0 || 3.7136 |- | 2 || 2.8699 |- | 5 || 2.3018 |- | 10 || 1.9335 |} Unlike sharply localized dilation fields, the oscillatory field produced slower entropy reduction and multiple probability concentration peaks distributed across the configuration space. After 10 iterations, the largest probability concentration remained distributed rather than collapsing into a single dominant state. This suggests that different classes of positive dilation fields may generate qualitatively different long-term iterative probability structures. The experiment is intended only as a finite-state demonstration of iterative PDT dynamics and should not be interpreted as physical evidence. === Multi-peak localized dilation fields === A broader class of PDT transformations may be generated using multiple localized dilation peaks distributed across the configuration space. One example is: <math> D(x) = \exp\!\left( \sum_k \lambda_k \exp\!\left( -\frac{(x-x_k)^2}{2\sigma_k^2} \right) \right) </math> where: * <math>x_k</math> are the locations of the dilation peaks; * <math>\lambda_k>0</math> control the amplification strength of each peak; * <math>\sigma_k</math> control the spatial width of each localized region. This construction generates a positive multimodal dilation landscape containing several competing amplification regions. Under repeated PDT iteration: <math> P_{n+1}(x) = \frac{ D(x)P_n(x) }{ \sum_y D(y)P_n(y) } </math> probability mass may evolve toward multiple partially localized concentration regions. Unlike single localized dilation fields, multi-peak fields may generate: * competing attractor-like regions; * hierarchical probability concentration; * partially stabilized multimodal distributions; * multiscale probability structure. Depending on the relative strengths and widths of the peaks, the iterative dynamics may favor: * dominance by a single peak; * coexistence of several concentration regions; * or slowly evolving metastable probability structures. === Conceptual interpretation === A qualitative iterative evolution may be visualized as: <pre> Broad initial distribution ↓ Multiple localized amplifications ↓ Competing concentration regions ↓ Emergent multimodal probability structure </pre> This class of dilation fields suggests that iterative PDT dynamics may generate richer probability organization than either single localized attractors or simple oscillatory fields alone. At present these behaviors remain exploratory computational observations within finite-state toy models. === Random and stochastic dilation fields === Another important class of PDT transformations arises when the dilation field itself varies stochastically. A simple stochastic dilation field may be written schematically as: <math> D_n(x) = \exp\!\left( \sigma \eta_n(x) \right) </math> where: * <math>\eta_n(x)</math> is a random field or stochastic fluctuation at iteration <math>n</math>; * <math>\sigma>0</math> controls the strength of the stochastic variation. Because the exponential is strictly positive, the dilation field remains positive for all realizations of the random process. Under repeated PDT iteration: <math> P_{n+1}(x) = \frac{ D_n(x)P_n(x) }{ \sum_y D_n(y)P_n(y) } </math> the probability landscape itself fluctuates dynamically from one iteration to the next. Unlike deterministic localized or oscillatory dilation fields, stochastic dilation fields may generate: * fluctuating concentration regions; * transient attractor-like structures; * noise-driven entropy evolution; * intermittent probability concentration; * metastable probabilistic configurations. === Conceptual interpretation === A qualitative stochastic evolution may be visualized as: <pre> Broad initial distribution ↓ Random localized amplification ↓ Fluctuating concentration regions ↓ Dynamic probabilistic structure </pre> Depending on the stochastic process used to generate the dilation fields, the long-term dynamics may exhibit: * partial concentration, * persistent fluctuations, * stochastic stabilization, * or continuously evolving probabilistic structure. These ideas connect PDT to broader areas of: * stochastic processes; * random multiplicative systems; * statistical mechanics; * noise-driven dynamical systems; * probabilistic geometry. At present these behaviors remain exploratory computational possibilities within finite-state toy models. == Qualitative classes of iterative PDT behavior == Different classes of positive dilation fields may generate qualitatively different long-term probability dynamics under repeated PDT transformation. The following table summarizes several representative classes explored within finite-state toy models. {| class="wikitable" ! Dilation-field class ! Typical iterative behavior ! Representative qualitative structure |- | Localized fields | Strong entropy reduction and concentration toward a dominant region | Single attractor-like concentration |- | Oscillatory fields | Distributed amplification with slower entropy reduction | Patterned multimodal structure |- | Multi-peak localized fields | Competition between several concentration regions | Hierarchical or metastable probability structure |- | Random and stochastic fields | Fluctuating amplification and noise-driven evolution | Dynamic probabilistic landscapes |} These examples suggest that iterative PDT reweighting may generate a broad spectrum of emergent statistical structures depending on the geometry and dynamics of the dilation field. Within the PDT framework, the iterative behavior of probability measures may therefore depend as strongly on the structure of the dilation field as on the initial probability distribution itself. At present these qualitative behaviors remain exploratory computational observations within finite-state toy models. == Numerical simulation and iterative models == === Simulation model description === In discrete demonstrations, the “state space” may be represented by a finite set such as bins, configurations, or catalog points. Two equivalent discrete implementations are common: * '''weighted evaluation''': retain all points and assign weights proportional to <math>D</math>; * '''importance resampling''': generate a new empirical catalog with sampling probabilities proportional to <math>D</math>. === Demonstration: reweighting mock galaxy catalogs === A simple computational demonstration of PDT may be constructed using synthetic galaxy catalogs in a periodic simulation box. The demonstration pipeline is: # generate a baseline mock catalog; # define a positive dilation field over the configuration space; # perform PDT-style importance resampling; # compute the resulting two-point correlation function <math>\xi(r)</math>; # compare transformed and baseline catalogs. One example dilation field is: <math> D(x)=\exp(\lambda\phi(x)) </math> where: * <math>\lambda>0</math> controls the strength of the dilation; * <math>\phi(x)\ge0</math> is a nonnegative configuration-space field. An example seed-field construction is: <math> \phi(x)=\sum_k \exp\!\left(-\frac{\|x-s_k\|^2}{2\sigma^2}\right) </math> where <math>s_k</math> are seed locations and <math>\sigma</math> controls the width of the seed influence. The two-point correlation function may be estimated using the normalized Landy–Szalay estimator: <math> \xi(r) = \frac{DD(r)-2DR(r)+RR(r)}{RR(r)} </math> where <math>DD</math>, <math>DR</math>, and <math>RR</math> are normalized pair counts. {{Note|Unless observational datasets are explicitly supplied, demonstrations may use synthetic target correlation curves for methodological illustration only. Synthetic demonstrations should not be interpreted as empirical cosmological evidence.}} When run using synthetic target curves, PDT-resampled catalogs may exhibit enhanced small-scale clustering relative to the baseline configuration. === Computational demonstrations === Reference implementations and supplementary simulation notebooks may be maintained on external repositories or supplementary Wikiversity pages. {{collapse top|Python demonstration placeholder}} <syntaxhighlight lang="python"> # Example implementations may be maintained separately # on GitHub, OSF, or supplementary Wikiversity pages. </syntaxhighlight> {{collapse bottom}} == Scope and Limitations == PDT is a mathematical framework for measure transformations. It does not claim: * a replacement theory for General Relativity or Quantum Mechanics; * empirical confirmation without explicit predictions and tests; * observational validation without independently reproducible analysis. The following discussion extends beyond the primary mathematical framework developed earlier in the article and explores possible conceptual implications and speculative generalizations. == Speculative Extensions and Geometric Renormalization == ''This section is speculative and exploratory in nature.'' Recent mathematical work published in the ''Journal of Applied Probability'' by Baryshnikov, Cao, Kahle, and Liu suggests a possible connection between probability distributions and intrinsic geometry. Studies of “Buffon deficits” on curved manifolds indicate that deviations from classical flat-space Buffon probabilities may encode curvature-dependent geometric information. Within the PDT framework, these observations motivate the broader possibility that geometric structure may influence iterative probabilistic dynamics through curvature-dependent statistical weighting effects. Within PDT, these results are conceptually relevant because they suggest that probabilistic weighting structures may encode nontrivial geometric information. In particular, the Cambridge analysis demonstrates that generalized Buffon-type probabilistic constructions can reflect Gaussian curvature in different geometries. PDT extends this probabilistic perspective by exploring how iterative probability-measure transformations under positive dilation fields may generate evolving statistical structure, entropy flow, and geometry-dependent probabilistic behavior under repeated transformation. At present these ideas remain exploratory and heuristic. No direct physical interpretation is presently established within the PDT framework. Within the PDT framework, this motivates the speculative possibility that curvature could act as a statistical weighting mechanism on classes of admissible paths or configurations. == Future directions == * develop canonical families of dilation fields and invariants; * clarify “structure-from-measure” diagnostics; * publish reproducible simulation notebooks and parameter sweeps; * compare multiple dilation families under shared evaluation criteria; * investigate connections between probabilistic geometry and curvature-dependent statistical measures. == Future Directions: Probability Element (PE) == A speculative extension of Probability Dilation Theory (PDT) is the introduction of a minimal invariant scale in probability-state space, referred to as a '''Probability Element (PE)'''. This concept lies outside standard Fisher information geometry and is not part of established physics. The PE hypothesis proposes that probability-state space may not be fully continuous, but may instead admit a smallest distinguishable scale of structure in terms of information-theoretic resolution. This can be expressed in terms of a dimensionless ratio: <math>\eta = \frac{\sigma_P}{\sigma}</math> where: <math>\sigma_P</math> is a hypothesized minimal probability-resolution scale, <math>\sigma</math> is an effective distinguishability scale in probability-state space. === Conceptual motivation === Standard Fisher information geometry treats probability distributions as points on a smooth manifold with arbitrarily fine distinguishability. The PE hypothesis explores the possibility that this distinguishability may have a lower bound, introducing a form of discreteness in probability-state geometry. === Illustrative toy model (not derived physics) === As a heuristic example, one may consider a modification to special relativistic time dilation of the form: <math>d\tau = dt\sqrt{1 - \frac{v^2}{c^2}}\sqrt{1 - \eta^2}</math> where: <math>v</math> is velocity, <math>c</math> is the speed of light, <math>\eta = \sigma_P / \sigma</math> encodes a proposed probability-resolution scale. This expression is constructed such that standard special relativity is recovered exactly in the limit <math>\eta \to 0</math>. === Status === The Probability Element concept is: Not part of standard Fisher information geometry not derived from quantum mechanics or general relativity not currently empirically established. It is included only as a speculative direction for exploring whether probability-state space admits a minimal geometric resolution scale. === Open questions === Key open research directions include: Whether a consistent discrete formulation of probability geometry can be constructed. Whether a fundamental probability-resolution scale <math>\sigma_P</math> can be derived from known physical principles. Whether such a structure could lead to measurable deviations from standard statistical or relativistic predictions. == Convergence behavior == Iterative PDT transformations may exhibit qualitatively different convergence behavior depending on the structure of the applied dilation field. Repeated probabilistic reweighting can produce entropy reduction, probability concentration, oscillatory behavior, or fluctuating stochastic dynamics over successive iterations. === Qualitative convergence classes === Exploratory finite-state PDT experiments suggest several broad classes of iterative behavior: * '''Concentrating regimes''' — repeated transformations progressively concentrate probability mass into localized regions, often accompanied by decreasing Shannon entropy. * '''Oscillatory regimes''' — probability structure evolves through recurring redistribution patterns without strong long-term concentration. * '''Multi-peak regimes''' — multiple semi-stable concentration regions emerge simultaneously, producing persistent structured probability distributions. * '''Stochastic regimes''' — fluctuating probabilistic structure evolves under partially random or time-dependent weighting behavior. === Entropy and convergence === In many exploratory PDT experiments, entropy reduction correlates with increasing probability concentration under repeated transformation. However, some oscillatory and stochastic field classes may preserve higher entropy distributions or exhibit fluctuating convergence behavior over time. The relationship between entropy evolution and convergence remains an open area of investigation. Future work may examine entropy rates, stability properties, and long-term probabilistic structure under repeated PDT transformations. === Attractor-like behavior === Some iterative PDT systems may exhibit transient attractor-like probabilistic structure in finite-state computational experiments. These behaviors are presently exploratory and are not established mathematical attractors in the formal dynamical-systems sense. Future investigation of PDT convergence behavior may include stability analysis, fixed-point structure, stochastic convergence properties, and comparison with established dynamical systems and probabilistic evolution frameworks. == Current limitations == PDT presently operates as an exploratory probabilistic and computational framework. The theory does not presently derive known physical laws from first principles, nor does it replace established formulations of quantum mechanics or general relativity. Current PDT investigations primarily focus on iterative probability transformations, entropy evolution, probabilistic weighting behavior, and computationally modeled structure formation. Many proposed physical interpretations associated with PDT remain speculative and exploratory. Existing computational experiments are finite-state toy models intended to illustrate qualitative probabilistic behavior rather than experimentally verified physical mechanisms. Future development of PDT would likely require additional mathematical formalization, convergence analysis, stochastic modeling, and comparison with established probabilistic and dynamical systems frameworks. == See also == * [[w:Buffon's needle problem|Buffon's needle problem]] * [[w:Probability measure|Probability measure]] * [[w:Importance sampling|Importance sampling]] * [[w:Radon–Nikodym theorem|Radon–Nikodym theorem]] * [[w:Dynamical system|Dynamical systems]] * [[w:Entropy (information theory)|Entropy]] * [[w:Information theory|Information theory]] * [[w:Measure theory|Measure theory]] * [[w:Geometric probability|Geometric probability]] * [[w:Shannon entropy|Shannon entropy]] * [[w:Stochastic process|Stochastic process]] * [[w:Fixed point (mathematics)|Fixed point]] * [[w:Convergence (mathematics)|Convergence]] == Subpages == The following subpages develop mathematical extensions and specialized topics related to Probability Dilation Theory (PDT). * [[Probability Dilation Theory/Fisher Geometry and Dilation Flows|Fisher Geometry and Dilation Flows]] – studies information geometry, Fisher distance, and geodesic properties of PDT trajectories. * [[Probability Dilation Theory/Logit Representation of PE|Logit Representation of PE]] – develops the log-odds representation of probability elements and exponential PDT flows. * [[Probability Dilation Theory/Convergence and Fixed Points|Convergence and Fixed Points]] – investigates invariant measures, attractors, and stability of iterative PDT transformations. * [[Probability Dilation Theory/Stochastic Dilation Fields|Stochastic Dilation Fields]] – studies random and time-dependent dilation fields, ergodicity, and stochastic measure evolution. * [[Probability Dilation Theory/Entropy Evolution|Entropy Evolution]] – examines Shannon entropy under repeated probability dilation. * [[Probability Dilation Theory/Wasserstein Geometry|Wasserstein Geometry]] – explores distances between probability measures and convergence in measure space. * [[Probability Dilation Theory/Measure-Theoretic Foundations|Measure-Theoretic Foundations]] – develops rigorous measure-theoretic aspects of PDT including normalization and existence conditions. * [[Probability Dilation Theory/Euler Methods and Continuous-Time PDT]] – investigates continuous probability flows and Euler approximations of PDT. * [[Probability Dilation Theory/Worked Example]] – canonical binary example illustrating PDT transformations and geometry. [[Probability Dilation Theory/Decoherence Analogy and Simulation]] [[Probability Dilation Theory / Dilation Vector Field]] [[Probability Dilation Theory / Dilation Flows]] [[Probability Dilation Theory / Matrix Dilation Operators]] [[Probability Dilation Theory / Spectral Analysis of Matrix Dilation Operators]] [[Probability Dilation Theory/Normalized Probability Dilation Paper]] == Notation == Throughout PDT, the following notation is used: {| class="wikitable" ! Symbol ! Meaning |- | <math>P</math> | Probability measure |- | <math>P_n</math> | nth iterate of PDT |- | <math>T_D</math> | Probability dilation operator |- | <math>D(x)</math> | Dilation field |- | <math>Z(P,D)</math> | Normalization factor |- | <math>H(P)</math> | Shannon entropy |- | <math>d_F</math> | Fisher-Rao distance |- | <math>W_p</math> | Wasserstein distance |- | <math>\ell</math> | Logit coordinate |- | <math>PE</math> | Probability Element |} == Related probabilistic and geometric literature == Related literature on probabilistic dilation, conditioning behavior, geometric probability, and curvature-dependent probabilistic structure includes the following works: * Augustin, T.; Coolen, F. P. A.; de Cooman, G.; Troffaes, M. C. M. ''Introduction to Imprecise Probabilities''. Wiley, 2014. * Baryshnikov, Y.; Cao, Y.; Kahle, M.; Liu, J. (2024). ''Buffon’s problem on curved surfaces and Gaussian curvature''. ''Journal of Applied Probability''. Cambridge University Press. doi:10.1017/jpr.2024.19 * Herron, T.; Seidenfeld, T.; Wasserman, L. ''Divisive Conditioning: Further Results on Dilation''. Philosophy of Science, Vol. 64, No. 3, 1997. * Herron, T.; Seidenfeld, T.; Wasserman, L. ''Distention for Sets of Probabilities''. Annals of Mathematics and Artificial Intelligence, Vol. 45, 2005. * Moral, S.; Wilson, N. ''Dilation Properties of Coherent Nearly-Linear Models''. International Journal of Approximate Reasoning, Vol. 45, 2007. * Shannon, C. E. (1948). ''A Mathematical Theory of Communication''. ''Bell System Technical Journal'', 27(3), 379–423; 27(4), 623–656. Text and original figures © Howard Richardson. Original contributions by the author. Content is available under the Creative Commons Attribution-ShareAlike license (CC BY-SA) as required by Wikiversity. Reuse permitted with attribution. pj22rpfdfilqif2tdidjl4svl6hxpk4 2 322855 2823852 2823326 2026-08-21T09:52:03Z U3247927 3005952 added 1st social contribution 2823852 wikitext text/x-wiki == About me == I am a third year student in [[motivation and emotion]] at the [https://www.canberra.edu.au University of Canberra] Some of my hobbies include : [[File:Bread Ahead Baking Courses.jpg|thumb|Figure 1. I find baking exciting as there is no limits]] * [[w:Baking|Baking]] * Colouring * Cooking * Walking * Travelling [[File:Colouring pencils.jpg|thumb|'''Figure 2.''' Colouring pencils that can be used for creating art]] == Book chapter I'm working on == [[Motivation and emotion/Book/2026/Romantic entertainment and love beliefs|Romantic entertainment and love beliefs]] == Social contributions == #[https://uclearn.canberra.edu.au/courses/20143/discussion_topics/455151?entry_id=806188 Joined discord server that was shared on canvas] d8fxv2f8j7yxgj3e5fay18pnb5rmfux 0 323153 2823751 2823552 2026-08-20T22:51:27Z U3284040 3106549 /* Emotion */ 2823751 wikitext text/x-wiki {{/Banner}} ==Motivation== # [[/Adolescent risk-taking and reward-system development/]] - How does reward circuit maturation influence adolescent sensation-seeking and impulsive behaviours? {{ME-By|U3280843}} # [[/Akrasia/]] - Why do people act against their better judgement? {{ME-By|U3269672}} # [[/Artificial intelligence and academic motivation/]] - How does artificial intelligence influence students’ motivation to learn, engage, and achieve? {{ME-By|U3280097}} # [[/Attachment styles and relatedness motivation/]] - How do attachment styles affect the need for relatedness? 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U3261207 # [[/Role-play and communication skills training/]] - How does role-play facilitate the development of effective communication skills? {{ME-By|User Name}} # [[/Scarcity versus abundance mindset/]] - How do scarcity and abundance mindsets develop and what are the motivational consequences? {{ME-By|User Name}} # [[/Self-concept and motivation/]] - How does self-concept relate to motivation? {{ME-By|U3253363}} # [[/Self-determination theory and dementia care/]] - How can autonomy, competence, and relatedness be supported in people living with dementia? {{ME-By|Ella Kay244}} # [[/Self-determination theory and military veteran reintegration/]] - How do autonomy, competence, and relatedness shape psychological adjustment after military service? {{ME-By|U3246286}} # [[/Self-determination theory and physical activity/]] - How do autonomy, competence, and relatedness predict engagement in physical activity and exercise adherence? - [[User:U3275908|U3275908]] # [[/Self-determination theory and social media use/]] - How do basic psychological needs explain patterns of social media engagement? {{ME-By|GraceInMind}} # [[/Sensation-seeking and dopamine/]] - What is the neurobiological relationship between sensation-seeking and dopamine? {{ME-By|SunnySideUp1300}} # [[/Sex differences in sexual arousal patterns/]] - How do patterns of sexual arousal differ between males and females? {{ME-By|U3236349}} # [[/Sex work motivation/]] - What motivates sex work and how does this impact worker experiences? {{ME-By|U3261376}} # [[/Social dominance and power motivation/]] - What is the relationship between social dominance and power motivation? {{ME-By|U3284302}} # [[/Subcortical structures and motivational drive/]] - How do subcortical brain regions generate basic motivational impulses and energy? {{ME-By|U3281503}} # [[/Sun exposure and protection motivation/]] - What motivates sun exposure and protection behaviours? {{ME-By|U3188047}} # [[/Surrender motivation/]] - What is the motivational state of surrender and what are its impacts? {{ME-By|User Name}} # [[/The quiet ego and motivation/]] - How does a quiet ego balance self-interest with concern for others? {{ME-By|User Name}} # [[/Thermoregulation and motivation/]] - How does the drive to maintain body temperature influence behaviour? {{ME-By|User Name}} # [[/Tonic-phasic model of dopamine regulation/]] - What is the tonic/phasic model of dopamine regulation and how does affect behaviour? {{ME-By|User Mame}} # [[/Types of impulsivity/]] - What are the different types of impulsivity and how do they affect motivation? {{ME-By|User Name}} # [[/Value congruence and motivation/]] - How does alignment between personal and situational values influence motivation? {{ME-By|U3275775}} # [[/Volunteer counsellor motivation/]] - What motivates people to become and remain volunteer counsellors? {{ME-By|J.M.A Watson}} # [[/Windfall gain effect/]] - How doe unexpected wealth influence behaviour and decision-making? {{ME-By|User Name}} # [[/Youth environmental activism motivation/]] - What motivates young people to engage in environmental activism? {{ME-By|SJPiper}} ==Emotion== # [[/Active versus passive social media use/]] - How do different patterns of social media engagement influence emotions and psychological wellbeing? {{ME-By|U3282656}} # [[/Adaptive versus maladaptive self-reflection/]] - When does self-reflection promote wellbeing and when does it contribute to psychological distress? {{ME-By|U3211150}} # [[/Affect heuristic/]] - What is the affect heuristic and how does it influence decision making? {{ME-By|User Name}} # [[/Alcohol use for emotion regulation/]] - Why and how do people use alcohol to regulate their emotions? {{ME-By|U3284266}} # [[/Apocalyptic fear/]] - What is apocalyptic fear, what are its consequences, and how can it be dealt with? {{ME-By|LazPulch}} # [[/Awe and the diminished self/]] - How does awe diminish the self and how can this be applied? {{ME-By|User Name}} # [[/Awe and nature/]] - What is the relationship between awe and nature? {{ME-By|U3269915}} # [[/Biofeedback and emotion regulation/]] - How does biofeedback help individuals monitor and regulate their emotional states? {{ME-By|User Name}} # [[/Body neutrality and emotional well-being/]] - How does a body-neutral perspective affect emotional well-being? {{ME-By|AmyUniversity}} # [[/Breathing exercises and relaxation/]] - How can breathing exercises promote relaxation? {{ME-By|E3297976}} # [[/Cancer screening and emotion/]] - How do emotions such as fear, anxiety, and relief influence cancer screening uptake? {{ME-By|User Name}} # [[/Cognitive hardiness and stress resilience/]] - How does cognitive hardiness promote resilience to stress and adversity? {{ME-By|u3068253}} # [[/Cognitive versus affective empathy/]] - What are the differences between cognitive and affective empathy and how do they contribute to prosociality? {{ME-By|User Name}} # [[/Dark empathy/]] - What is dark empathy, what are its consequences, and what can be done to address it? {{ME-By|U3228742}} # [[/Dreams and emotional problem-solving/]] - How do REM dreams contribute to emotional processing and adaptive coping? {{ME-By|U3270398}} # [[/Durability bias in affective forecasting/]] - What role does durability bias play in affective forecasting? {{ME-By|User Name}} # [[/Eco-emotions/]] - What are eco-emotions, how do they influence behaviour, and how can they be managed? {{ME-By|User Name}} # [[/Emotional effects of incarceration on Indigenous Australians/]] - What are the emotional effects of incarcertation on Indigenous Australians? {{ME-By|Lilfish215}} # [[/Emotional expressivity/]] - What is emotional expressivity, why does it matter, and how can it be developed? {{ME-By|U3283812}} # [[/Emotional flooding in relationships/]] - Why does emotional flooding occur, how does it affect relationships, and what can be done about it? {{ME-By|Tofu05}} # [[/Emotional intelligence and emotional wellbeing/]] - How does emotional intelligence affect emotional wellbeing? {{ME-By|u3239236}} # [[/Emotional role-playing/]] - How does role-playing influence emotional experience, expression, and regulation? {{ME-By|User Name}} # [[/Emotion detection using artificial intelligence/]] - How can emotion be detected using artificial intelligence? {{ME-By|User Name}} # [[/Emotion dysregulation/]] - What is emotion dysregulation, what are its consequences, and how can it be managed? {{ME-By|U3285438}} # [[/Emotion regulation ability and strategy/]] - How do ability and strategy differ in shaping emotion regulation? {{ME-By|User Name}} # [[/Emotion regulation through exercise/]] - How do people use exercise to regulate their emotional states? {{ME-By|KB3250298}} # [[/Emotions in activism/]] - How do emotions motivate, shape, and sustain activism? {{ME-By|User Name}} # [[/Empathy and jury decision-making/]] - How does empathy toward defendants and victims influence jurors' reasoning and verdict decisions? {{ME-By|U3254168}} # [[/Empathy fatigue and emotional exhaustion/]] - How does sustained empathic engagement contribute to emotional exhaustion? {{ME-By|U3143751}} # [[/Enjoyment and learning/]] - How does enjoyment influence learning? {{ME-By|User Name}} # [[/Envy in the workplace/]] - What role does envy play in workplace behaviour? {{ME-By|Flickstar888}} # [[/Environmental volunteering and wellbeing/]] - How does participation in environmental volunteering influence volunteers' subjective wellbeing? {{ME-By|User Name}} # [[/Excitement as an emotion/]] - What is the emotional excitement and how does it influence behaviour and wellbeing? {{ME-By|U3292769}} # [[/Fear extinction/]] - What psychological and neural processes underlie the extinction of fear responses? {{ME-By|ChillPsychGuy0607}} # [[/Focalism in affective forecasting/]] - What is focalism and how does it bias predictions about future emotional experiences? {{ME-By|User Name}} # [[/Gloatrage/]] - What is gloatrage, what causes it, and what are its consequences? {{ME-By|User Name}} # [[/Growth mindset and psychological wellbeing/]] - How does a growth mindset influence psychological wellbeing? {{ME-By|Avj.06}} # [[/Human trust of robots/]] - What psychological factors shape human trust of robots? {{ME-By|User Name}} # [[/Identify exploration through role-playing games/]] - How do role-playing games facilitate identity exploration and self-discovery? {{ME-By|User Name}} # [[/Immersive therapy for PTSD treatment/]] - How does it work and what are the effects? {{ME-By|StretchBeyond}} # [[/Indigenous Australian funeral practices and grieving/]] - How do Indigenous Australian funeral practices assist with grieving? {{ME-By|User Name}} # [[/Interpersonal psychotherapy and emotion/]] - How does interpersonal psychotherapy improve emotional wellbeing through changes in relationships? {{ME-By|User Name}} # [[/Introjection and guilt-based motivation/]] - What role do shame and guilt play in introjected forms of behavioural regulation? {{ME-By|U3330981}} # [[/Irritability/]] - What is irritability, what causes it, what are its consequences, and how can it be managed? {{ME-By|U3275992}} # [[/Love styles and relationships/]] - How do love styles influence relationship satisfaction and stability? {{ME-By|U3246588}} # [[/Melatonin and seasonal mood/]] - What role does melatonin play in seasonal mood changes? {{ME-By|U3224236{{ME-By| # [[/Mental health first aid and helping behaviour/]] - What motivates people to recognise, approach, and support someone with a mental health problem? {{ME-By|Katelyn Rod}} # [[/Mindfulness and nature connectedness/]] - How does mindfulness influence nature connectedness? {{ME-By|User Name}} # [[/Mood and cognitive performance/]] - How do different mood states impact attention, memory, and problem solving? {{ME-By|U3283879}} # [[/Moodiness/]] - What is moodiness, why does it occur, and how can it be managed? {{ME-By|User Name}} # [[/Moral disgust and jury decision-making/]] - How does moral disgust influence jurors' judgments of guilt, blame, and punishment? {{ME-By|Yellowvines}} # [[/Neurobiology of love/]] - What neural systems and biochemical processes underlie love? {{ME-By|Honeybelle11}} # [[/Neurofeedback and emotional regulation/]] - How can neurofeedback influence enhance emotional regulation? {{ME-By|User Name}} # [[/Nitrous oxide and emotion/]] - How does nitrous oxide influence emotional experience and mood? {{ME-By|User Name}} # [[/Noise and emotion/]] - How do different types of noise affect emotional experience and wellbeing? {{ME-By|User Name}} # [[/Opponent process theory and emotion/]] - What role do opposing affective states play in emotional experience? {{ME-By|User Name}} # [[/Outdoor play and children's emotional well-being/]] - How does outdoor play influence children's emotional well-being? {{ME-By|Mymunu}} # [[/Perfectionism and athlete mental health/]] - How does perfectionism affect athlete mental health? {{ME-By|Leilab23}} # [[/Phubbing and emotion/]] - What are the emotional causes and consequences of phubbing? {{ME-By|U3243961}} # [[/Positive emotion dysregulation/]] - What is positive emotion dysregulation and how does it affect psychological functioning? {{ME-By|P U3270518}} # [[/Psychological preparation for natural disasters/]] - How can people psychologically prepare for natural disasters? {{ME-By|User Name}} # [[/Psychological safety and feedback uptake/]] - How does psychological safety influence openness to feedback? {{ME-By|User Name}} # [[/Reflected glory/]] - What is reflected glory and what are its pros and cons? {{ME-By|User Name}} # [[/Remote work and well-being/]] - How does remote work influence employee well-being? {{ME-By|User Name}} # [[/Responsiveness and interpersonal trust/]] - How does responsiveness foster trust in relationships? {{ME-By|U3282586}} # [[/Romantic entertainment and love beliefs/]] - How do romantic entertainment influence beliefs and expectations about love and romantic relationships? {{ME-By|U3247927}} # [[/Romantic jealousy/]] - Why does romantic jealousy occur, what are its impacts, and how can it be managed?{{ME-By|U3279062}} # [[/Secondary trauma in healthcare workers/]] - What are the emotional consequences of secondary trauma in healthcare settings? {{ME-By|U3257744}} # [[/Seasonal affective disorder/]] - What is SAD, why does it occur, and how can it be managed? {{ME-By|Greg Philips}} # [[/Self-blame and emotion/]] - How does self-blame influence emotional responses to negative events? {{ME-By|User Name}} # [[/Self-disclosure and emotional intimacy/]] - How does self-disclosure foster emotional closeness in relationships? {{ME-By|U3283302}} # [[/Self-stigma and emotion/]] - How does self-stigma impact emotional well-being? {{ME-By|User Name}} # [[/Social connection and emotion regulation/]] - How do social relationships help regulate people's emotions? {{ME-By|U3284040}} # [[/Socioemotional selectivity theory and wellbeing in ageing/]] - How do social and emotional experiences affect wellbeing as people age? {{ME-By|User Name}} # [[/Spirituality and resilience/]] - What is the relationship between spirituality and psychological resilience? {{ME-By|User Name}} # [[/Subjective wellbeing homeostasis theory/]] - How does homeostatic theory explain the stability and regulation of subjective wellbeing? {{ME-By|User Name}} # [[/Technology-based pain management/]] - How can technology-based tools alter pain perception and pain management? {{ME-By|ChelsSchofield}} # [[/Theory of positive disintegration and personal growth/]] - What is the TPD and how can it be applied to personal growth? {{ME-By|User Name}} # [[/Time perception in mood disorders/]] - How do anxiety and depression alter the subjective experience of time? {{ME-By|User Name}} # [[/Trust in artificial intelligence/]] - What psychological factors shape human trust of artificial intelligence systems? {{ME-By|User Name}} # [[/Trust rebuilding after trauma/]] - How can trauma survivors develop trust in similar situations again? {{ME-By|User Name}} # [[/Volunteer wellbeing/]] - How does volunteering affect volunteer's subjective wellbeing? {{ME-By|U3216851}} # [[/Wayfinding and affective experience/]] - How do emotions influence navigation and spatial behaviour? {{ME-By|User Name}} ==Motivation and emotion== # [[/Boredom and interest/]] - How do boredom and interest shape emotional and motivational states? {{ME-By|U3239431}} # [[/Falling in love/]] - What motivational and emotional processes underlie romantic attraction and falling in love? {{ME-By|Mort006}} # [[/Life purpose and well-being/]] - How does a sense of purpose contribute to well-being and how can it be cultivated? {{ME-By|U3286962}} # [[/Moral emotions and ethical behaviour/]] - How do moral emotions motivate ethical and prosocial action? {{ME-By|U3263365}} # [[/Oxytocin as a neuromodulator/]] - What are the motivational and emotional effects of oxytocin as a neuromodulator? {{ME-By|User Name}} # [[/Reward prediction error/]] - How does discrepancy between expected and actual rewards influence learning, emotion, and motivation? {{ME-By|User Name}} # [[/Reinforcement sensitivity theory/]] - How does reinforcement sensitivity theory explain individual differences in motivation and emotion? {{ME-By|User Name}} # [[/Reward prediction error/]] - How do reward prediction errors influence learning, emotion, and motivation? {{ME-By|User Name}} # [[/Social and emotional well-being in Indigenous Australians/]] - How does the holistic social and emotional well-being model reframe Indigenous Australian health and well-being? {{ME-By|User Name}} # [[/Strengths-based Indigenous Australian psychology/]] - How can strengths-based perspectives enhance understanding of Indigenous motivation and emotion? {{ME-By|User Name}} # [[/Warm-glow giving/]] - Why does giving feel good and how does this influence prosocial behaviour? {{ME-By|User Name}} # [[/Wisdom, motivation, and emotion/]] - How do motivational and emotional processes contribute to wisdom? {{ME-By|User Name}} [[Category:Motivation and emotion/Book/2026]] 0lhrtihu2frnekvoa3t1g86qnv09lno 2823816 2823751 2026-08-21T04:32:37Z Jtneill 10242 Fix user name 2823816 wikitext text/x-wiki {{/Banner}} ==Motivation== # [[/Adolescent risk-taking and reward-system development/]] - How does reward circuit maturation influence adolescent sensation-seeking and impulsive behaviours? {{ME-By|U3280843}} # [[/Akrasia/]] - Why do people act against their better judgement? {{ME-By|U3269672}} # [[/Artificial intelligence and academic motivation/]] - How does artificial intelligence influence students’ motivation to learn, engage, and achieve? {{ME-By|U3280097}} # [[/Attachment styles and relatedness motivation/]] - How do attachment styles affect the need for relatedness? {{ME-By|HawaSA}} # [[/Athletic identity loss and returning to sport after injury/]] - How does injury related disruption to athletic identity affect motivation to return to sport? {{ME-By|Tammysaurus}} # [[/Automaticity and goal pursuit/]] - How do habits and environmental cues drive unconscious goal pursuit? {{ME-By|Revial76}} # [[/Basal ganglia and motivation/]] - What is the role of the basal ganglia in motivated behaviour? {{ME-By|U3233213}} # [[/Building therapeutic alliance/]] - What psychological factors contribute to the development of a strong therapeutic alliance? {{ME-By|Amirrorslens}} # [[/Charismatic leadership and follower motivation/]] - How does charismatic leadership inspire follower motivation? {{ME-By|U3275984}} # [[/Citizen science motivation/]] - What motivates participation in citizen science projects? {{ME-By|User Name}} # [[/Competence motivation in self-determination theory/]] - How does the need for competence function within self-determination theory to shape motivation and behaviour? {{ME-By|User Name}} # [[/Consumer emotion measurement/]] - How can consumer emotion be measured? {{ME-By|Sienna33309}} # [[/Creative inspiration and effort/]] - How do inspiration and effort interact during the creative process? {{ME-By|User Name}} # [[/Deliberative vs implemental mindset/]] - What are the motivational and cognitive differences between deliberative and implemental mindsets? {{ME-By|User Name}} # [[/Developing a growth mindset/]] - How can a growth mindset be cultivated and sustained? {{ME-By|LMM26}} # [[/Dopamine and reward prediction/]] - How does dopamine affect the anticipation of rewards and subsequent emotional responses? {{ME-By|U3228742}} # [[/Effort regulation and cost-benefit decision-making/]] - How is effort dynamically adjusted based on changing cost-benefit analysis during goal pursuit? {{ME-By|User Name}} # [[/End-of-history illusion and motivation/]] - How does the EOHI influence motivation and what strategies mitigate its impact? {{ME-By|User Name}} # [[/ERG theory and motivation/]] - What is Alderfer's ERG theory and how does it explain human motivation? {{ME-By|User Name}} # [[/Epistemic motivation and the need for cognitive closure/]] - How does epistematic motivation and the need for cognitive closure influence our lives? {{ME-By|U3221734}} # [[/Exercise gamification motivation/]] - How can gamification affect exercise motivation and behaviour? {{ME-By|U3260591}} # [[/Expectancy-value theory of educational motivation/|Expectancy-value theory of educational motivation]] - What is expectancy-value theory and how can it be applied to understand and enhance educational motivation? {{ME-By|StudentUC2026}} # [[/Extended process model of emotion regulation/]] - What is the extended process model and how does it explain how people regulate emotions? {{ME-By|U3259641}} # [[/Feedback literacy/]] - What is feedback literacy, why does it matter, and how can it be developed? {{ME-By|User Name}} # [[/Fogg behaviour model/]] - How can the FBM be applied to understanding and changing behaviour? {{ME-By|User Name}} # [[/Functional motives theory and environmental activism/]] - How does functional motives theory explain the motivations behind environmental activism? {{ME-By|User Name}} # [[/Future orientation and criminal behaviour/]] - How does future orientation influence the risk of criminal activity? {{ME-By|U3275899}} # [[/Game of dice task and decision-making/]] - What does the game of dice task reveal about risk-based decision-making? {{ME-By|U3216724}} # [[/Gender and achievement motivation/]] - How does gender shape where, how, and under what conditions achievement motivation is expressed? {{ME-By|U3242837}} # [[/Generativity/]] - What is generativity and how does it impact behaviour and life outcomes? {{ME-By|Monuc9}} # [[/Getting started/]] - Why is task initiation difficult and how to overcome it? {{ME-By|U3286643}} # [[/Goal striving dynamics/]] - What is the role of pushing and coasting in goal striving? {{ME-By|User Name}} # [[/Hygiene motivation/]] - What motivates maintenance of personal hygiene? {{ME-By|U3275940}} # [[/Hypothalamus and homeostatic motivation/]] - How do hypothalamic circuits regulate hunger, thirst, and other survival-related motivations? {{ME-By|User Name}} # [[/Impulsivity versus sensation-seeking/]] - What is the distinction between impulsivity and sensation-seeking and how does this affect behaviour? {{ME-By|Reillyu3280706}} # [[/Indigenous Australian role models and motivation/]] - How do role models influence aspirations, identity development, and motivation among Indigenous Australians? {{ME-By|Jshottt}} # [[/Interrogation and compliance/]] - What psychological processes influence resistance and compliance during interrogation? {{ME-By|U3283643}} # [[/Investment model of commitment and social motivation/]] - How does the investment model of commitment relate to social motivation? {{ME-By|User Name}} # [[/Lifelong learning motivation/]] - What motivates lifelong learning? {{ME-By|U3280251}} # [[/Machiavellian motivation/]] - What is the motivational role of Machiavellianism? {{ME-By|Mim0502}} # [[/Mesolimbic pathway and addiction motivation/]] - What role does the ventral tegmental area to nucleus accumbens pathway play in addictive behaviours? {{ME-By|U3280499}} # [[/Metacognitive monitoring and productivity/]] - How does metacognitive monitoring influence goal attainment and productivity? {{ME-By|User Name}} # [[/Mindsets and stigma/]] - What role do growth versus fixed mindsets play in prejudice and stigma? {{ME-By|U3275909}} # [[/Motivations for using sex work services/]] - What motivates use of sex work services? {{ME-By|U3261236}} # [[/Motivating virtual teams/]] - How can motivation in virtual teams be optimised? {{ME-By|User Name}} # [[/Motivational effects of incarceration on Indigenous Australians/]] - What are the motivational effects of incarcertation on Indigenous Australians?{{ME-By|U3183521}} # [[/Need to love and be loved/]] - How does the desire to give and receive love influence motivation? {{ME-By|U3280743}} # [[/Non-residential energy conservation motivation/]] - How can non-residential building energy conservation be motivated and behaviour changed? {{ME-By|User Name}} # [[/Occupational violence, emotion, and coping/]] - What are the emotional impacts of occupational violence and how can employees cope? # [[/Overconfidence in decision-making/]] - How does overconfidence bias affect judgement and decision-making? {{ME-By|BellaJohnson1}} # [[/Parental educational aspirations and student achievement/]] - How do parental aspirations shape children’s academic motivation and performance? {{ME-By|User Name}} # [[/Parental motivations for homeschooling/]] - What motivates parents to homeschool their children? {{ME-By|User Name}} # [[/Perfectionism and procrastination/]] - What is the role of perfectionism in procrastination and what can be done about it? {{ME-By|U3222012}} # [[/Pleasure anticipation and dopamine/]] - How does the brain's reward system generate motivation through expected rather than experienced pleasure? u3284308 # [[/Possible selves and goal pursuit/]] - How do possible selves influence motivation and goal-directed behaviour? {{ME-By|Jack4234}} # [[/Power motivation in leadership/]] - How does power motivation influence leadership styles and effectiveness? {{ME-By|PsychstudentUniversity!}} # [[/Prevention versus promotion mindset/]] - What are the motivational differences between prevention and promotion mindsets? {{ME-By|Bronte.H}} # [[/Protection motivation theory and environmental behaviour/]] - How does protection motivation theory explain engagement in pro-environmental behaviour? {{ME-By|User Name}} # [[/Relatedness motivation in self-determination theory/]] - How does the need for relatedness function within self-determination theory to shape motivation and behaviour? {{ME-By|User Name}} # [[/Retirement motivation/]] - What motivates retirement from work? U3261207 # [[/Role-play and communication skills training/]] - How does role-play facilitate the development of effective communication skills? {{ME-By|User Name}} # [[/Scarcity versus abundance mindset/]] - How do scarcity and abundance mindsets develop and what are the motivational consequences? {{ME-By|User Name}} # [[/Self-concept and motivation/]] - How does self-concept relate to motivation? {{ME-By|U3253363}} # [[/Self-determination theory and dementia care/]] - How can autonomy, competence, and relatedness be supported in people living with dementia? {{ME-By|Ella Kay244}} # [[/Self-determination theory and military veteran reintegration/]] - How do autonomy, competence, and relatedness shape psychological adjustment after military service? {{ME-By|U3246286}} # [[/Self-determination theory and physical activity/]] - How do autonomy, competence, and relatedness predict engagement in physical activity and exercise adherence? - [[User:U3275908|U3275908]] # [[/Self-determination theory and social media use/]] - How do basic psychological needs explain patterns of social media engagement? {{ME-By|GraceInMind}} # [[/Sensation-seeking and dopamine/]] - What is the neurobiological relationship between sensation-seeking and dopamine? {{ME-By|SunnySideUp1300}} # [[/Sex differences in sexual arousal patterns/]] - How do patterns of sexual arousal differ between males and females? {{ME-By|U3236349}} # [[/Sex work motivation/]] - What motivates sex work and how does this impact worker experiences? {{ME-By|U3261376}} # [[/Social dominance and power motivation/]] - What is the relationship between social dominance and power motivation? {{ME-By|U3284302}} # [[/Subcortical structures and motivational drive/]] - How do subcortical brain regions generate basic motivational impulses and energy? {{ME-By|U3281503}} # [[/Sun exposure and protection motivation/]] - What motivates sun exposure and protection behaviours? {{ME-By|U3188047}} # [[/Surrender motivation/]] - What is the motivational state of surrender and what are its impacts? {{ME-By|User Name}} # [[/The quiet ego and motivation/]] - How does a quiet ego balance self-interest with concern for others? {{ME-By|User Name}} # [[/Thermoregulation and motivation/]] - How does the drive to maintain body temperature influence behaviour? {{ME-By|User Name}} # [[/Tonic-phasic model of dopamine regulation/]] - What is the tonic/phasic model of dopamine regulation and how does affect behaviour? {{ME-By|User Mame}} # [[/Types of impulsivity/]] - What are the different types of impulsivity and how do they affect motivation? {{ME-By|User Name}} # [[/Value congruence and motivation/]] - How does alignment between personal and situational values influence motivation? {{ME-By|U3275775}} # [[/Volunteer counsellor motivation/]] - What motivates people to become and remain volunteer counsellors? {{ME-By|J.M.A Watson}} # [[/Windfall gain effect/]] - How doe unexpected wealth influence behaviour and decision-making? {{ME-By|User Name}} # [[/Youth environmental activism motivation/]] - What motivates young people to engage in environmental activism? {{ME-By|SJPiper}} ==Emotion== # [[/Active versus passive social media use/]] - How do different patterns of social media engagement influence emotions and psychological wellbeing? {{ME-By|U3282656}} # [[/Adaptive versus maladaptive self-reflection/]] - When does self-reflection promote wellbeing and when does it contribute to psychological distress? {{ME-By|U3211150}} # [[/Affect heuristic/]] - What is the affect heuristic and how does it influence decision making? {{ME-By|User Name}} # [[/Alcohol use for emotion regulation/]] - Why and how do people use alcohol to regulate their emotions? {{ME-By|U3284266}} # [[/Apocalyptic fear/]] - What is apocalyptic fear, what are its consequences, and how can it be dealt with? {{ME-By|LazPulch}} # [[/Awe and the diminished self/]] - How does awe diminish the self and how can this be applied? {{ME-By|User Name}} # [[/Awe and nature/]] - What is the relationship between awe and nature? {{ME-By|U3269915}} # [[/Biofeedback and emotion regulation/]] - How does biofeedback help individuals monitor and regulate their emotional states? {{ME-By|User Name}} # [[/Body neutrality and emotional well-being/]] - How does a body-neutral perspective affect emotional well-being? {{ME-By|AmyUniversity}} # [[/Breathing exercises and relaxation/]] - How can breathing exercises promote relaxation? {{ME-By|E3297976}} # [[/Cancer screening and emotion/]] - How do emotions such as fear, anxiety, and relief influence cancer screening uptake? {{ME-By|User Name}} # [[/Cognitive hardiness and stress resilience/]] - How does cognitive hardiness promote resilience to stress and adversity? {{ME-By|u3068253}} # [[/Cognitive versus affective empathy/]] - What are the differences between cognitive and affective empathy and how do they contribute to prosociality? {{ME-By|User Name}} # [[/Dark empathy/]] - What is dark empathy, what are its consequences, and what can be done to address it? {{ME-By|U3228742}} # [[/Dreams and emotional problem-solving/]] - How do REM dreams contribute to emotional processing and adaptive coping? {{ME-By|U3270398}} # [[/Durability bias in affective forecasting/]] - What role does durability bias play in affective forecasting? {{ME-By|User Name}} # [[/Eco-emotions/]] - What are eco-emotions, how do they influence behaviour, and how can they be managed? {{ME-By|User Name}} # [[/Emotional effects of incarceration on Indigenous Australians/]] - What are the emotional effects of incarcertation on Indigenous Australians? {{ME-By|Lilfish215}} # [[/Emotional expressivity/]] - What is emotional expressivity, why does it matter, and how can it be developed? {{ME-By|U3283812}} # [[/Emotional flooding in relationships/]] - Why does emotional flooding occur, how does it affect relationships, and what can be done about it? {{ME-By|Tofu05}} # [[/Emotional intelligence and emotional wellbeing/]] - How does emotional intelligence affect emotional wellbeing? {{ME-By|u3239236}} # [[/Emotional role-playing/]] - How does role-playing influence emotional experience, expression, and regulation? {{ME-By|User Name}} # [[/Emotion detection using artificial intelligence/]] - How can emotion be detected using artificial intelligence? {{ME-By|User Name}} # [[/Emotion dysregulation/]] - What is emotion dysregulation, what are its consequences, and how can it be managed? {{ME-By|U3285438}} # [[/Emotion regulation ability and strategy/]] - How do ability and strategy differ in shaping emotion regulation? {{ME-By|User Name}} # [[/Emotion regulation through exercise/]] - How do people use exercise to regulate their emotional states? {{ME-By|KB3250298}} # [[/Emotions in activism/]] - How do emotions motivate, shape, and sustain activism? {{ME-By|User Name}} # [[/Empathy and jury decision-making/]] - How does empathy toward defendants and victims influence jurors' reasoning and verdict decisions? {{ME-By|U3254168}} # [[/Empathy fatigue and emotional exhaustion/]] - How does sustained empathic engagement contribute to emotional exhaustion? {{ME-By|U3143751}} # [[/Enjoyment and learning/]] - How does enjoyment influence learning? {{ME-By|User Name}} # [[/Envy in the workplace/]] - What role does envy play in workplace behaviour? {{ME-By|Flickstar888}} # [[/Environmental volunteering and wellbeing/]] - How does participation in environmental volunteering influence volunteers' subjective wellbeing? {{ME-By|User Name}} # [[/Excitement as an emotion/]] - What is the emotional excitement and how does it influence behaviour and wellbeing? {{ME-By|U3292769}} # [[/Fear extinction/]] - What psychological and neural processes underlie the extinction of fear responses? {{ME-By|ChillPsychGuy0607}} # [[/Focalism in affective forecasting/]] - What is focalism and how does it bias predictions about future emotional experiences? {{ME-By|User Name}} # [[/Gloatrage/]] - What is gloatrage, what causes it, and what are its consequences? {{ME-By|User Name}} # [[/Growth mindset and psychological wellbeing/]] - How does a growth mindset influence psychological wellbeing? {{ME-By|Avj.06}} # [[/Human trust of robots/]] - What psychological factors shape human trust of robots? {{ME-By|User Name}} # [[/Identify exploration through role-playing games/]] - How do role-playing games facilitate identity exploration and self-discovery? {{ME-By|User Name}} # [[/Immersive therapy for PTSD treatment/]] - How does it work and what are the effects? {{ME-By|StretchBeyond}} # [[/Indigenous Australian funeral practices and grieving/]] - How do Indigenous Australian funeral practices assist with grieving? {{ME-By|User Name}} # [[/Interpersonal psychotherapy and emotion/]] - How does interpersonal psychotherapy improve emotional wellbeing through changes in relationships? {{ME-By|User Name}} # [[/Introjection and guilt-based motivation/]] - What role do shame and guilt play in introjected forms of behavioural regulation? {{ME-By|U3330981}} # [[/Irritability/]] - What is irritability, what causes it, what are its consequences, and how can it be managed? {{ME-By|U3275992}} # [[/Love styles and relationships/]] - How do love styles influence relationship satisfaction and stability? {{ME-By|U3246588}} # [[/Melatonin and seasonal mood/]] - What role does melatonin play in seasonal mood changes? {{ME-By|U3224236{{ME-By| # [[/Mental health first aid and helping behaviour/]] - What motivates people to recognise, approach, and support someone with a mental health problem? {{ME-By|Katelyn Rod}} # [[/Mindfulness and nature connectedness/]] - How does mindfulness influence nature connectedness? {{ME-By|User Name}} # [[/Mood and cognitive performance/]] - How do different mood states impact attention, memory, and problem solving? {{ME-By|U3283879}} # [[/Moodiness/]] - What is moodiness, why does it occur, and how can it be managed? {{ME-By|User Name}} # [[/Moral disgust and jury decision-making/]] - How does moral disgust influence jurors' judgments of guilt, blame, and punishment? {{ME-By|Yellowvines}} # [[/Neurobiology of love/]] - What neural systems and biochemical processes underlie love? {{ME-By|Honeybelle11}} # [[/Neurofeedback and emotional regulation/]] - How can neurofeedback influence enhance emotional regulation? {{ME-By|User Name}} # [[/Nitrous oxide and emotion/]] - How does nitrous oxide influence emotional experience and mood? {{ME-By|User Name}} # [[/Noise and emotion/]] - How do different types of noise affect emotional experience and wellbeing? {{ME-By|User Name}} # [[/Opponent process theory and emotion/]] - What role do opposing affective states play in emotional experience? {{ME-By|User Name}} # [[/Outdoor play and children's emotional well-being/]] - How does outdoor play influence children's emotional well-being? {{ME-By|Mymunu}} # [[/Perfectionism and athlete mental health/]] - How does perfectionism affect athlete mental health? {{ME-By|Leilab23}} # [[/Phubbing and emotion/]] - What are the emotional causes and consequences of phubbing? {{ME-By|U3243961}} # [[/Positive emotion dysregulation/]] - What is positive emotion dysregulation and how does it affect psychological functioning? {{ME-By|P U3270518}} # [[/Psychological preparation for natural disasters/]] - How can people psychologically prepare for natural disasters? {{ME-By|User Name}} # [[/Psychological safety and feedback uptake/]] - How does psychological safety influence openness to feedback? {{ME-By|User Name}} # [[/Reflected glory/]] - What is reflected glory and what are its pros and cons? {{ME-By|User Name}} # [[/Remote work and well-being/]] - How does remote work influence employee well-being? {{ME-By|User Name}} # [[/Responsiveness and interpersonal trust/]] - How does responsiveness foster trust in relationships? {{ME-By|U3282586}} # [[/Romantic entertainment and love beliefs/]] - How do romantic entertainment influence beliefs and expectations about love and romantic relationships? {{ME-By|U3247927}} # [[/Romantic jealousy/]] - Why does romantic jealousy occur, what are its impacts, and how can it be managed?{{ME-By|U3279062}} # [[/Secondary trauma in healthcare workers/]] - What are the emotional consequences of secondary trauma in healthcare settings? {{ME-By|U3257744}} # [[/Seasonal affective disorder/]] - What is SAD, why does it occur, and how can it be managed? {{ME-By|Greg Philips}} # [[/Self-blame and emotion/]] - How does self-blame influence emotional responses to negative events? {{ME-By|User Name}} # [[/Self-disclosure and emotional intimacy/]] - How does self-disclosure foster emotional closeness in relationships? {{ME-By|U3283302}} # [[/Self-stigma and emotion/]] - How does self-stigma impact emotional well-being? {{ME-By|User Name}} # [[/Social connection and emotion regulation/]] - How do social relationships help regulate people's emotions? {{ME-By|U3284040}} # [[/Socioemotional selectivity theory and wellbeing in ageing/]] - How do social and emotional experiences affect wellbeing as people age? {{ME-By|User Name}} # [[/Spirituality and resilience/]] - What is the relationship between spirituality and psychological resilience? {{ME-By|User Name}} # [[/Subjective wellbeing homeostasis theory/]] - How does homeostatic theory explain the stability and regulation of subjective wellbeing? {{ME-By|User Name}} # [[/Technology-based pain management/]] - How can technology-based tools alter pain perception and pain management? {{ME-By|ChelsSchofield}} # [[/Theory of positive disintegration and personal growth/]] - What is the TPD and how can it be applied to personal growth? {{ME-By|User Name}} # [[/Time perception in mood disorders/]] - How do anxiety and depression alter the subjective experience of time? {{ME-By|User Name}} # [[/Trust in artificial intelligence/]] - What psychological factors shape human trust of artificial intelligence systems? {{ME-By|User Name}} # [[/Trust rebuilding after trauma/]] - How can trauma survivors develop trust in similar situations again? {{ME-By|User Name}} # [[/Volunteer wellbeing/]] - How does volunteering affect volunteer's subjective wellbeing? {{ME-By|U3216851}} # [[/Wayfinding and affective experience/]] - How do emotions influence navigation and spatial behaviour? {{ME-By|User Name}} ==Motivation and emotion== # [[/Boredom and interest/]] - How do boredom and interest shape emotional and motivational states? {{ME-By|U3239431}} # [[/Falling in love/]] - What motivational and emotional processes underlie romantic attraction and falling in love? {{ME-By|Mort006}} # [[/Life purpose and well-being/]] - How does a sense of purpose contribute to well-being and how can it be cultivated? {{ME-By|U3286962}} # [[/Moral emotions and ethical behaviour/]] - How do moral emotions motivate ethical and prosocial action? {{ME-By|U3263365}} # [[/Oxytocin as a neuromodulator/]] - What are the motivational and emotional effects of oxytocin as a neuromodulator? {{ME-By|User Name}} # [[/Reward prediction error/]] - How does discrepancy between expected and actual rewards influence learning, emotion, and motivation? {{ME-By|User Name}} # [[/Reinforcement sensitivity theory/]] - How does reinforcement sensitivity theory explain individual differences in motivation and emotion? {{ME-By|User Name}} # [[/Reward prediction error/]] - How do reward prediction errors influence learning, emotion, and motivation? {{ME-By|User Name}} # [[/Social and emotional well-being in Indigenous Australians/]] - How does the holistic social and emotional well-being model reframe Indigenous Australian health and well-being? {{ME-By|User Name}} # [[/Strengths-based Indigenous Australian psychology/]] - How can strengths-based perspectives enhance understanding of Indigenous motivation and emotion? {{ME-By|User Name}} # [[/Warm-glow giving/]] - Why does giving feel good and how does this influence prosocial behaviour? {{ME-By|User Name}} # [[/Wisdom, motivation, and emotion/]] - How do motivational and emotional processes contribute to wisdom? {{ME-By|User Name}} [[Category:Motivation and emotion/Book/2026]] s53dj5nozwqb3ol0vx73dpx3uvg2y1l 2823818 2823816 2026-08-21T04:34:15Z Jtneill 10242 Fix user name 2823818 wikitext text/x-wiki {{/Banner}} ==Motivation== # [[/Adolescent risk-taking and reward-system development/]] - How does reward circuit maturation influence adolescent sensation-seeking and impulsive behaviours? {{ME-By|U3280843}} # [[/Akrasia/]] - Why do people act against their better judgement? {{ME-By|U3269672}} # [[/Artificial intelligence and academic motivation/]] - How does artificial intelligence influence students’ motivation to learn, engage, and achieve? {{ME-By|U3280097}} # [[/Attachment styles and relatedness motivation/]] - How do attachment styles affect the need for relatedness? {{ME-By|HawaSA}} # [[/Athletic identity loss and returning to sport after injury/]] - How does injury related disruption to athletic identity affect motivation to return to sport? {{ME-By|Tammysaurus}} # [[/Automaticity and goal pursuit/]] - How do habits and environmental cues drive unconscious goal pursuit? {{ME-By|Revial76}} # [[/Basal ganglia and motivation/]] - What is the role of the basal ganglia in motivated behaviour? {{ME-By|U3233213}} # [[/Building therapeutic alliance/]] - What psychological factors contribute to the development of a strong therapeutic alliance? {{ME-By|Amirrorslens}} # [[/Charismatic leadership and follower motivation/]] - How does charismatic leadership inspire follower motivation? {{ME-By|U3275984}} # [[/Citizen science motivation/]] - What motivates participation in citizen science projects? {{ME-By|User Name}} # [[/Competence motivation in self-determination theory/]] - How does the need for competence function within self-determination theory to shape motivation and behaviour? {{ME-By|User Name}} # [[/Consumer emotion measurement/]] - How can consumer emotion be measured? {{ME-By|Sienna33309}} # [[/Creative inspiration and effort/]] - How do inspiration and effort interact during the creative process? {{ME-By|User Name}} # [[/Deliberative vs implemental mindset/]] - What are the motivational and cognitive differences between deliberative and implemental mindsets? {{ME-By|User Name}} # [[/Developing a growth mindset/]] - How can a growth mindset be cultivated and sustained? {{ME-By|LMM26}} # [[/Dopamine and reward prediction/]] - How does dopamine affect the anticipation of rewards and subsequent emotional responses? {{ME-By|U3228742}} # [[/Effort regulation and cost-benefit decision-making/]] - How is effort dynamically adjusted based on changing cost-benefit analysis during goal pursuit? {{ME-By|User Name}} # [[/End-of-history illusion and motivation/]] - How does the EOHI influence motivation and what strategies mitigate its impact? {{ME-By|User Name}} # [[/ERG theory and motivation/]] - What is Alderfer's ERG theory and how does it explain human motivation? {{ME-By|User Name}} # [[/Epistemic motivation and the need for cognitive closure/]] - How does epistematic motivation and the need for cognitive closure influence our lives? {{ME-By|U3221734}} # [[/Exercise gamification motivation/]] - How can gamification affect exercise motivation and behaviour? {{ME-By|U3260591}} # [[/Expectancy-value theory of educational motivation/|Expectancy-value theory of educational motivation]] - What is expectancy-value theory and how can it be applied to understand and enhance educational motivation? {{ME-By|StudentUC2026}} # [[/Extended process model of emotion regulation/]] - What is the extended process model and how does it explain how people regulate emotions? {{ME-By|U3259641}} # [[/Feedback literacy/]] - What is feedback literacy, why does it matter, and how can it be developed? {{ME-By|User Name}} # [[/Fogg behaviour model/]] - How can the FBM be applied to understanding and changing behaviour? {{ME-By|User Name}} # [[/Functional motives theory and environmental activism/]] - How does functional motives theory explain the motivations behind environmental activism? {{ME-By|User Name}} # [[/Future orientation and criminal behaviour/]] - How does future orientation influence the risk of criminal activity? {{ME-By|U3275899}} # [[/Game of dice task and decision-making/]] - What does the game of dice task reveal about risk-based decision-making? {{ME-By|U3216724}} # [[/Gender and achievement motivation/]] - How does gender shape where, how, and under what conditions achievement motivation is expressed? {{ME-By|U3242837}} # [[/Generativity/]] - What is generativity and how does it impact behaviour and life outcomes? {{ME-By|Monuc9}} # [[/Getting started/]] - Why is task initiation difficult and how to overcome it? {{ME-By|U3286643}} # [[/Goal striving dynamics/]] - What is the role of pushing and coasting in goal striving? {{ME-By|User Name}} # [[/Hygiene motivation/]] - What motivates maintenance of personal hygiene? {{ME-By|U3275940}} # [[/Hypothalamus and homeostatic motivation/]] - How do hypothalamic circuits regulate hunger, thirst, and other survival-related motivations? {{ME-By|User Name}} # [[/Impulsivity versus sensation-seeking/]] - What is the distinction between impulsivity and sensation-seeking and how does this affect behaviour? {{ME-By|Reillyu3280706}} # [[/Indigenous Australian role models and motivation/]] - How do role models influence aspirations, identity development, and motivation among Indigenous Australians? {{ME-By|Jshottt}} # [[/Interrogation and compliance/]] - What psychological processes influence resistance and compliance during interrogation? {{ME-By|U3283643}} # [[/Investment model of commitment and social motivation/]] - How does the investment model of commitment relate to social motivation? {{ME-By|User Name}} # [[/Lifelong learning motivation/]] - What motivates lifelong learning? {{ME-By|U3280251}} # [[/Machiavellian motivation/]] - What is the motivational role of Machiavellianism? {{ME-By|Mim0502}} # [[/Mesolimbic pathway and addiction motivation/]] - What role does the ventral tegmental area to nucleus accumbens pathway play in addictive behaviours? {{ME-By|U3280499}} # [[/Metacognitive monitoring and productivity/]] - How does metacognitive monitoring influence goal attainment and productivity? {{ME-By|User Name}} # [[/Mindsets and stigma/]] - What role do growth versus fixed mindsets play in prejudice and stigma? {{ME-By|U3275909}} # [[/Motivations for using sex work services/]] - What motivates use of sex work services? {{ME-By|U3261236}} # [[/Motivating virtual teams/]] - How can motivation in virtual teams be optimised? {{ME-By|User Name}} # [[/Motivational effects of incarceration on Indigenous Australians/]] - What are the motivational effects of incarcertation on Indigenous Australians?{{ME-By|U3183521}} # [[/Need to love and be loved/]] - How does the desire to give and receive love influence motivation? {{ME-By|U3280743}} # [[/Non-residential energy conservation motivation/]] - How can non-residential building energy conservation be motivated and behaviour changed? {{ME-By|User Name}} # [[/Occupational violence, emotion, and coping/]] - What are the emotional impacts of occupational violence and how can employees cope? # [[/Overconfidence in decision-making/]] - How does overconfidence bias affect judgement and decision-making? {{ME-By|BellaJohnson1}} # [[/Parental educational aspirations and student achievement/]] - How do parental aspirations shape children’s academic motivation and performance? {{ME-By|User Name}} # [[/Parental motivations for homeschooling/]] - What motivates parents to homeschool their children? {{ME-By|User Name}} # [[/Perfectionism and procrastination/]] - What is the role of perfectionism in procrastination and what can be done about it? {{ME-By|U3222012}} # [[/Pleasure anticipation and dopamine/]] - How does the brain's reward system generate motivation through expected rather than experienced pleasure? u3284308 # [[/Possible selves and goal pursuit/]] - How do possible selves influence motivation and goal-directed behaviour? {{ME-By|Jack4234}} # [[/Power motivation in leadership/]] - How does power motivation influence leadership styles and effectiveness? {{ME-By|PsychstudentUniversity!}} # [[/Prevention versus promotion mindset/]] - What are the motivational differences between prevention and promotion mindsets? {{ME-By|Bronte.H}} # [[/Protection motivation theory and environmental behaviour/]] - How does protection motivation theory explain engagement in pro-environmental behaviour? {{ME-By|User Name}} # [[/Relatedness motivation in self-determination theory/]] - How does the need for relatedness function within self-determination theory to shape motivation and behaviour? {{ME-By|User Name}} # [[/Retirement motivation/]] - What motivates retirement from work? U3261207 # [[/Role-play and communication skills training/]] - How does role-play facilitate the development of effective communication skills? {{ME-By|User Name}} # [[/Scarcity versus abundance mindset/]] - How do scarcity and abundance mindsets develop and what are the motivational consequences? {{ME-By|User Name}} # [[/Self-concept and motivation/]] - How does self-concept relate to motivation? {{ME-By|U3253363}} # [[/Self-determination theory and dementia care/]] - How can autonomy, competence, and relatedness be supported in people living with dementia? {{ME-By|Ella Kay244}} # [[/Self-determination theory and military veteran reintegration/]] - How do autonomy, competence, and relatedness shape psychological adjustment after military service? {{ME-By|U3246286}} # [[/Self-determination theory and physical activity/]] - How do autonomy, competence, and relatedness predict engagement in physical activity and exercise adherence? {{ME-By|U3275908}} # [[/Self-determination theory and social media use/]] - How do basic psychological needs explain patterns of social media engagement? {{ME-By|GraceInMind}} # [[/Sensation-seeking and dopamine/]] - What is the neurobiological relationship between sensation-seeking and dopamine? {{ME-By|SunnySideUp1300}} # [[/Sex differences in sexual arousal patterns/]] - How do patterns of sexual arousal differ between males and females? {{ME-By|U3236349}} # [[/Sex work motivation/]] - What motivates sex work and how does this impact worker experiences? {{ME-By|U3261376}} # [[/Social dominance and power motivation/]] - What is the relationship between social dominance and power motivation? {{ME-By|U3284302}} # [[/Subcortical structures and motivational drive/]] - How do subcortical brain regions generate basic motivational impulses and energy? {{ME-By|U3281503}} # [[/Sun exposure and protection motivation/]] - What motivates sun exposure and protection behaviours? {{ME-By|U3188047}} # [[/Surrender motivation/]] - What is the motivational state of surrender and what are its impacts? {{ME-By|User Name}} # [[/The quiet ego and motivation/]] - How does a quiet ego balance self-interest with concern for others? {{ME-By|User Name}} # [[/Thermoregulation and motivation/]] - How does the drive to maintain body temperature influence behaviour? {{ME-By|User Name}} # [[/Tonic-phasic model of dopamine regulation/]] - What is the tonic/phasic model of dopamine regulation and how does affect behaviour? {{ME-By|User Mame}} # [[/Types of impulsivity/]] - What are the different types of impulsivity and how do they affect motivation? {{ME-By|User Name}} # [[/Value congruence and motivation/]] - How does alignment between personal and situational values influence motivation? {{ME-By|U3275775}} # [[/Volunteer counsellor motivation/]] - What motivates people to become and remain volunteer counsellors? {{ME-By|J.M.A Watson}} # [[/Windfall gain effect/]] - How doe unexpected wealth influence behaviour and decision-making? {{ME-By|User Name}} # [[/Youth environmental activism motivation/]] - What motivates young people to engage in environmental activism? {{ME-By|SJPiper}} ==Emotion== # [[/Active versus passive social media use/]] - How do different patterns of social media engagement influence emotions and psychological wellbeing? {{ME-By|U3282656}} # [[/Adaptive versus maladaptive self-reflection/]] - When does self-reflection promote wellbeing and when does it contribute to psychological distress? {{ME-By|U3211150}} # [[/Affect heuristic/]] - What is the affect heuristic and how does it influence decision making? {{ME-By|User Name}} # [[/Alcohol use for emotion regulation/]] - Why and how do people use alcohol to regulate their emotions? {{ME-By|U3284266}} # [[/Apocalyptic fear/]] - What is apocalyptic fear, what are its consequences, and how can it be dealt with? {{ME-By|LazPulch}} # [[/Awe and the diminished self/]] - How does awe diminish the self and how can this be applied? {{ME-By|User Name}} # [[/Awe and nature/]] - What is the relationship between awe and nature? {{ME-By|U3269915}} # [[/Biofeedback and emotion regulation/]] - How does biofeedback help individuals monitor and regulate their emotional states? {{ME-By|User Name}} # [[/Body neutrality and emotional well-being/]] - How does a body-neutral perspective affect emotional well-being? {{ME-By|AmyUniversity}} # [[/Breathing exercises and relaxation/]] - How can breathing exercises promote relaxation? {{ME-By|E3297976}} # [[/Cancer screening and emotion/]] - How do emotions such as fear, anxiety, and relief influence cancer screening uptake? {{ME-By|User Name}} # [[/Cognitive hardiness and stress resilience/]] - How does cognitive hardiness promote resilience to stress and adversity? {{ME-By|u3068253}} # [[/Cognitive versus affective empathy/]] - What are the differences between cognitive and affective empathy and how do they contribute to prosociality? {{ME-By|User Name}} # [[/Dark empathy/]] - What is dark empathy, what are its consequences, and what can be done to address it? {{ME-By|U3228742}} # [[/Dreams and emotional problem-solving/]] - How do REM dreams contribute to emotional processing and adaptive coping? {{ME-By|U3270398}} # [[/Durability bias in affective forecasting/]] - What role does durability bias play in affective forecasting? {{ME-By|User Name}} # [[/Eco-emotions/]] - What are eco-emotions, how do they influence behaviour, and how can they be managed? {{ME-By|User Name}} # [[/Emotional effects of incarceration on Indigenous Australians/]] - What are the emotional effects of incarcertation on Indigenous Australians? {{ME-By|Lilfish215}} # [[/Emotional expressivity/]] - What is emotional expressivity, why does it matter, and how can it be developed? {{ME-By|U3283812}} # [[/Emotional flooding in relationships/]] - Why does emotional flooding occur, how does it affect relationships, and what can be done about it? {{ME-By|Tofu05}} # [[/Emotional intelligence and emotional wellbeing/]] - How does emotional intelligence affect emotional wellbeing? {{ME-By|u3239236}} # [[/Emotional role-playing/]] - How does role-playing influence emotional experience, expression, and regulation? {{ME-By|User Name}} # [[/Emotion detection using artificial intelligence/]] - How can emotion be detected using artificial intelligence? {{ME-By|User Name}} # [[/Emotion dysregulation/]] - What is emotion dysregulation, what are its consequences, and how can it be managed? {{ME-By|U3285438}} # [[/Emotion regulation ability and strategy/]] - How do ability and strategy differ in shaping emotion regulation? {{ME-By|User Name}} # [[/Emotion regulation through exercise/]] - How do people use exercise to regulate their emotional states? {{ME-By|KB3250298}} # [[/Emotions in activism/]] - How do emotions motivate, shape, and sustain activism? {{ME-By|User Name}} # [[/Empathy and jury decision-making/]] - How does empathy toward defendants and victims influence jurors' reasoning and verdict decisions? {{ME-By|U3254168}} # [[/Empathy fatigue and emotional exhaustion/]] - How does sustained empathic engagement contribute to emotional exhaustion? {{ME-By|U3143751}} # [[/Enjoyment and learning/]] - How does enjoyment influence learning? {{ME-By|User Name}} # [[/Envy in the workplace/]] - What role does envy play in workplace behaviour? {{ME-By|Flickstar888}} # [[/Environmental volunteering and wellbeing/]] - How does participation in environmental volunteering influence volunteers' subjective wellbeing? {{ME-By|User Name}} # [[/Excitement as an emotion/]] - What is the emotional excitement and how does it influence behaviour and wellbeing? {{ME-By|U3292769}} # [[/Fear extinction/]] - What psychological and neural processes underlie the extinction of fear responses? {{ME-By|ChillPsychGuy0607}} # [[/Focalism in affective forecasting/]] - What is focalism and how does it bias predictions about future emotional experiences? {{ME-By|User Name}} # [[/Gloatrage/]] - What is gloatrage, what causes it, and what are its consequences? {{ME-By|User Name}} # [[/Growth mindset and psychological wellbeing/]] - How does a growth mindset influence psychological wellbeing? {{ME-By|Avj.06}} # [[/Human trust of robots/]] - What psychological factors shape human trust of robots? {{ME-By|User Name}} # [[/Identify exploration through role-playing games/]] - How do role-playing games facilitate identity exploration and self-discovery? {{ME-By|User Name}} # [[/Immersive therapy for PTSD treatment/]] - How does it work and what are the effects? {{ME-By|StretchBeyond}} # [[/Indigenous Australian funeral practices and grieving/]] - How do Indigenous Australian funeral practices assist with grieving? {{ME-By|User Name}} # [[/Interpersonal psychotherapy and emotion/]] - How does interpersonal psychotherapy improve emotional wellbeing through changes in relationships? {{ME-By|User Name}} # [[/Introjection and guilt-based motivation/]] - What role do shame and guilt play in introjected forms of behavioural regulation? {{ME-By|U3330981}} # [[/Irritability/]] - What is irritability, what causes it, what are its consequences, and how can it be managed? {{ME-By|U3275992}} # [[/Love styles and relationships/]] - How do love styles influence relationship satisfaction and stability? {{ME-By|U3246588}} # [[/Melatonin and seasonal mood/]] - What role does melatonin play in seasonal mood changes? {{ME-By|U3224236{{ME-By| # [[/Mental health first aid and helping behaviour/]] - What motivates people to recognise, approach, and support someone with a mental health problem? {{ME-By|Katelyn Rod}} # [[/Mindfulness and nature connectedness/]] - How does mindfulness influence nature connectedness? {{ME-By|User Name}} # [[/Mood and cognitive performance/]] - How do different mood states impact attention, memory, and problem solving? {{ME-By|U3283879}} # [[/Moodiness/]] - What is moodiness, why does it occur, and how can it be managed? {{ME-By|User Name}} # [[/Moral disgust and jury decision-making/]] - How does moral disgust influence jurors' judgments of guilt, blame, and punishment? {{ME-By|Yellowvines}} # [[/Neurobiology of love/]] - What neural systems and biochemical processes underlie love? {{ME-By|Honeybelle11}} # [[/Neurofeedback and emotional regulation/]] - How can neurofeedback influence enhance emotional regulation? {{ME-By|User Name}} # [[/Nitrous oxide and emotion/]] - How does nitrous oxide influence emotional experience and mood? {{ME-By|User Name}} # [[/Noise and emotion/]] - How do different types of noise affect emotional experience and wellbeing? {{ME-By|User Name}} # [[/Opponent process theory and emotion/]] - What role do opposing affective states play in emotional experience? {{ME-By|User Name}} # [[/Outdoor play and children's emotional well-being/]] - How does outdoor play influence children's emotional well-being? {{ME-By|Mymunu}} # [[/Perfectionism and athlete mental health/]] - How does perfectionism affect athlete mental health? {{ME-By|Leilab23}} # [[/Phubbing and emotion/]] - What are the emotional causes and consequences of phubbing? {{ME-By|U3243961}} # [[/Positive emotion dysregulation/]] - What is positive emotion dysregulation and how does it affect psychological functioning? {{ME-By|P U3270518}} # [[/Psychological preparation for natural disasters/]] - How can people psychologically prepare for natural disasters? {{ME-By|User Name}} # [[/Psychological safety and feedback uptake/]] - How does psychological safety influence openness to feedback? {{ME-By|User Name}} # [[/Reflected glory/]] - What is reflected glory and what are its pros and cons? {{ME-By|User Name}} # [[/Remote work and well-being/]] - How does remote work influence employee well-being? {{ME-By|User Name}} # [[/Responsiveness and interpersonal trust/]] - How does responsiveness foster trust in relationships? {{ME-By|U3282586}} # [[/Romantic entertainment and love beliefs/]] - How do romantic entertainment influence beliefs and expectations about love and romantic relationships? {{ME-By|U3247927}} # [[/Romantic jealousy/]] - Why does romantic jealousy occur, what are its impacts, and how can it be managed?{{ME-By|U3279062}} # [[/Secondary trauma in healthcare workers/]] - What are the emotional consequences of secondary trauma in healthcare settings? {{ME-By|U3257744}} # [[/Seasonal affective disorder/]] - What is SAD, why does it occur, and how can it be managed? {{ME-By|Greg Philips}} # [[/Self-blame and emotion/]] - How does self-blame influence emotional responses to negative events? {{ME-By|User Name}} # [[/Self-disclosure and emotional intimacy/]] - How does self-disclosure foster emotional closeness in relationships? {{ME-By|U3283302}} # [[/Self-stigma and emotion/]] - How does self-stigma impact emotional well-being? {{ME-By|User Name}} # [[/Social connection and emotion regulation/]] - How do social relationships help regulate people's emotions? {{ME-By|U3284040}} # [[/Socioemotional selectivity theory and wellbeing in ageing/]] - How do social and emotional experiences affect wellbeing as people age? {{ME-By|User Name}} # [[/Spirituality and resilience/]] - What is the relationship between spirituality and psychological resilience? {{ME-By|User Name}} # [[/Subjective wellbeing homeostasis theory/]] - How does homeostatic theory explain the stability and regulation of subjective wellbeing? {{ME-By|User Name}} # [[/Technology-based pain management/]] - How can technology-based tools alter pain perception and pain management? {{ME-By|ChelsSchofield}} # [[/Theory of positive disintegration and personal growth/]] - What is the TPD and how can it be applied to personal growth? {{ME-By|User Name}} # [[/Time perception in mood disorders/]] - How do anxiety and depression alter the subjective experience of time? {{ME-By|User Name}} # [[/Trust in artificial intelligence/]] - What psychological factors shape human trust of artificial intelligence systems? {{ME-By|User Name}} # [[/Trust rebuilding after trauma/]] - How can trauma survivors develop trust in similar situations again? {{ME-By|User Name}} # [[/Volunteer wellbeing/]] - How does volunteering affect volunteer's subjective wellbeing? {{ME-By|U3216851}} # [[/Wayfinding and affective experience/]] - How do emotions influence navigation and spatial behaviour? {{ME-By|User Name}} ==Motivation and emotion== # [[/Boredom and interest/]] - How do boredom and interest shape emotional and motivational states? {{ME-By|U3239431}} # [[/Falling in love/]] - What motivational and emotional processes underlie romantic attraction and falling in love? {{ME-By|Mort006}} # [[/Life purpose and well-being/]] - How does a sense of purpose contribute to well-being and how can it be cultivated? {{ME-By|U3286962}} # [[/Moral emotions and ethical behaviour/]] - How do moral emotions motivate ethical and prosocial action? {{ME-By|U3263365}} # [[/Oxytocin as a neuromodulator/]] - What are the motivational and emotional effects of oxytocin as a neuromodulator? {{ME-By|User Name}} # [[/Reward prediction error/]] - How does discrepancy between expected and actual rewards influence learning, emotion, and motivation? {{ME-By|User Name}} # [[/Reinforcement sensitivity theory/]] - How does reinforcement sensitivity theory explain individual differences in motivation and emotion? {{ME-By|User Name}} # [[/Reward prediction error/]] - How do reward prediction errors influence learning, emotion, and motivation? {{ME-By|User Name}} # [[/Social and emotional well-being in Indigenous Australians/]] - How does the holistic social and emotional well-being model reframe Indigenous Australian health and well-being? {{ME-By|User Name}} # [[/Strengths-based Indigenous Australian psychology/]] - How can strengths-based perspectives enhance understanding of Indigenous motivation and emotion? {{ME-By|User Name}} # [[/Warm-glow giving/]] - Why does giving feel good and how does this influence prosocial behaviour? {{ME-By|User Name}} # [[/Wisdom, motivation, and emotion/]] - How do motivational and emotional processes contribute to wisdom? {{ME-By|User Name}} [[Category:Motivation and emotion/Book/2026]] 72qgq11pokddqgw75noxjtu7aybhsox 2 326640 2823850 2822394 2026-08-21T09:30:51Z Atcovi 276019 /* June 2026 - August 2026 */ updates 2823850 wikitext text/x-wiki == Application Goal == '''Fall 2027''' == Subpages == * [[User:Atcovi/Journey to Clinical PhD/Potential Clinical PhD programs]] * [[User:Atcovi/Journey to Clinical PhD/Research Interest?]] ** [[Suicide]] (WJ publication to improve [[w:Suicidology#Theories_of_suicide|Suicidology#Theories_of_suicide]]?) *[[User:Atcovi/Journey to Clinical PhD/Solid advice I've seen]] == Current tasks == === January 2026 - May 2026 === ==== Ongoing {{Ongoing}} ==== '''<u>High-priority</u>''' #Work on the CPARL Lab: [[User:Atcovi/Dr. Dzokoto/Emotion Lexicon Project]] {{Ongoing}} #Get ready for the call: [[User:Atcovi/Journey to Clinical PhD/feb19 zoom call|feb 19 zoom call info]] {{Done}} #Continue work on [[WikiJournal Preprints/Mental health in Sri Lanka]] [1] {{Done}} #start one on [[w:Overgeneral_autobiographical_memory|OGM]] [2]. {{Ongoing}} #*could this be qualitative? #**'''JULY 20, 2026:''' being worked off-wiki at the moment, hopefully will be published in september 2026. #Continue reaching out to PIs {{Ongoing}} '''<u>Less-priority</u>''' ---------------------------------------------------------------------------------------------------------------------------------------------- #[[User:Atcovi/Journey to Clinical PhD/Posters guidance|Try to go for posters/publications]] (writing committee [[User:Atcovi/Dr. Dzokoto|Dr. Dzokoto]]?). #* '''aim for 1-2 posters''' {{Ongoing}} #[[User:Atcovi/Journey to Clinical PhD/Researchers|Get a concrete list of researchers you'd like to work with and who are within your niche.]] {{Done}} #Attend MORE conferences (keep up with the American Association of Suicidology; virtual is valid as well). {{Ongoing}} #Secure a full-time, research-oriented job if you can. {{Ongoing}} #* [[User:Atcovi/Journey to Clinical PhD/tips for job search]] #Guest lecture? Adjunct professor? ==== Completed {{Completed}} ==== *Graduate college with a 4.0 GPA. {{Completed}} * Email [https://vipbg.vcu.edu/ Virginia Institute for Psychiatric and Behavioral Genetics] and try to get 1-2 professors to study under relating to suicidal ideation. {{Completed}} ** '''UPDATE:''' None available; probably due to emailing late, decent chance of getting a role in a year's time--important to grind in the meantime. *RE-SUBMIT [[Association Between Screen Time and Sleep: An Online Survey|undergrad thesis]] to PsyArXiv, then update WV page. {{Done}} ==== MAY 2026 PROGRESS REPORT: ==== 3 potential papers in the making, aim to get them published by fall 2026: # [[User:Atcovi/OGM & Suicide/The Paper]] # [[WikiJournal Preprints/Mental health in Sri Lanka]] {{Done}} # [[User:Atcovi/Dr. Dzokoto/Emotion Lexicon Project]] - Emotions paper 1 poster to present # [[User:Atcovi/APA2026 Abstract]] ← derived from paper #2. Continued internships? # Dr. Dzokoto (strengthen letter of recommendations) # '''EARLY AUGUST''' - reach out to professors at [https://vipbg.vcu.edu/ Virginia Institute for Psychiatric and Behavioral Genetics]. Continue applying everywhere. Job changes could change things dramatically. === June 2026 - August 2026 === * [[User:Atcovi/APA2026 Abstract]] - August 8th presentation - {{Done}} * [[User:Atcovi/Journey to Clinical PhD/Dr. Nadorff Meeting]] - {{Done}} * Email [https://vipbg.vcu.edu/ Virginia Institute for Psychiatric and Behavioral Genetics] and try to get 1-2 professors to study under relating to suicidal ideation. {{Done}} ** Potential opportunity in October 2026, reach out again for meeting. === September 2026 - December 2026 === ==== September 2026 PROGRESS REPORT: ==== * Finished 10-15 professors to apply to? [TBD] [[Category:Atcovi/Clinical Psychology]] 4vd1ybq9yy1dt5tjtuqhtk0m59yrf7o 2823851 2823850 2026-08-21T09:31:09Z Atcovi 276019 /* MAY 2026 PROGRESS REPORT: */ {{done}} 2823851 wikitext text/x-wiki == Application Goal == '''Fall 2027''' == Subpages == * [[User:Atcovi/Journey to Clinical PhD/Potential Clinical PhD programs]] * [[User:Atcovi/Journey to Clinical PhD/Research Interest?]] ** [[Suicide]] (WJ publication to improve [[w:Suicidology#Theories_of_suicide|Suicidology#Theories_of_suicide]]?) *[[User:Atcovi/Journey to Clinical PhD/Solid advice I've seen]] == Current tasks == === January 2026 - May 2026 === ==== Ongoing {{Ongoing}} ==== '''<u>High-priority</u>''' #Work on the CPARL Lab: [[User:Atcovi/Dr. Dzokoto/Emotion Lexicon Project]] {{Ongoing}} #Get ready for the call: [[User:Atcovi/Journey to Clinical PhD/feb19 zoom call|feb 19 zoom call info]] {{Done}} #Continue work on [[WikiJournal Preprints/Mental health in Sri Lanka]] [1] {{Done}} #start one on [[w:Overgeneral_autobiographical_memory|OGM]] [2]. {{Ongoing}} #*could this be qualitative? #**'''JULY 20, 2026:''' being worked off-wiki at the moment, hopefully will be published in september 2026. #Continue reaching out to PIs {{Ongoing}} '''<u>Less-priority</u>''' ---------------------------------------------------------------------------------------------------------------------------------------------- #[[User:Atcovi/Journey to Clinical PhD/Posters guidance|Try to go for posters/publications]] (writing committee [[User:Atcovi/Dr. Dzokoto|Dr. Dzokoto]]?). #* '''aim for 1-2 posters''' {{Ongoing}} #[[User:Atcovi/Journey to Clinical PhD/Researchers|Get a concrete list of researchers you'd like to work with and who are within your niche.]] {{Done}} #Attend MORE conferences (keep up with the American Association of Suicidology; virtual is valid as well). {{Ongoing}} #Secure a full-time, research-oriented job if you can. {{Ongoing}} #* [[User:Atcovi/Journey to Clinical PhD/tips for job search]] #Guest lecture? Adjunct professor? ==== Completed {{Completed}} ==== *Graduate college with a 4.0 GPA. {{Completed}} * Email [https://vipbg.vcu.edu/ Virginia Institute for Psychiatric and Behavioral Genetics] and try to get 1-2 professors to study under relating to suicidal ideation. {{Completed}} ** '''UPDATE:''' None available; probably due to emailing late, decent chance of getting a role in a year's time--important to grind in the meantime. *RE-SUBMIT [[Association Between Screen Time and Sleep: An Online Survey|undergrad thesis]] to PsyArXiv, then update WV page. {{Done}} ==== MAY 2026 PROGRESS REPORT: ==== 3 potential papers in the making, aim to get them published by fall 2026: # [[User:Atcovi/OGM & Suicide/The Paper]] # [[WikiJournal Preprints/Mental health in Sri Lanka]] {{Done}} # [[User:Atcovi/Dr. Dzokoto/Emotion Lexicon Project]] - Emotions paper 1 poster to present # [[User:Atcovi/APA2026 Abstract]] ← derived from paper #2. Continued internships? # Dr. Dzokoto (strengthen letter of recommendations) # '''EARLY AUGUST''' - reach out to professors at [https://vipbg.vcu.edu/ Virginia Institute for Psychiatric and Behavioral Genetics]. {{Done}} Continue applying everywhere. Job changes could change things dramatically. === June 2026 - August 2026 === * [[User:Atcovi/APA2026 Abstract]] - August 8th presentation - {{Done}} * [[User:Atcovi/Journey to Clinical PhD/Dr. Nadorff Meeting]] - {{Done}} * Email [https://vipbg.vcu.edu/ Virginia Institute for Psychiatric and Behavioral Genetics] and try to get 1-2 professors to study under relating to suicidal ideation. {{Done}} ** Potential opportunity in October 2026, reach out again for meeting. === September 2026 - December 2026 === ==== September 2026 PROGRESS REPORT: ==== * Finished 10-15 professors to apply to? [TBD] [[Category:Atcovi/Clinical Psychology]] iupqgiaxezshdqmke4ttiyvui8fun5a 1 328020 2823643 2816499 2026-08-20T13:17:35Z Amélie E. Pereira 3042711 2823643 wikitext text/x-wiki == Link to Python script generating the == This script generated the table https://gist.github.com/fnielsen/70069b61da9f7eb09b721e4d82b63710 [[User:Fnielsen|Fnielsen]] ([[User talk:Fnielsen|discuss]] • [[Special:Contributions/Fnielsen|contribs]]) 22:40, 27 February 2026 (UTC) == Ontology, categories and social sciences == Summary of a discussion with @[[User:Solstag|Solstag]] : - Science and technology studies developped by Callon and Latour invite to observe the social world without predefined categories in mind and to allow categories to emerge in a non-rigid way. Wikidata allows for such flexible ontology and category building. As for what is the ideal ontology, it does not have to be static, the ontology should stay connected to research practices. - When we do qualitative research (what is called "coding") we build categories to build our own perspective on our data. We rarely consider that what we do is building a database of data, concepts, categories and relations between them. However, it can be meaningful to share this database with others to help them build their own perspective. [[User:Jeanne Noiraud|Jeanne Noiraud]] ([[User talk:Jeanne Noiraud|discuss]] • [[Special:Contributions/Jeanne Noiraud|contribs]]) 15:43, 4 June 2026 (UTC) :Thanks for the notes! [[User:Solstag|Solstag]] ([[User talk:Solstag|discuss]] • [[Special:Contributions/Solstag|contribs]]) 21:47, 22 June 2026 (UTC) == Advantages == *Structured queries via SPARQL: the ability to dynamically query the literature (authors, methods, concepts, results) rather than producing a static summary — consistent with the concept of a ‘living review’ *Interoperability and links to other databases (ORCID, DOI, OpenAlex, VIAF) to automatically enrich bibliographic metadata *Native multilingual support for items, useful for an international research field *Collaborative, version-controlled model: traceability of changes, distributed contributions == Limitations / ontology issues == *Wikidata’s item-property-value model is well suited to factual information (dates, authors, affiliations) but struggles to handle contested or socially constructed concepts — ‘justice’, ‘power’ and ‘just transition’ do not have established definitions, contrary to what ontology modelling requires *Difficulty in representing nuance and context: a scientific claim in the social sciences is often conditional, contested, or dependent on the theoretical framework — Wikidata’s ‘qualifiers’ mechanism allows for partial reification but remains limited in its ability to capture theoretical disagreements *Lack of nuanced properties for qualitative social sciences (compared to the hard sciences, which are better covered) *Risk of reduction or oversimplification: encoding a rich concept as a single item can flatten disciplinary debates == Community limitations == *A knowledge base dominated by contributors with technical backgrounds (who are often unfamiliar with the social sciences), which influences modelling priorities *Notability criteria and modelling practices that are sometimes ill-suited to subjects in the humanities and social sciences *High maintenance burden for a ‘living review’: who updates the entries as new publications emerge? Risk of a disconnect between the database and the actual literature if the dedicated Wikibase community is not sustainable? *Quality control and potential vandalism on topics that may become politically sensitive (environmental justice, etc.) 7zms2ifvs8egp99f3d8x2wxdku0g8ju 2823644 2823643 2026-08-20T13:17:44Z Amélie E. Pereira 3042711 /* Limitations / ontology issues */ 2823644 wikitext text/x-wiki == Link to Python script generating the == This script generated the table https://gist.github.com/fnielsen/70069b61da9f7eb09b721e4d82b63710 [[User:Fnielsen|Fnielsen]] ([[User talk:Fnielsen|discuss]] • [[Special:Contributions/Fnielsen|contribs]]) 22:40, 27 February 2026 (UTC) == Ontology, categories and social sciences == Summary of a discussion with @[[User:Solstag|Solstag]] : - Science and technology studies developped by Callon and Latour invite to observe the social world without predefined categories in mind and to allow categories to emerge in a non-rigid way. Wikidata allows for such flexible ontology and category building. As for what is the ideal ontology, it does not have to be static, the ontology should stay connected to research practices. - When we do qualitative research (what is called "coding") we build categories to build our own perspective on our data. We rarely consider that what we do is building a database of data, concepts, categories and relations between them. However, it can be meaningful to share this database with others to help them build their own perspective. [[User:Jeanne Noiraud|Jeanne Noiraud]] ([[User talk:Jeanne Noiraud|discuss]] • [[Special:Contributions/Jeanne Noiraud|contribs]]) 15:43, 4 June 2026 (UTC) :Thanks for the notes! [[User:Solstag|Solstag]] ([[User talk:Solstag|discuss]] • [[Special:Contributions/Solstag|contribs]]) 21:47, 22 June 2026 (UTC) == Advantages == *Structured queries via SPARQL: the ability to dynamically query the literature (authors, methods, concepts, results) rather than producing a static summary — consistent with the concept of a ‘living review’ *Interoperability and links to other databases (ORCID, DOI, OpenAlex, VIAF) to automatically enrich bibliographic metadata *Native multilingual support for items, useful for an international research field *Collaborative, version-controlled model: traceability of changes, distributed contributions == Limitations / ontology issues == *Wikidata’s item-property-value model is well suited to factual information (dates, authors, affiliations) but struggles to handle contested or socially constructed concepts — ‘justice’, ‘power’ and ‘just transition’ do not have established definitions, contrary to what ontology modelling requires *Difficulty in representing nuance and context: a scientific claim in the social sciences is often conditional, contested, or dependent on the theoretical framework — Wikidata’s ‘qualifiers’ mechanism allows for partial reification but remains limited in its ability to capture theoretical disagreements *Lack of nuanced properties for qualitative social sciences (compared to the hard sciences, which are better covered) *Risk of reduction or oversimplification: encoding a rich concept as a single item can flatten disciplinary debates == Community limitations == *A knowledge base dominated by contributors with technical backgrounds (who are often unfamiliar with the social sciences), which influences modelling priorities *Notability criteria and modelling practices that are sometimes ill-suited to subjects in the humanities and social sciences *High maintenance burden for a ‘living review’: who updates the entries as new publications emerge? Risk of a disconnect between the database and the actual literature if the dedicated Wikibase community is not sustainable? *Quality control and potential vandalism on topics that may become politically sensitive (environmental justice, etc.) 6f1xc7ilfpgf5i91ot9pajr03wtwy5r 0 329548 2823636 2823105 2026-08-20T12:05:02Z Athene241 3100061 /* Data */ 2823636 wikitext text/x-wiki {{mathematics}} '''Athena problem''' is an [[:w:List of unsolved problems in mathematics|unsolved problem]] in [[:w:Number theory|number theory]] and [[:w:Formal language theory|formal language theory]] and [[:w:Order theory|order theory]], this problem is named after the ancient Greek goddess [[:w:Athena|Athena]] (which is associated with [[:w:Wisdom|wisdom]]). Athena problem is: Give a [[:w:Natural number|natural number]] ''b'' > 1, find the [[:w:Set (mathematics)|set]] of the [[:w:Minimal element|minimal element]]s of the set of the "[[:w:Prime number|prime number]] [[:w:Greater than|>]] ''b''" [[:w:Numerical digit|digit]] [[:w:String (computer science)|string]]s in the [[:w:Positional numeral system|positional numeral system]] with [[:w:Radix|base]] ''b'' for the [[:w:Subsequence|subsequence]] [[:w:Partially ordered set|ordering]]. (A string ''x'' is a subsequence of another string ''y'', if ''x'' can be obtained from ''y'' by deleting zero or more of the [[:w:Character (computing)|character]]s in ''y''. For example, 514 is a subsequence of 352148, "string" is a subsequence of "meistersinger". In contrast, 758 is not a subsequence of 378259, "abc" is not a subsequence of "cbacacba", since the characters must be in the same order) (Unlike [[:w:Substring|substring]], subsequence is not required to occupy consecutive positions within the original sequences, e.g. the [[:w:Longest common subsequence|longest common subsequence problem]] is different from the [[:w:Longest common substring|longest common substring problem]]) Using [[:w:Formal language theory|formal language theory]] terminology, Athena problem is finding the [[:w:Set (mathematics)|set]] of the [[:w:Minimal element|minimal element]]s of the [[:w:Formal language|language]] of base-''b'' [[:w:Representation (mathematics)|representation]]s of the [[:w:Prime number|prime number]]s [[:w:Greater than|>]] ''b'' (which is a set of [[:w:String (computer science)|string]]s of [[:w:Symbol|symbol]]s over the [[:w:Alphabet (formal languages)|alphabet]] ''Σ''_''b'' := {0, 1, ..., ''b''−1}), under the subsequence ordering (i.e. the [[:w:Binary relation|binary relation]] "is a subsequence of", which is a [[:w:Partially ordered set|partial ordering]]), for a given natural number ''b'' > 1 (You can draw this partial ordering as a [[:w:Hasse diagram|Hasse diagram]] to find all [[:w:Minimal element|minimal element]]s), this set is called '''Athena set''', and the prime numbers in this set are called '''Athena primes'''. By [[:w:Higman's lemma|Higman's lemma]], there are no [[:w:Infinite set|infinite]] [[:w:Antichain|antichain]]s for the subsequence ordering (i.e. the subsequence ordering is always a [[:w:Well-quasi-ordering|well quasi order]]) (i.e. under the subsequence ordering (i.e. the [[:w:Binary relation|binary relation]] "is a subsequence of", which is a [[:w:Partially ordered set|partial ordering]]), every set of pairwise incomparable (i.e. not [[:w:Comparability|comparable]]) strings is finite), thus there must be only finitely many such minimal elements. In other words, the Athena set in every base ''b'' must be a [[:w:Finite set|finite set]], and every base ''b'' ≥ 2 has only finitely many Athena primes, e.g. in [[:w:Decimal|decimal]] (base ''b'' = 10), the Athena set has exactly 77 [[:w:Element of a set|element]]s (they are exactly the Athena primes in decimal (base ''b'' = 10)): {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027}. Determining the set of the minimal elements of a arbitrary set of strings under the subsequence ordering is in general [[:w:List of unsolved problems in mathematics|unsolvable]], and can be difficult even when this set is relatively simple (such as the base ''b'' representations of the prime numbers > ''b''). Although the set ''M''(''S'') of minimal strings is necessarily [[:w:Finite set|finite]], determining it explicitly for a given ''S'' can be a difficult computational problem. We use some [[:w:Number theory|numbertheoretic]] [[:w:Heuristic argument|heuristic]]s to [[:w:Computing|compute]] ''M''(''L''_''b''), where ''L''_''b'' is the [[:w:Formal language|language]] of [[:w:Radix|base]]-''b'' representations of the [[:w:Prime number|prime number]]s which are [[:w:Greater than|>]] ''b'', for 2 ≤ ''b'' ≤ 36. For bases 2 ≤ ''b'' ≤ 36, Athena problem is fully solved in bases ''b'' = 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 24, and also solved in bases ''b'' = 11, 13, 16, 22, 30 if [[:w:Probable prime|probable prime]]s are allowed. For the unsolved bases ''b'' = 17, 19, 21, 23, 25, 26, 27, 28, 29, 31, 32, 34, 35, 36, Athena problem is solved (if probable primes are allowed) except 771 [[:w:Indexed family|families]] of the form ''x''{''y''}''z'' (where ''x'' and ''z'' are strings (may be [[:w:Empty string|empty]]) of digits in base ''b'', ''y'' is a digit in base ''b'') = sequence {''xz'', ''xyz'', ''xyyz'', ''xyyyz'', ''xyyyyz'', ''xyyyyyz'', ...} (i.e. "''xy''⁺''z''" in [[:w:Regular expression|regular expression]]), all of these 771 families contain no primes > ''b'' or probable primes > ''b'' with length ≤ 100000. == Solve the problem == To solve the Athena problem for a given base ''b'', we must [[:w:Computing|compute]] the elements up to families of the form ''x''{''y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''y'' is a digit in base ''b''), and find the smallest prime > ''b'' in all such families. We call families of the form ''x''{''y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''y'' is a digit in base ''b'') "linear" families, and we reduce these families by removing all trailing digits ''y'' from ''x'', and removing all leading digits ''y'' from ''z'', to make the families be easier, e.g. family 12333{3}33345 in base ''b'' is reduced to family 12{3}45 in base ''b'', since they are in fact the same family. Our [[:w:Algorithm|algorithm]] then proceeds as follows: * 1. ''M'' := {minimal primes in base ''b'' of length 2 or 3}, ''L'' := union of all ''x''{''Y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'') such that ''x'' ≠ 0 and ''gcd''(''z'', ''b'') = 1 and ''Y'' is the set of digits ''y'' in base ''b'' such that ''xyz'' has no subsequence in ''M''. * 2. While ''L'' contains nonlinear families (families which are not linear families): Explore each family of ''L'', and update ''L''. Examine each family of ''L'' by: * 2.1. Let ''w'' be the shortest string in the family. If ''w'' has a subsequence in ''M'', then remove the family from ''L''. If ''w'' represents a prime, then add ''w'' to ''M'' and remove the family from ''L''. * 2.2. If possible, simplify the family. * 2.3. Using the techniques below (covering congruence, algebraic factorization, or combine of them), check if the family can be proven to only contain composites (only count the numbers > ''b''), and if so then remove the family from ''L''. * 3. Update ''L'', after each split examine the new families as in step 2. e.g. in decimal (base ''b'' = 10): ''M'' := {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991} ''L'' := {2{0,2}1, 2{0,8}7, 3{0,3,6,9}3, 3{0,3,6,9}9, 4{6}9, 5{0,5,8}1, 5{0,2}7, 6{0,3,6,9}3, 6{0,3,4,6,9}9, 7{0,7}7, 8{0,5}1, 8{0}7, 9{0,2,5,8}1, 9{0,3,6,9}3, 9{0,3,4,6,9}9} and since 2221 is prime, it follows that the family 2{0,2}1 splits into the families 2{0}1 and 2{0}2{0}1 and since the family 2{0}1 can be proven to contain no primes > base (since all numbers in this family are divisible by 3), it can be removed and since 20201 is prime, it follows that the family 2{0}2{0}1 splits into the families 2{0}21 and 22{0}1 221 and 2021 are composites, but 20021 is prime, thus add 20021 to ''L'' none of 221, 2201, 22001, 220001, 2200001 are primes, but 22000001 is prime, thus add 22000001 to ''L'' and since the family 3{0,3,6,9}3 can be proven to contain no primes > base (since all numbers in this family are divisible by 3), it can be removed etc. Since the number of possible (first digit,last digit) (also called (initial digit,final digit)) combos ([[:w:Ordered pair|ordered pair]]s) of a prime > ''b'' in base ''b'' is (''b''−1)×''[[:w:Euler's totient function|eulerphi]]''(''b'') (all digits except 0 can be the first digit of a prime > ''b'' in base ''b'' (thus ''b''−1 possible digits), but only the digits coprime to ''b'' can be the last digit of a prime > ''b'' in base ''b'' (thus ''eulerphi''(''b'') possible digits), and by the [[:w:Rule of product|rule of product]], there are (''b''−1)×''eulerphi''(''b'') choices of the (first digit,last digit) combo, also, both "numbers of Athena primes in base ''b''" and "length of the largest Athena prime in base ''b''" are [[:w:Asymptotic analysis|roughly]] ''[[:w:E (mathematical_constant)|e]]''^{''[[:w:Euler's constant|γ]]''×(''b''−1)×''[[:w:Euler's totient function|eulerphi]]''(*b*)}. Shrinking the family ''x''{''Y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''Y'' is a set of digits in base ''b'') * If ''y'' ∈ ''Y'' and the string ''xyyz'' represents a prime > ''b'' in base ''b'' (in this case, add this prime to the list) or has a subsequence which represents a prime > ''b'' in base ''b'', then ''x''{''Y''}''z'' can be replaced with ''x''{''Y'' \ ''y''}''z'' ∪ ''x''{''Y'' \ ''y''}''y''{''Y'' \ ''y''}''z''. * If ''y''₁ ∈ ''Y'' and ''y''₂ ∈ ''Y'' and ''y''₁ ≠ ''y''₂ and the string ''xy''₁''y''₂''z'' represents a prime > ''b'' in base ''b'' (in this case, add this prime to the list) or has a subsequence which represents a prime > ''b'' in base ''b'', then ''x''{''Y''}''z'' can be replaced with ''x''{''Y'' \ ''y''₁}{''Y'' \ ''y''₂}''z''. * If ''y''₁ ∈ ''Y'' and ''y''₂ ∈ ''Y'' and ''y''₁ ≠ ''y''₂ and both the strings ''xy''₁''y''₂''z'' and ''xy''₂''y''₁''z'' represent a prime > ''b'' in base ''b'' (in this case, add this prime to the list) or have a subsequence which represents a prime > ''b'' in base ''b'', then ''x''{''Y''}''z'' can be replaced with ''x''{''Y'' \ ''y''₁}''z'' ∪ ''x''{''Y'' \ ''y''₂}''z''. e.g. in decimal (base ''b'' = 10): * 2221 is a prime > 10, thus the family 2{0,2}1 splits into the two families 2{0}1 and 2{0}2{0}1. * 227 is a prime > 10, and it is a subsequence of 5227, thus the family 5{0,2}7 splits into the two families 5{0}7 and 5{0}2{0}7. * 449 is a prime > 10, and it is a subsequence of 6449, thus the family 6{0,3,4,6,9}9 splits into the two families 6{0,3,6,9}9 and 6{0,3,6,9}4{0,3,6,9}9. * Both 5051 and 5501 are primes > 10, thus the family 5{0,5}1 splits into the two families 5{0}1 and 5{5}1 = {5}1. * 8501 is a prime > 10, thus the family 8{0,5}1 splits into the family 8{0}{5}1. * 887 is a prime > 10, and it is a subsequence of 2887, also 2087 is a prime > 10, thus the family 2{0,8}7 splits into the two families 2{0}7 and 28{0}7. * 349 and 449 are primes > 10, and they are subsequences of 9349 and 9449, respectively, also 9049, 9649, 9949 are primes > 10, thus the family 9{0,3,4,6,9}9 splits into the two families 9{0,3,6,9}9 and 94{0,3,6,9}9. * 251, 281, 521, 821, 881 are primes > 10, and they are subsequences of 9251, 9281, 9521, 9821, 9881, respectively, also 9001, 9221, 9551, 9851 are primes > 10, thus the family 9{0,2,5,8}1 splits into the numbers {91, 901, 921, 951, 981, 9021, 9051, 9081, 9201, 9501, 9581, 9801, 90581, 95081, 95801}. If the methods we have discussed cannot be used to rule out or shrink ''x''{''Y''}''z'' where ''Y'' = {''y''₁, ''y''₂, ..., ''y''_''n''}, then we can replace ''x''{''Y''}''z'' by ''xy''₁{''Y''}''z'' ∪ ''xy''₂{''Y''}''z'' ∪ ... ∪ ''xy''_''n''{''Y''}''z'' and re-run the methods on this new [[:w:Formal language|language]]. If all remain families are linear families (i.e. of the form ''x''{''y''}''z'', where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''y'' is a digit in base ''b''), then we search the smallest (probable) primes in these families and add these primes to the list. e.g. in decimal (base ''b'' = 10): * The smallest prime in the family 5{0}27 is 5000000000000000000000000000027. * The smallest prime in the family {5}1 is 555555555551. * The smallest prime in the family 8{5}1 is 8555555555555555555551, but 8555555555555555555551 is not a minimal element since 555555555551 is a subsequence of 8555555555555555555551. There is no guarantee that the techniques discussed will ever terminate, but in practice they often do. They are able to determine the Athena set in base ''b'' for 2 ≤ ''b'' ≤ 16 and ''b'' = 18, 20, 22, 24, 30. The bases ''b'' = 17, 19, 21, 23, 25 ≤ ''b'' ≤ 29, 31 ≤ ''b'' ≤ 36 are solved with the exception of 771 families of the form ''x''{''y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''y'' is a digit in base ''b''). The following is a "[[:w:Semi-algorithm|semi-algorithm]]" that is guaranteed to solve the Athena problem for a given base ''b'', but it is not so easy to implement: # ''M'' = ''[[:w:Empty string|∅]]'' # while (''L'' ≠ ''∅'') do # choose ''x'', a shortest string in ''L'' # ''M'' := ''M'' ∪ {''x''} # ''L'' := ''L'' − ''sup''({''x''}) In practice, for arbitrary ''L'', we cannot feasibly carry out step 5. Instead, we work with ''L''&#39;, some regular overapproximation to ''L'', until we can show ''L''&#39; = ''∅'' (which implies ''L'' = ''∅''). In practice, ''L''&#39; is usually chosen to be a finite [[:w:Union (set theory)|union]] of sets of the form ''L''₁{''L''₂}''L''₃, where each of ''L''₁, ''L''₂, ''L''₃ is finite. In the case we consider in this project, we then have to determine whether such a family contains a prime or not. Thus, the [[:w:Time complexity|time complexity]] of the Athena problem in base ''b'' may be ''[[:w:Big O notation|O]]''(''[[:w:E (mathematical_constant)|e]]''^{''[[:w:Euler's constant|γ]]''×(''b''−1)×''[[:w:Euler's totient function|eulerphi]]''(*b*)}), and the [[:w:CPU time|CPU time]] of the Athena problem in base ''b'' may be longer than [[:w:Age of the universe|the age of the universe]] for bases ''b'' = 19, 23, 25, 27, 29, 31, 32, 33, 34, 35, also, Athena problem in bases ''b'' around 500 may be [[:w:NP-complete|NP-complete]] or [[:w:NP-hard|NP-hard]], or an [[:w:Undecidable problem|undecidable problem]], or an example of [[:w:Gödel's incompleteness theorems|Gödel's incompleteness theorems]] (like the [[:w:Continuum hypothesis|continuum hypothesis]] and the [[:w:Halting problem|halting problem]]). To solve the Athena problem (i.e. to compute the Athena set), we need to determine whether a given family contains a prime. In practice, if family ''x''{''Y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''Y'' is a set of digits in base ''b'') could not be ruled out as only containing composites and ''Y'' contains two or more digits, then a relatively small prime > ''b'' could always be found in this family. Intuitively, this is because there are a large number of small strings in such a family, and at least one is likely to be prime (e.g. there are 2^''n''−2 strings of length ''n'' in the family 1{3,7}9, and there are over a thousand strings of length 12 in the family 1{3,7}9, thus it is very impossible that these numbers are all composite). In the case ''Y'' contains only one digit, this family is of the form ''x''{''y''}''z'', and there is only a single string of each length > (the length of ''x'' + the length of ''z''), and it is not known if the following [[:w:Decision problem|decision problem]] is recursively solvable (just like [[:w:Sierpiński number|Sierpiński problem]] and [[:w:Riesel number|Riesel problem]], Sierpiński problem and Riesel problem can be generalized to other bases ''b'' (references: http://www.noprimeleftbehind.net/crus/Sierp-conjectures.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjectures-powers2.htm, http://www.noprimeleftbehind.net/crus/Sierp-conjecture-reserves.htm, http://www.noprimeleftbehind.net/crus/Riesel-conjecture-reserves.htm), in fact, Athena problem base ''b'' covers the Sierpiński problem base ''b'' and the Riesel problem base ''b'' with ''k'' < ''b'', i.e. finding the smallest prime of the form ''k''×''b''^''n''+1 and ''k''×''b''^''n''−1 (or prove such prime does not exist) with ''k'' < ''b'' (specially, for bases ''b'' such that the conjectured smallest Sierpiński number or the conjectured smallest Riesel number is < ''b'', Athena problem base ''b'' covers the Sierpiński problem base ''b'' or the Riesel problem base ''b'', respectively), since the smallest prime of the form ''k''×''b''^''n''+1 and ''k''×''b''^''n''−1 (if exists) must be a minimal element in base ''b'', also, Athena problem base ''b'' covers finding the smallest prime of these forms in base ''b'' (or proving that such prime does not exist): (''b''^''n''−1)/(''b''−1) (for this form, ''n'' must be prime, and we want ''n'' ≥ 2) (references of this form: http://www.fermatquotient.com/PrimSerien/GenRepu.txt, https://web.archive.org/web/20021111141203/http://www.users.globalnet.co.uk/~aads/primes.html, http://www.primenumbers.net/Henri/us/MersFermus.htm, http://www.bitman.name/math/table/379, https://pzktupel.de/Primetables/TableRepunitGen.php, https://oeis.org/A084740, https://oeis.org/A084738, https://oeis.org/A128164, https://oeis.org/A285642; or for prime bases ''b'': https://oeis.org/A065854, https://oeis.org/A279068), ''b''^''n''+1 (for this form, ''n'' must be power of 2, and we want ''n'' ≥ 1) (references of this form: http://jeppesn.dk/generalized-fermat.html, http://www.noprimeleftbehind.net/crus/GFN-primes.htm, https://web.archive.org/web/20231002190634/http://yves.gallot.pagesperso-orange.fr/primes/index.html, https://pzktupel.de/Primetables/TableFermatGFBB.php, https://oeis.org/A079706, https://oeis.org/A084712, https://oeis.org/A228101), (''b''^''n''+1)/2 (for odd ''b'') (for this form, ''n'' must be power of 2, and we want ''n'' ≥ 2) (reference of this form: http://www.fermatquotient.com/PrimSerien/GenFermOdd.txt), (''sqrt''(''b'')×''b''^''n''+1)/(''sqrt''(''b'')+1) (for square ''b'') (for this form, 2×''n''+1 must be prime, and we want ''n'' ≥ 2) (references of this form: http://www.fermatquotient.com/PrimSerien/GenRepuP.txt, http://www.primenumbers.net/Henri/us/MersFermus.htm, http://www.bitman.name/math/table/488, https://pzktupel.de/Primetables/TableWagstaffGen.php, https://oeis.org/A084742, https://oeis.org/A084741; or for bases ''b'' with ''sqrt''(''b'') prime: https://oeis.org/A065507), ((''b''−2)×''b''^''n''+1)/(''b''−1) (''n'' ≥ 2) (reference of this form: https://oeis.org/A243404), 2×''b''^''n''+1 (''n'' ≥ 1) (references of this form: https://www.mersenneforum.org/showthread.php?t=6918, https://www.mersenneforum.org/showthread.php?t=19725, https://oeis.org/A119624), 2×''b''^''n''−1 (''n'' ≥ 1) (references of this form: https://www.mersenneforum.org/showthread.php?t=24576, https://www.mersenneforum.org/attachment.php?attachmentid=20976&d=1567314217, https://oeis.org/A119591), ''b''^''n''+2 (''n'' ≥ 1) (references of this form: https://oeis.org/A138066, https://oeis.org/A084713, https://oeis.org/A138067), ''b''^''n''−2 (''n'' ≥ 2) (references of this form: https://www.primepuzzles.net/puzzles/puzz_887.htm, https://oeis.org/A250200, https://oeis.org/A255707, https://oeis.org/A084714; or for prime bases ''b'': https://oeis.org/A292201), (''b''−1)×''b''^''n''+1 (''n'' ≥ 1) (references of this form: http://www.noprimeleftbehind.net/Williams-primes-MP.htm, http://www.bitman.name/math/table/477, https://pzktupel.de/Primetables/TableWilliams2.php, https://oeis.org/A305531; or for prime bases ''b'': https://oeis.org/A087139), (''b''−1)×''b''^''n''−1 (''n'' ≥ 1) (references of this form: https://harvey563.tripod.com/wills.txt, http://www.noprimeleftbehind.net/Williams-primes-MM.htm, http://www.bitman.name/math/table/484, https://pzktupel.de/Primetables/TableWilliams1.php; or for prime bases ''b'': https://oeis.org/A122396), ''b''^''n''+(''b''−1) (''n'' ≥ 1) (references of this form: http://www.bitman.name/math/table/795, https://pzktupel.de/Primetables/TableWilliams6.php, https://oeis.org/A076845, https://oeis.org/A076846, https://oeis.org/A078178, https://oeis.org/A078179), ''b''^''n''−(''b''−1) (''n'' ≥ 2) (references of this form: http://www.bitman.name/math/table/792, https://pzktupel.de/Primetables/TableWilliams5.php, https://oeis.org/A113516, https://oeis.org/A343589; or for prime bases ''b'': https://cs.uwaterloo.ca/journals/JIS/VOL3/mccranie.html, http://www.bitman.name/math/table/435)): Problem: Given strings ''x'', ''z'' (may be empty), a digit ''y'', and a base ''b'' (''x'' does not [[:w:Leading zero|start with the digit 0]], ''z'' ends with a digit which [[:w:Coprime integers|coprime]] to ''b'', ''y'' is not 0 if ''x'' is empty, ''y'' is coprime to ''b'' if ''z'' is empty), does there exist a prime number whose base-''b'' expansion is of the form ''xy''_''n''''z'' for some ''n'' ≥ 0? Some families can be ruled out to contain no prime > ''b'' by [[:w:Covering set|covering congruence]], [[:w:Factorization of polynomials|algebraic factorization]] (e.g. [[:w:Difference of two squares|difference of two squares]], [[:w:Sum of two cubes|sum of two cubes]], [[:w:Sophie Germain's identity|Sophie Germain's identity of ''x''⁴+4×''y''⁴]]), or combine of them, e.g. * The base 9 family 2{7}: Always divisible by 2 or 5 * The base 11 family 2{5}: Always divisible by 2 or 3 * The base 14 family B{0}1: Always divisible by 3 or 5 * The base 13 family 95{0}3: Always divisible by 5, 7, or 17 * The base 16 family {4}D: Always divisible by 3, 7, or 13 * The base 16 family {8}F: Always divisible by 3, 7, or 13 * The base 21 family {7}D: Always divisible by 2, 13, or 17 * The base 23 family {D}GA: Always divisible by 2, 5, 7, 37, or 79 * The base 9 family {1}: Can be written as (9^''n''−1)/8 and can be factored as (3^''n''−1) × (3^''n''+1) / 8 * The base 8 family 1{0}1: Can be written as 8^''n''+1 and can be factored as (2^''n''+1) × (4^''n''−2^''n''+1) * The base 9 family 3{8}: Can be written as 4×9^''n''−1 and can be factored as (2×3^''n''−1) × (2×3^''n''+1) * The base 16 family 1{5}: Can be written as (4×16^''n''−1)/3 and can be factored as (2×3^''n''−1) × (2×3^''n''+1) / 3 * The base 16 family {4}1: Can be written as (4×16^''n''−49)/15 and can be factored as (2×3^''n''−7) × (2×3^''n''+7) / 15 * The base 27 family 7{Q}: Can be written as 8×27^''n''−1 and can be factored as (2×3^''n''−1) × (4×9^''n''+2×3^''n''+1) * The base 27 family 9{G}: Can be written as (125×27^''n''−8)/13 and can be factored as (5×3^''n''−2) × (25×9^''n''+10×3^''n''+4) * The base 16 family {C}D: Can be written as (4×16^''n''+1)/5 and can be factored as (2×4^''n''−2×2^''n''+1) × (2×4^''n''+2×2^''n''+1) / 5 * The base 14 family 8{D}: Can be written as 9×14^''n''−1, it is divisible by 5 if ''n'' is odd and can be factored as (3×14^''n''/2−1) × (3×14^''n''/2+1) if ''n'' is even * The base 12 family {B}9B: Can be written as 12^''n''−25, it is divisible by 13 if ''n'' is odd and can be factored as (12^''n''/2−5) × (12^''n''/2+5) if ''n'' is even * The base 14 family {D}5: Can be written as 14^''n''−9, it is divisible by 5 if ''n'' is odd and can be factored as (14^''n''/2−3) × (14^''n''/2+3) if ''n'' is even * The base 17 family 1{9}: Can be written as (25×17^''n''−9)/16, it is divisible by 2 if ''n'' is odd and can be factored as (5×17^''n''/2−3) × (5×17^''n''/2+3) / 16 if ''n'' is even * The base 17 family 7{9}: Can be written as (121×17^''n''−9)/16, it is divisible by 2 if ''n'' is odd and can be factored as (11×17^''n''/2−3) × (11×17^''n''/2+3) / 16 if ''n'' is even * The base 19 family 1{6}: Can be written as (4×19^''n''−1)/3, it is divisible by 5 if ''n'' is odd and can be factored as (2×19^''n''/2−1) × (2×19^''n''/2+1) / 3 if ''n'' is even * The base 24 family 3{N}: Can be written as 4×24^''n''−1, it is divisible by 5 if ''n'' is odd and can be factored as (2×24^''n''/2−1) × (2×24^''n''/2+1) if ''n'' is even * The base 24 family 5{N}: Can be written as 6×24^''n''−1, it is divisible by 5 if ''n'' is even and can be factored as (12×24^{(''n''−1)/2}−1) × (12×24^{(''n''−1)/2}+1) if ''n'' is odd By the [[:w:Prime number theorem|prime number theorem]], the [[:w:Probability|chance]] that a [[:w:Random number|random]] ''n''-digit base ''b'' number is prime is [[:w:Asymptotic analysis|approximately]] 1/''n'' (more accurately, the chance is approximately 1/(''n''×''ln''(''b'')), where ''ln'' is the [[:w:Natural logarithm|natural logarithm]]). If one conjectures the numbers ''x''{''y''}''z'' behave similarly (i.e. the numbers ''x''{''y''}''z'' is a [[:w:Pseudorandomness|pseudorandom sequence]]) you would expect [[:w:Harmonic_series (mathematics)|1/1 + 1/2 + 1/3 + 1/4 + ... = ∞]] primes of the form ''x''{''y''}''z'' (of course, this does not always happen, since some ''x''{''y''}''z'' families can be ruled out to contain no prime > ''b'' (by covering congruence, algebraic factorization, or combine of them), but it is at least a reasonable conjecture in the absence of evidence to the contrary. Hence, the [[:w:Heuristic argument|heuristic argument]] suggests there are always infinitely many primes in family ''x''{''y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''y'' is a digit in base ''b'') if it cannot be ruled out to contain no prime or only contain finitely many primes, by covering congruence, algebraic factorization, or combine of them. However, some families ''x''{''y''}''z'' could not be proven to contain no primes > ''b'' (by covering congruence, algebraic factorization, or combine of them) but no primes > ''b'' could be found in the family, even after searching through numbers with over 100000 digits. In such a case, the only way to proceed is to [[:w:Primality test|test the primality]] of larger and larger numbers of such form and hope a prime is eventually discovered. e.g. the smallest (probable) prime in the family A{3}A in base ''b'' = 13 is A3₅₉₂₁₉₇A, its algebraic form is (41×13⁵⁹²¹⁹⁸+27)/4, when written in decimal contains 659677 digits (it is only probable prime, i.e. not definitely prime, since technically, probable primality tests were used to show this (which have a ''very'' small chance of making an error, see https://t5k.org/notes/prp_prob.html) because all known primality tests run far too slowly to run on numbers of this size unless either [https://t5k.org/prove/prove3_1.html ''N''−1] or [https://t5k.org/prove/prove3_2.html ''N''+1] (or both) can be ≥ 1/3 factored). '''Athena conjecture''': If family ''xy''_''n''''z'' (with fixed strings ''x'', ''z'' (may be empty), fixed digit ''y'', and variable ''n'') in base ''b'' (with fixed ''b'' ≥ 2) (''x'' does not start with the digit 0, ''z'' ends with a digit which coprime to ''b'', ''y'' is not 0 if ''x'' is empty, ''y'' is coprime to ''b'' if ''z'' is empty) cannot be proven to only contain composites or only contain finitely many primes (by covering congruence, algebraic factorization, or combine of them), then family ''xy''_''n''''z'' in base ''b'' contains infinitely many primes (this is equivalent to: If form (''a''×''b''^''n''+''c'')/''gcd''(''a''+''c'',''b''−1) (with fixed integers ''a'' ≥ 1, ''b'' ≥ 2, ''c'' ≠ 0 (with ''gcd''(''a'',''c'') = 1 and ''gcd''(''b'',''c'') = 1), and variable ''n'') cannot be proven to only contain composites or only contain finitely many primes (by covering congruence, algebraic factorization, or combine of them), then form (''a''×''b''^''n''+''c'')/''gcd''(''a''+''c'',''b''−1) contains infinitely many primes) The numbers in family ''x''{''y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''y'' is a digit in base ''b'') are of the form (''a''×''b''^''n''+''c'')/''gcd''(''a''+''c'',''b''−1) for some fixed ''a'', ''b'', ''c'' such that ''a'' ≥ 1, ''b'' ≥ 2 (''b'' is the base), ''c'' ≠ 0, ''gcd''(''a'',''c'') = 1, ''gcd''(''b'',''c'') = 1. Except in the [[:w:Special case|special case]] ''c'' = ±1 and ''gcd''(''a''+''c'',''b''−1) = 1 (the only case which [https://t5k.org/prove/prove3_1.html ''N''−1] or [https://t5k.org/prove/prove3_2.html ''N''+1] is [[:w:Triviality (mathematics)|trivially]] fully factored), when ''n'' is large the known [[:w:Primality test|primality test]]s for such a number are too inefficient to run (since they are [https://t5k.org/glossary/xpage/OrdinaryPrime.html ordinary primes]). In this case one must resort to a [[:w:Probabilistic algorithm|probable]] primality test such as a [[:w:Miller–Rabin primality test|Miller–Rabin primality test]] or a [[:w:Baillie–PSW primality test|Baillie–PSW primality test]], unless a divisor of the number can be found. Since we are testing many numbers in an [[:w:Exponential growth|exponential sequence]], it is possible to use a sieving process to find divisors rather than using [[:w:Trial division|trial division]]. To do this, we made use of Geoffrey Reynolds' ''srsieve'' software (download: https://pzktupel.de/Software/srsieve_1.1.4.7z). This program uses the [[:w:Baby-step giant-step|baby-step giant-step]] [[:w:Algorithm|algorithm]] to find all primes ''p'' which divide ''a''×''b''^''n''+''c'' where ''p'' and ''n'' lie in a [[:w:Interval_(mathematics)|specified range]]. Since this program cannot handle the general case (''a''×''b''^''n''+''c'')/''gcd''(''a''+''c'',''b''−1) when ''gcd''(''a''+''c'',''b''−1) > 1 we only used it to sieve the sequence ''a''×''b''^''n''+''c'' for primes ''p'' not dividing ''gcd''(''a''+''c'',''b''−1), and initialized the list of candidates to not include ''n'' for which there is some prime ''p'' dividing ''gcd''(''a''+''c'',''b''−1) for which ''p'' dividing (''a''×''b''^''n''+''c'')/''gcd''(''a''+''c'',''b''−1). The program had to be modified slightly to remove a check which would prevent it from running in the case when ''a'', ''b'', and ''c'' were all odd (since then 2 divides ''a''×''b''^''n''+''c'', but 2 may not divide (''a''×''b''^''n''+''c'')/''gcd''(''a''+''c'',''b''−1)). Once the numbers with small divisors had been removed, it remained to test the remaining numbers using a probable primality test. For this we used the software ''LLR'' by Jean Penné. (download: http://jpenne.free.fr/index2.html). Although undocumented, it is possible to run this program on numbers of the form (''a''×''b''^''n''+''c'')/''gcd''(''a''+''c'',''b''−1) when ''gcd''(''a''+''c'',''b''−1) > 1, so this program required no modifications. A script was also written which allowed one to run ''srsieve'' while ''LLR'' was testing the remaining candidates, so that when a divisor was found by srsieve on a number which had not yet been tested by ''LLR'' it would be removed from the list of candidates. For the primes < 10²⁵⁰⁰⁰ for the "easy" bases (bases ''b'' with ≤ 150 primes > 10²⁹⁹ (base ''b'' = 26 has 83 known primes > 10²⁹⁹ and 3 unsolved families, base ''b'' = 36 has 75 known primes > 10²⁹⁹ and 4 unsolved families, base ''b'' = 17 has 99 known primes > 10²⁹⁹ and 18 unsolved families, base ''b'' = 21 has 80 known primes > 10²⁹⁹ and 12 unsolved families, base ''b'' = 19 has 201 known primes > 10²⁹⁹ and 23 unsolved families), i.e. bases *b* = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 24, 26, 28, 30, 36), we employed ''CM'' by Andreas Enge (download: https://www.multiprecision.org/cm/download.html), an elliptic curve primality proving implementation. == Data == These are the results of the Athena problem in bases 2 ≤ ''b'' ≤ 36 (we stop at base 36 since this base is the maximum base for which it is possible to write the numbers with the [[:w:Symbol|symbol]]s 0, 1, 2, ..., 9 and A, B, C, ..., Z (i.e. the 10 [[:w:Arabic numerals|Arabic numerals]] and the 26 [[:w:Latin script|Latin letters]]): (some large Athena primes are only probable primes, i.e. not definitely primes, since they are too large to be [[:w:Elliptic curve primality|ECPP proved]] and [[:w:Pocklington primality test#Extensions and variants|neither ''N''−1 nor ''N''+1 can be ≥ 1/3 factored]], all of them pass the [[:w:Baillie–PSW primality test|Baillie–PSW primality test]] and the [[:w:Strong pseudoprime|strong primality test]] (i.e. the [[:w:Miller–Rabin primality test|Miller–Rabin primality test]]) with all prime bases ''p'' ≤ 61, however, all Athena primes < 10²⁵⁰⁰⁰ for bases ''b'' = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 22, 24, 26, 28, 30, 36 are definitely primes, most of them > 10²⁹⁹ are proven primes with [[:w:Elliptic curve primality|ECPP proving]], others > 10²⁹⁹ are proven primes with [[:w:Pocklington primality test#Extensions and variants|''N''−1 or ''N''+1 proving]]) The Athena primes > 10²⁹⁹ in bases ''b'' = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 24, 26, 28, 30, 36 which are proven primes with ''N''−1 or ''N''+1 proving includes the Athena primes whose ''N''−1 or ''N''+1 is trivially fully factored: * the 3176th Athena prime in base 13, 81010₄₁₅1, which equals 17746×13⁴¹⁶+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000003590431555, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000003590431556&open=ecm * the 3177th Athena prime in base 13, 8110₄₃₅1, which equals 1366×13⁴³⁶+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000002373259109, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000002373259124&open=ecm * the 3188th Athena prime in base 13, 930₁₅₅₁1, which equals 120×13¹⁵⁵²+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000765961452, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000765961453&open=ecm * the 3191st Athena prime in base 13, 390₆₂₆₆1, which equals 48×13⁶²⁶⁷+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000765961441, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000765961451&open=ecm * the 649th Athena prime in base 14, 34D₇₀₈, which equals 47×14⁷⁰⁸−1, ''N''+1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000001540144903, for the factorization of ''N''+1 in ''factordb'' see http://factordb.com/index.php?id=1100000001540144907&open=ecm * the 650th Athena prime in base 14, 4D₁₉₆₉₈, which equals 5×14¹⁹⁶⁹⁸−1, ''N''+1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000884560233, for the factorization of ''N''+1 in ''factordb'' see http://factordb.com/index.php?id=1100000000884560625&open=ecm * the 2335th Athena prime in base 16, 88F₅₄₅, which equals 137×16⁵⁴⁵−1, ''N''+1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000413679658, for the factorization of ''N''+1 in ''factordb'' see http://factordb.com/index.php?id=1100000000413877337&open=ecm * the 10317th Athena prime in base 17, 5A70₂₇₄1, which equals 1622×17²⁷⁵+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000003782940709, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000003782941930&open=ecm * the 10359th Athena prime in base 17, 9D0₁₀₆₇1, which equals 166×17¹⁰⁶⁸+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000765961369, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000765961370&open=ecm * the 10370th Athena prime in base 17, A0₁₃₅₅1, which equals 10×17¹³⁵⁶+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000034167087, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000271866825&open=ecm * the 10386th Athena prime in base 17, 530₄₈₆₇1, which equals 88×17⁴⁸⁶⁸+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000762660735, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000762660737&open=ecm * the 10408th Athena prime in base 17, 570₅₁₃₁₀1, which equals 92×17⁵¹³¹¹+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000765961389, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000785469616&open=ecm * the 10412th Athena prime in base 17, 970₁₆₆₀₄₇1, which equals 160×17¹⁶⁶⁰⁴⁸+1, ''N''−1 is trivially fully factored, but it has no helper file in ''factordb'' since it is too large (>10¹⁹⁹⁹⁹⁹) to be PRP-tested in ''factordb'', for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000890817312&open=ecm * the 10413th Athena prime in base 17, F70₁₈₆₇₆₇1, which equals 262×17¹⁸⁶⁷⁶⁸+1, ''N''−1 is trivially fully factored, but it has no helper file in ''factordb'' since it is too large (>10¹⁹⁹⁹⁹⁹) to be PRP-tested in ''factordb'', for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000890817317&open=ecm * the 3310th Athena prime in base 20, JCJ₆₂₉, which equals 393×20⁶²⁹−1, ''N''+1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000001559454258, for the factorization of ''N''+1 in ''factordb'' see http://factordb.com/index.php?id=1100000001559454271&open=ecm * the 13373rd Athena prime in base 21, 5D0₁₉₈₄₈1, which equals 118×21¹⁹⁸⁴⁹+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000777265872, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000785469310&open=ecm * the 3408th Athena prime in base 24, 88N₅₉₅₁, which equals 201×24⁵⁹⁵¹−1, ''N''+1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000003593275880, for the factorization of ''N''+1 in ''factordb'' see http://factordb.com/index.php?id=1100000003593373246&open=ecm * the 25509th Athena prime in base 28, EB0₄₀₅1, which equals 403×28⁴⁰⁶+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000001534442374, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000001534442380&open=ecm * the 2616th Athena prime in base 30, C0₁₀₂₂1, which equals 12×30¹⁰²³+1, ''N''−1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000785448736, for the factorization of ''N''−1 in ''factordb'' see http://factordb.com/index.php?id=1100000000785448737&open=ecm * the 2619th Athena prime in base 30, OT₃₄₂₀₅, which equals 25×30³⁴²⁰⁵−1, ''N''+1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000800812865, for the factorization of ''N''+1 in ''factordb'' see http://factordb.com/index.php?id=1100000000819405041&open=ecm * the 35237th Athena prime in base 36, P8Z₃₉₀, which equals 909×36³⁹⁰−1, ''N''+1 is trivially fully factored, for its helper file in ''factordb'' see http://factordb.com/helper.php?id=1100000000764100228, for the factorization of ''N''+1 in ''factordb'' see http://factordb.com/index.php?id=1100000000764100231&open=ecm and the Athena primes > 10²⁹⁹ in bases ''b'' = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 24, 26, 28, 30, 36 whose ''N''−1 or ''N''+1 is ≥ 1/3 factored: (''R''_''n''(''b'') means the [[:w:Repunit|repunit]] in base ''b'' with length ''n''), i.e. ''R''_''n''(''b'') = (''b''^''n''−1)/(''b''−1), "''S''_''n''(''b'')" means ''b''^''n''+1) * the 3168th Athena prime in base 13, 9₃₀₈1, ''N''−1 is 117×''R''₃₀₈(13), thus factor ''N''−1 is equivalent to factor the Cunningham number 13³⁰⁸−1, and for the algebraic factors of 13³⁰⁸−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=13&Exp=308&LBIDPMList=A&LBIDLODList=D, and for the prime factorization of 13³⁰⁸−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=13&Exp=308&c0=-&EN=&LM= * the 3179th Athena prime in base 13, B₅₆₃C, ''N''−1 is 11×''R''₅₆₄(13), thus factor ''N''−1 is equivalent to factor the Cunningham number 13⁵⁶⁴−1, and for the algebraic factors of 13⁵⁶⁴−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=13&Exp=564&LBIDPMList=A&LBIDLODList=D, and for the prime factorization of 13⁵⁶⁴−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=13&Exp=564&c0=-&EN=&LM= * the 3180th Athena prime in base 13, 1B₅₇₆, ''N''−1 is 23×''R''₅₇₆(13), thus factor ''N''−1 is equivalent to factor the Cunningham number 13⁵⁷⁶−1, and for the algebraic factors of 13⁵⁷⁶−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=13&Exp=576&LBIDPMList=A&LBIDLODList=D, and for the prime factorization of 13⁵⁷⁶−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=13&Exp=576&c0=-&EN=&LM= * the 10320th Athena prime in base 17, 9₂₉₂1, ''N''−1 is 153×''R''₂₉₂(17), thus factor ''N''−1 is equivalent to factor the Cunningham number 17²⁹²−1, and for the algebraic factors of 17²⁹²−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=17&Exp=292&LBIDPMList=A&LBIDLODList=D, and for the prime factorization of 17²⁹²−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=17&Exp=292&c0=-&EN=&LM= * the 13304th Athena prime in base 21, 7₂₃₀1, ''N''−1 is 147×''R''₂₃₀(21), thus factor ''N''−1 is equivalent to factor the Cunningham number 21²³⁰−1, and for the algebraic factors of 21²³⁰−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=21&Exp=230&LBIDPMList=A&LBIDLODList=D, and for the prime factorization of 21²³⁰−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=21&Exp=230&c0=-&EN=&LM= * the 13355th Athena prime in base 21, 3₁₀₆₃2, ''N''+1 is 3×''R''₁₀₆₄(21), thus factor ''N''−1 is equivalent to factor the Cunningham number 21¹⁰⁶⁴−1, and for the algebraic factors of 21¹⁰⁶⁴−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=21&Exp=1064&LBIDPMList=A&LBIDLODList=D, and for the prime factorization of 21¹⁰⁶⁴−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=21&Exp=1064&c0=-&EN=&LM= * the 25199th Athena prime in base 26, 9K₃₄₃AP, ''N''+1 is 6370×''R''₃₄₄(26), thus factor ''N''+1 is equivalent to factor the Cunningham number 26³⁴⁴−1, and for the algebraic factors of 26³⁴⁴−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=26&Exp=344&LBIDPMList=A&LBIDLODList=D, and for the prime factorization of 26³⁴⁴−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=26&Exp=344&c0=-&EN=&LM= * the 25200th Athena prime in base 26, 8₃₅₄1, ''N''−1 is 208×''R''₃₅₄(26), thus factor ''N''−1 is equivalent to factor the Cunningham number 26³⁵⁴−1, and for the algebraic factors of 26³⁵⁴−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showExplorer?Base=26&Exp=354&LBIDPMList=A&LBIDLODList=D, and for the prime factorization of 26³⁵⁴−1, see http://myfactorcollection.mooo.com:8090/cgi-bin/showSingleEntry?Base=26&Exp=354&c0=-&EN=&LM= All numbers are written in base ''b'', [[:w:Senary#Base 36 as senary compression|using A to Z to represent digit values 10 to 35]], "{}" means repeating, e.g. family 12{3}45 means the sequence {1245, 12345, 123345, 1233345, 12333345, 123333345, ...} (where the members are expressed as base ''b'' strings), subscripts are used to indicate repetitions of digits, e.g. 123₄567 means 123333567 (all subscripts are written in decimal). Base 2: 1 Athena prime (the largest of which has 2 digits (it is 11, and its value is 3 in decimal)): {11} Base 3: 3 Athena primes (the largest of which has 3 digits (it is 111, and its value is 13 in decimal)): {12, 21, 111} Base 4: 5 Athena primes (the largest of which has 3 digits (it is 221, and its value is 41 in decimal)): {11, 13, 23, 31, 221} Base 5: 22 Athena primes (the largest of which has 96 digits (it is 10₉₃13, and its algebraic form is 5⁹⁵+8)): {12, 21, 23, 32, 34, 43, 104, 111, 131, 133, 313, 401, 414, 3101, 10103, 14444, 30301, 33001, 33331, 44441, 300031, 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000013} Base 6: 11 Athena primes (the largest of which has 5 digits (it is 40041, and its value is 5209 in decimal)): {11, 15, 21, 25, 31, 35, 45, 51, 4401, 4441, 40041} Base 7: 71 Athena primes (the largest of which has 17 digits (it is 3₁₆1, and its algebraic form is (7¹⁷−5)/2)): {14, 16, 23, 25, 32, 41, 43, 52, 56, 61, 65, 113, 115, 131, 133, 155, 212, 221, 304, 313, 335, 344, 346, 364, 445, 515, 533, 535, 544, 551, 553, 1022, 1051, 1112, 1202, 1211, 1222, 2111, 3031, 3055, 3334, 3503, 3505, 3545, 4504, 4555, 5011, 5455, 5545, 5554, 6034, 6634, 11111, 11201, 30011, 30101, 31001, 31111, 33001, 33311, 35555, 40054, 100121, 150001, 300053, 351101, 531101, 1100021, 33333301, 5100000001, 33333333333333331} Base 8: 75 Athena primes (the largest of which has 221 digits (it is 4₂₂₀7, and its algebraic form is (4×8²²¹+17)/7)): {13, 15, 21, 23, 27, 35, 37, 45, 51, 53, 57, 65, 73, 75, 107, 111, 117, 141, 147, 161, 177, 225, 255, 301, 343, 361, 401, 407, 417, 431, 433, 463, 467, 471, 631, 643, 661, 667, 701, 711, 717, 747, 767, 3331, 3411, 4043, 4443, 4611, 5205, 6007, 6101, 6441, 6477, 6707, 6777, 7461, 7641, 47777, 60171, 60411, 60741, 444641, 500025, 505525, 3344441, 4444477, 5500525, 5550525, 55555025, 444444441, 744444441, 77774444441, 7777777777771, 555555555555525, 44444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444447} Base 9: 151 Athena primes (the largest of which has 1161 digits (it is 30₁₁₅₈11, and its algebraic form is 3×9¹¹⁶⁰+10)): {12, 14, 18, 21, 25, 32, 34, 41, 45, 47, 52, 58, 65, 67, 74, 78, 81, 87, 117, 131, 135, 151, 155, 175, 177, 238, 272, 308, 315, 331, 337, 355, 371, 375, 377, 438, 504, 515, 517, 531, 537, 557, 564, 601, 638, 661, 702, 711, 722, 735, 737, 751, 755, 757, 771, 805, 838, 1011, 1015, 1101, 1701, 2027, 2207, 3017, 3057, 3101, 3501, 3561, 3611, 3688, 3868, 5035, 5051, 5071, 5101, 5501, 5554, 5705, 5707, 7017, 7075, 7105, 7301, 8535, 8544, 8555, 8854, 20777, 22227, 22777, 30161, 33388, 50161, 50611, 53335, 55111, 55535, 55551, 57061, 57775, 70631, 71007, 77207, 100037, 100071, 100761, 105007, 270707, 301111, 305111, 333035, 333385, 333835, 338885, 350007, 500075, 530005, 555611, 631111, 720707, 2770007, 3030335, 7776662, 30300005, 30333335, 38333335, 51116111, 70000361, 300030005, 300033305, 351111111, 1300000007, 5161111111, 8333333335, 300000000035, 311111111161, 544444444444, 2000000000007, 5700000000001, 7270000000007, 88888888833335, 100000000000507, 5111111111111161, 7277777777777777707, 8888888888888888888335, 30000000000000000000051, 1000000000000000000000000057, 56111111111111111111111111111111111111, 7666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666662, 27777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777707, 300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011} Base 10: 77 Athena primes (the largest of which has 31 digits (it is 50₂₈27, and its algebraic form is 5×10³⁰+27)): {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027} Base 11: 1068 Athena (probable) primes (including 1 unproven probable prime: 57₆₂₆₆₈), the largest of which has 62669 digits (it is 57₆₂₆₆₈, and its algebraic form is (57×11⁶²⁶⁶⁸−7)/10), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel11 Data of Athena (probable) primes base 11] Base 12: 106 Athena primes (the largest of which has 42 digits (it is 40₃₉77, and its algebraic form is 4×12⁴¹+91)): {11, 15, 17, 1B, 25, 27, 31, 35, 37, 3B, 45, 4B, 51, 57, 5B, 61, 67, 6B, 75, 81, 85, 87, 8B, 91, 95, A7, AB, B5, B7, 221, 241, 2A1, 2B1, 2BB, 401, 421, 447, 471, 497, 565, 655, 665, 701, 70B, 721, 747, 771, 77B, 797, 7A1, 7BB, 907, 90B, 9BB, A41, B21, B2B, 2001, 200B, 202B, 222B, 229B, 292B, 299B, 4441, 4707, 4777, 6A05, 6AA5, 729B, 7441, 7B41, 929B, 9777, 992B, 9947, 997B, 9997, A0A1, A201, A605, A6A5, AA65, B001, B0B1, BB01, BB41, 600A5, 7999B, 9999B, AAAA1, B04A1, B0B9B, BAA01, BAAA1, BB09B, BBBB1, 44AAA1, A00065, BBBAA1, AAA0001, B00099B, AA000001, BBBBBB99B, B0000000000000000000000000009B, 400000000000000000000000000000000000000077} Base 13: 3197 Athena (probable) primes (including 4 unproven probable primes: C5₂₃₇₅₅C, 80₃₂₀₁₇111, 95₁₉₇₄₂₀, A3₅₉₂₁₉₇A), the largest of which has 592199 digits (it is A3₅₉₂₁₉₇A, and its algebraic form is (41×13⁵⁹²¹⁹⁸+27)/4), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel13 Data of Athena (probable) primes base 13] Base 14: 650 Athena primes, the largest of which has 19699 digits (it is 4D₁₉₆₉₈, and its algebraic form is 5×14¹⁹⁶⁹⁸−1), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel14 Data of Athena primes base 14] Base 15: 1284 Athena primes, the largest of which has 157 digits (it is 7₁₅₅97, and its algebraic form is (15¹⁵⁷+59)/2), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel15 Data of Athena primes base 15] Base 16: 2347 Athena (probable) primes (including 3 unproven probable primes: DB₃₂₂₃₄, 4₇₂₇₈₅DD, 3₁₁₆₁₃₇AF), the largest of which has 116139 digits (it is 3₁₁₆₁₃₇AF, and its algebraic form is (16¹¹⁶¹³⁹+619)/5), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel16 Data of Athena (probable) primes base 16] Base 17: 10415 known Athena (probable) primes (including many unproven probable primes) and 12 unsolved families (1{7}, 1F{0}7, 4{7}A, 70F{0}D, 8{B}9, 9{5}9, A{D}F, B{0}B3, {B}E9, {B}EE, F1{9}, FD0{D}, no primes or probable primes with length ≤ 200000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel17 Data of known Athena (probable) primes base 17] Base 18: 549 Athena primes, the largest of which has 6271 digits (it is C0₆₂₆₈C5, and its algebraic form is 12×18⁶²⁷⁰+221), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel18 Data of Athena primes base 18] Base 19: 31417 known Athena (probable) primes (including many unproven probable primes) and 17 unsolved families (4B5{0}H, {5}3, 5{H}05, 5{H}0H, 5{H}5, 66{B}, 71{0}177, 7AF{0}H, 97{0}3, C{H}C, EE1{6}, F{7}5, F{B}G, F{D}F, H0F{0}7A, HB{0}5B5, II{D}, no primes or probable primes with length ≤ 200000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel19 Data of known Athena (probable) primes base 19] Base 20: 3314 Athena primes, the largest of which has 6271 digits (it is G0₆₂₆₉D, and its algebraic form is 16×20⁶²⁷⁰+13), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel20 Data of Athena primes base 20] Base 21: 13386 known Athena (probable) primes (including many unproven probable primes) and 8 unsolved families (5{0}DJ, {9}D, B3{0}EB, B{H}6H, C{F}0K, {F}35, G{0}FK, H{0}7771, no primes or probable primes with length ≤ 200000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel21 Data of known Athena (probable) primes base 21] Base 22: 8003 Athena (probable) primes (including 1 unproven probable prime: BK₂₂₀₀₁5), the largest of which has 22003 digits (it is BK₂₂₀₀₁5, and its algebraic form is (251×22²²⁰⁰²−335)/21), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel22 Data of Athena (probable) primes base 22] Base 23: 65178 known Athena (probable) primes (including many unproven probable primes) and 87 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel23 Data of known Athena (probable) primes base 23] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left23 Data of unsolved families for Athena problem base 23] Base 24: 3409 Athena primes, the largest of which has 8134 digits (it is N00N₈₁₂₉LN, and its algebraic form is 13249×24⁸¹³¹−49), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel24 Data of Athena primes base 24] Base 25: 133639 known Athena (probable) primes (including many unproven probable primes) and 85 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel25 Data of known Athena (probable) primes base 25] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left25 Data of unsolved families for Athena problem base 25] Base 26: 25256 known Athena (probable) primes (including 7 unproven probable primes: 5₁₉₃₉₁6F, 7₂₀₂₇₉OL, LD0₂₀₉₇₅7, 6K₂₃₃₀₀5, J0₄₄₃₀₃KCB, M0₆₁₁₈₆2BB, 85M₁₉₇₀₆₀B) and 3 unsolved families ({A}6F, {H}MH, {I}GL, no primes or probable primes with length ≤ 200000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel26 Data of known Athena (probable) primes base 26] Base 27: 102852 known Athena (probable) primes (including many unproven probable primes) and 44 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel27 Data of known Athena (probable) primes base 27] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left27 Data of unsolved families for Athena problem base 27] Base 28: 25528 known Athena (probable) primes (including 3 unproven probable primes: N6₂₄₀₅₁LR, 5OA₃₁₂₃₈F, O4O₉₄₅₃₅9) and 1 unsolved family (O{A}F, no primes or probable primes with length ≤ 900000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel28 Data of known Athena (probable) primes base 28] Base 29: 355242 known Athena (probable) primes (including many unproven probable primes) and 125 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel29 Data of known Athena (probable) primes base 29] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left29 Data of unsolved families for Athena problem base 29] Base 30: 2619 Athena (probable) primes (including 1 unproven probable prime: I0₂₄₆₀₈D), the largest of which has 34206 digits (it is OT₃₄₂₀₅, and its algebraic form is 25×30³⁴²⁰⁵−1), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel30 Data of Athena (probable) primes base 30] Base 31: 569323 known Athena (probable) primes (including many unproven probable primes) and 77 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel31 Data of known Athena (probable) primes base 31] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left31 Data of unsolved families for Athena problem base 31] Base 32: 168882 known Athena (probable) primes (including many unproven probable primes) and 120 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel32 Data of known Athena (probable) primes base 32] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left32 Data of unsolved families for Athena problem base 32] Base 33: 280012 known Athena (probable) primes (including many unproven probable primes) and 81 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel33 Data of known Athena (probable) primes base 33] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left33 Data of unsolved families for Athena problem base 33] Base 34: 184785 known Athena (probable) primes (including many unproven probable primes) and 47 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel34 Data of known Athena (probable) primes base 34] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left34 Data of unsolved families for Athena problem base 34] Base 35: 720002 known Athena (probable) primes (including many unproven probable primes) and 60 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel35 Data of known Athena (probable) primes base 35] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left35 Data of unsolved families for Athena problem base 35] Base 36: 35286 known Athena (probable) primes (including 3 unproven probable primes: 7K₂₆₅₆₇Z, S0₇₅₀₀₇8H, P₈₁₉₉₃SZ) and 4 unsolved families (B{0}EUV, HM{0}N, N{0}YYN, O{L}Z, no primes or probable primes with length ≤ 200000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel36 Data of known Athena (probable) primes base 36] == Condensed table for bases 2 ≤ ''b'' ≤ 36 == {|class="wikitable" ||''b''||number of Athena primes (or probable primes, which are Athena primes assuming their primality) in base ''b''||base-''b'' form of the top 10 known Athena primes (or probable primes, which are Athena primes assuming their primality) in base ''b'' (write "''d''_''n''" if there are 5 or more (''n'') consecutive same digits ''d'')||length of the top 10 known Athena primes (or probable primes, which are Athena primes assuming their primality) in base ''b''||length of the top 10 known Athena primes (or probable primes, which are Athena primes assuming their primality) in base ''b'' in decimal||algebraic ((''a''×''b''^''n''+''c'')/''gcd''(''a''+''c'',''b''−1)) form of the top 10 known Athena primes (or probable primes, which are Athena primes assuming their primality) in base ''b''||''factordb'' entry of the top 10 known Athena primes (or probable primes, which are Athena primes assuming their primality) in base ''b''||the top 10 known Athena primes (or probable primes, which are Athena primes assuming their primality) in base ''b'' written in base ''b'' (use lower case letters instead of upper case letters)||number of unsolved families in the Athena problem in base ''b'' (all of these left families are linear families)||searching limit of length for the unsolved families in the Athena problem in base ''b'' (if there are different searching limits for the unsolved families in the Athena problem in base ''b'', choose the lowest searching limit)|| |- ||2||1||11||2||1||3||http://factordb.com/index.php?id=3&open=ecm||http://factordb.com/index.php?showid=3&base=2||0||–|| |- ||3||3||111<br>21<br>12||3<br>2<br>2||2<br>1<br>1||13<br>7<br>5||http://factordb.com/index.php?id=13&open=ecm<br>http://factordb.com/index.php?id=7&open=ecm<br>http://factordb.com/index.php?id=5&open=ecm<nowiki/>||http://factordb.com/index.php?showid=13&base=3<br>http://factordb.com/index.php?showid=7&base=3<br>http://factordb.com/index.php?showid=5&base=3<nowiki/>||0||–|| |- ||4||5||221<br>31<br>23<br>13<br>11||3<br>2<br>2<br>2<br>2||2<br>2<br>2<br>1<br>1||41<br>13<br>11<br>7<br>5||http://factordb.com/index.php?id=41&open=ecm<br>http://factordb.com/index.php?id=13&open=ecm<br>http://factordb.com/index.php?id=11&open=ecm<br>http://factordb.com/index.php?id=7&open=ecm<br>http://factordb.com/index.php?id=5&open=ecm<nowiki/>||http://factordb.com/index.php?showid=41&base=4<br>http://factordb.com/index.php?showid=13&base=4<br>http://factordb.com/index.php?showid=11&base=4<br>http://factordb.com/index.php?showid=7&base=4<br>http://factordb.com/index.php?showid=5&base=4<nowiki/>||0||–|| |- ||5||22||10₉₃13<br>300031<br>44441<br>33331<br>33001<br>30301<br>14444<br>10103<br>3101<br>414||96<br>6<br>5<br>5<br>5<br>5<br>5<br>5<br>4<br>3||67<br>4<br>4<br>4<br>4<br>4<br>4<br>3<br>3<br>3||5⁹⁵+8<br>9391<br>3121<br>2341<br>2251<br>1951<br>1249<br>653<br>401<br>109||http://factordb.com/index.php?id=1100000000034686071&open=ecm<br>http://factordb.com/index.php?id=9391&open=ecm<br>http://factordb.com/index.php?id=3121&open=ecm<br>http://factordb.com/index.php?id=2341&open=ecm<br>http://factordb.com/index.php?id=2251&open=ecm<br>http://factordb.com/index.php?id=1951&open=ecm<br>http://factordb.com/index.php?id=1249&open=ecm<br>http://factordb.com/index.php?id=653&open=ecm<br>http://factordb.com/index.php?id=401&open=ecm<br>http://factordb.com/index.php?id=109&open=ecm<nowiki/>||http://factordb.com/index.php?showid=1100000000034686071&base=5<br>http://factordb.com/index.php?showid=9391&base=5<br>http://factordb.com/index.php?showid=3121&base=5<br>http://factordb.com/index.php?showid=2341&base=5<br>http://factordb.com/index.php?showid=2251&base=5<br>http://factordb.com/index.php?showid=1951&base=5<br>http://factordb.com/index.php?showid=1249&base=5<br>http://factordb.com/index.php?showid=653&base=5<br>http://factordb.com/index.php?showid=401&base=5<br>http://factordb.com/index.php?showid=109&base=5<nowiki/>||0||–|| |- ||6||11||40041<br>4441<br>4401<br>51<br>45<br>35<br>31<br>25<br>21<br>15||5<br>4<br>4<br>2<br>2<br>2<br>2<br>2<br>2<br>2||4<br>4<br>4<br>2<br>2<br>2<br>2<br>2<br>2<br>2||5209<br>1033<br>1009<br>31<br>29<br>23<br>19<br>17<br>13<br>11||http://factordb.com/index.php?id=5209&open=ecm<br>http://factordb.com/index.php?id=1033&open=ecm<br>http://factordb.com/index.php?id=1009&open=ecm<br>http://factordb.com/index.php?id=31&open=ecm<br>http://factordb.com/index.php?id=29&open=ecm<br>http://factordb.com/index.php?id=23&open=ecm<br>http://factordb.com/index.php?id=19&open=ecm<br>http://factordb.com/index.php?id=17&open=ecm<br>http://factordb.com/index.php?id=13&open=ecm<br>http://factordb.com/index.php?id=11&open=ecm<nowiki/>||http://factordb.com/index.php?showid=5209&base=6<br>http://factordb.com/index.php?showid=1033&base=6<br>http://factordb.com/index.php?showid=1009&base=6<br>http://factordb.com/index.php?showid=31&base=6<br>http://factordb.com/index.php?showid=29&base=6<br>http://factordb.com/index.php?showid=23&base=6<br>http://factordb.com/index.php?showid=19&base=6<br>http://factordb.com/index.php?showid=17&base=6<br>http://factordb.com/index.php?showid=13&base=6<br>http://factordb.com/index.php?showid=11&base=6<nowiki/>||0||–|| |- 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|- 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|- 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|- 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||15||1284||7₁₅₅97<br>E₁₄₅397<br>96₁₀₄08<br>7₇₃CE<br>7₅₉CCE<br>50₃₃17<br>EB₃₁<br>6330₂₆1<br>7050₂₄B<br>B70₂₄1||157<br>148<br>107<br>75<br>62<br>36<br>32<br>30<br>28<br>27||185<br>175<br>126<br>88<br>73<br>42<br>38<br>35<br>33<br>32||(15¹⁵⁷+59)/2<br>15¹⁴⁸−2558<br>(66×15¹⁰⁶−619)/7<br>(15⁷⁵+163)/2<br>(15⁶²+2413)/2<br>5×15³⁵+22<br>(207×15³¹−11)/14<br>1398×15²⁷+1<br>1580×15²⁵+11<br>172×15²⁵+1||http://factordb.com/index.php?id=1100000002454891840&open=ecm<br>http://factordb.com/index.php?id=1100000002454900849&open=ecm<br>http://factordb.com/index.php?id=1100000000823937997&open=ecm<br>http://factordb.com/index.php?id=1100000003588407143&open=ecm<br>http://factordb.com/index.php?id=1100000003588407386&open=ecm<br>http://factordb.com/index.php?id=1100000002632398579&open=ecm<br>http://factordb.com/index.php?id=1100000002321033312&open=ecm<br>http://factordb.com/index.php?id=1100000002391199877&open=ecm<br>http://factordb.com/index.php?id=1100000003588407806&open=ecm<br>http://factordb.com/index.php?id=1100000000851967288&open=ecm<nowiki/>||http://factordb.com/index.php?showid=1100000002454891840&base=15<br>http://factordb.com/index.php?showid=1100000002454900849&base=15<br>http://factordb.com/index.php?showid=1100000000823937997&base=15<br>http://factordb.com/index.php?showid=1100000003588407143&base=15<br>http://factordb.com/index.php?showid=1100000003588407386&base=15<br>http://factordb.com/index.php?showid=1100000002632398579&base=15<br>http://factordb.com/index.php?showid=1100000002321033312&base=15<br>http://factordb.com/index.php?showid=1100000002391199877&base=15<br>http://factordb.com/index.php?showid=1100000003588407806&base=15<br>http://factordb.com/index.php?showid=1100000000851967288&base=15<nowiki/>||0||–|| |- ||16||2347||3₁₁₆₁₃₇AF<br>4₇₂₇₈₅DD<br>DB₃₂₂₃₄<br>D0B₁₇₈₀₄<br>5BC₃₇₀₀D<br>90₃₅₄₂91<br>300F₁₉₆₀AF<br>20₁₇₁₃321<br>F8₁₅₁₇F<br>FAF₁₀₆₂45||116139<br>72787<br>32235<br>17806<br>3703<br>3545<br>1965<br>1717<br>1519<br>1066||139845<br>87644<br>38815<br>21441<br>4459<br>4269<br>2366<br>2067<br>1830<br>1284||(16¹¹⁶¹³⁹+619)/5<br>(4×16⁷²⁷⁸⁷+2291)/15<br>(206×16³²²³⁴−11)/15<br>(3131×16¹⁷⁸⁰⁴−11)/15<br>(459×16³⁷⁰¹+1)/5<br>9×16³⁵⁴⁴+145<br>769×16¹⁹⁶²−81<br>2×16¹⁷¹⁶+801<br>(233×16¹⁵¹⁸+97)/15<br>251×16¹⁰⁶⁴−187||http://factordb.com/index.php?id=1100000003851731988&open=prime<br>http://factordb.com/index.php?id=1100000003615909841&open=prime<br>http://factordb.com/index.php?id=1100000002383583629&open=prime<br>http://factordb.com/index.php?id=1100000003589278511&open=prime<br>http://factordb.com/index.php?id=1100000000993764322&open=prime<br>http://factordb.com/index.php?id=1100000000633424191&open=prime<br>http://factordb.com/index.php?id=1100000003588368750&open=prime<br>http://factordb.com/index.php?id=1100000003588386735&open=prime<br>http://factordb.com/index.php?id=1100000000633744824&open=prime<br>http://factordb.com/index.php?id=1100000003588387610&open=prime<nowiki/>||http://factordb.com/index.php?showid=1100000003851731988&base=16<br>http://factordb.com/index.php?showid=1100000003615909841&base=16<br>http://factordb.com/index.php?showid=1100000002383583629&base=16<br>http://factordb.com/index.php?showid=1100000003589278511&base=16<br>http://factordb.com/index.php?showid=1100000000993764322&base=16<br>http://factordb.com/index.php?showid=1100000000633424191&base=16<br>http://factordb.com/index.php?showid=1100000003588368750&base=16<br>http://factordb.com/index.php?showid=1100000003588386735&base=16<br>http://factordb.com/index.php?showid=1100000000633744824&base=16<br>http://factordb.com/index.php?showid=1100000003588387610&base=16<nowiki/>||0||–|| |- ||17||10415~10427||95F₁₉₈₈₅₅<br>B0₁₈₉₀₈₃DB<br>F70₁₈₆₇₆₇1<br>970₁₆₆₀₄₇1<br>510₁₂₄₀₇₄D<br>49₁₁₁₃₃₃<br>B₆₇₁₀₃2E<br>570₅₁₃₁₀1<br>E9B₄₄₇₃₂<br>D0GD₃₇₀₉₆||198857<br>189086<br>186770<br>166050<br>124077<br>111334<br>67105<br>51313<br>44734<br>37099||244684<br>232661<br>229811<br>204316<br>152670<br>136991<br>82570<br>63138<br>55043<br>45649||(2543×17¹⁹⁸⁸⁵⁵−15)/16<br>11×17¹⁸⁹⁰⁸⁵+232<br>262×17¹⁸⁶⁷⁶⁸+1<br>160×17¹⁶⁶⁰⁴⁸+1<br>86×17¹²⁴⁰⁷⁵+13<br>(73×17¹¹¹³³³−9)/16<br>(11×17⁶⁷¹⁰⁵−2411)/16<br>92×17⁵¹³¹¹+1<br>(3963×17⁴⁴⁷³²−11)/16<br>(60381×17³⁷⁰⁹⁶−13)/16||http://factordb.com/index.php?id=1100000008610514108&open=prime<br>http://factordb.com/index.php?id=1100000008610515753&open=prime<br>http://factordb.com/index.php?id=1100000000765961429&open=prime<br>http://factordb.com/index.php?id=1100000000765961411&open=prime<br>http://factordb.com/index.php?id=1100000008610516879&open=prime<br>http://factordb.com/index.php?id=1100000000808118219&open=prime<br>http://factordb.com/index.php?id=1100000003993647842&open=prime<br>http://factordb.com/index.php?id=1100000000765961389&open=prime<br>http://factordb.com/index.php?id=1100000003883765450&open=prime<br>http://factordb.com/index.php?id=1100000003848346668&open=prime<nowiki/>||http://factordb.com/index.php?showid=1100000008610514108&base=17<br>http://factordb.com/index.php?showid=1100000008610515753&base=17<br>http://factordb.com/index.php?showid=1100000000765961429&base=17<br>http://factordb.com/index.php?showid=1100000000765961411&base=17<br>http://factordb.com/index.php?showid=1100000008610516879&base=17<br>http://factordb.com/index.php?showid=1100000000808118219&base=17<br>http://factordb.com/index.php?showid=1100000003993647842&base=17<br>http://factordb.com/index.php?showid=1100000000765961389&base=17<br>http://factordb.com/index.php?showid=1100000003883765450&base=17<br>http://factordb.com/index.php?showid=1100000003848346668&base=17<nowiki/>||12||200000|| |- ||18||549||C0₆₂₆₈C5<br>H₇₆₆FH<br>80₂₉₈B<br>C0₁₁₆F5<br>HD₉₃<br>GG0₃₀1<br>CF₃₀5<br>B₁₉6B<br>CCF₁₄5<br>7₁₄G7||6271<br>768<br>300<br>119<br>94<br>33<br>32<br>21<br>17<br>16||7872<br>965<br>377<br>150<br>118<br>42<br>41<br>27<br>22<br>20||12×18⁶²⁷⁰+221<br>18⁷⁶⁸−37<br>8×18²⁹⁹+11<br>12×18¹¹⁸+275<br>(302×18⁹³−13)/17<br>304×18³¹+1<br>(219×18³¹−185)/17<br>(11×18²¹−1541)/17<br>(3891×18¹⁵−185)/17<br>(7×18¹⁶+2747)/17||http://factordb.com/index.php?id=1100000003590442437&open=prime<br>http://factordb.com/index.php?id=1100000003590430490&open=prime<br>http://factordb.com/index.php?id=1100000002355574745&open=prime<br>http://factordb.com/index.php?id=1100000002632837015&open=ecm<br>http://factordb.com/index.php?id=1100000002321052894&open=ecm<br>http://factordb.com/index.php?id=1100000000819230161&open=ecm<br>http://factordb.com/index.php?id=1100000002631240657&open=ecm<br>http://factordb.com/index.php?id=1100000003590430474&open=ecm<br>http://factordb.com/index.php?id=1100000003590430470&open=ecm<br>http://factordb.com/index.php?id=1100000003590430465&open=ecm<nowiki/>||http://factordb.com/index.php?showid=1100000003590442437&base=18<br>http://factordb.com/index.php?showid=1100000003590430490&base=18<br>http://factordb.com/index.php?showid=1100000002355574745&base=18<br>http://factordb.com/index.php?showid=1100000002632837015&base=18<br>http://factordb.com/index.php?showid=1100000002321052894&base=18<br>http://factordb.com/index.php?showid=1100000000819230161&base=18<br>http://factordb.com/index.php?showid=1100000002631240657&base=18<br>http://factordb.com/index.php?showid=1100000003590430474&base=18<br>http://factordb.com/index.php?showid=1100000003590430470&base=18<br>http://factordb.com/index.php?showid=1100000003590430465&base=18<nowiki/>||0||–|| |- ||19||31417~31434||1E70₁₂₂₈₉₆1<br>40₁₂₁₈₄₆HB5<br>35₁₂₀₅₆₂<br>FH0H₁₁₂₆₅₉<br>FG6₁₁₀₉₈₄<br>H₈₆₂₉₁6<br>D90₇₃₀₄₆9<br>4F0₄₉₈₄₇6<br>2₄₈₂₂₄7<br>2₄₅₈₈₆7A||122900<br>121850<br>120563<br>112662<br>110986<br>86292<br>73049<br>49850<br>48225<br>45888||157158<br>155816<br>154170<br>144067<br>110347<br>141924<br>93412<br>63746<br>61667<br>58679||634×19¹²²⁸⁹⁷+1<br>4×19¹²¹⁸⁴⁹+6351<br>(59×19¹²⁰⁵⁶²−5)/18<br>(103301×19¹¹²⁶⁵⁹−17)/18<br>(904×19¹¹⁰⁹⁸⁴−1)/3<br>(17×19⁸⁶²⁹²−215)/18<br>256×19⁷³⁰⁴⁷+9<br>91×19⁴⁹⁸⁴⁸+6<br>(19⁴⁸²²⁵+44)/9<br>(19⁴⁵⁸⁸⁸+926)/9||http://factordb.com/index.php?id=1100000001582289581&open=prime<br>http://factordb.com/index.php?id=1100000008755307222&open=prime<br>http://factordb.com/index.php?id=1100000005513825027&open=prime<br>http://factordb.com/index.php?id=1100000008755311453&open=prime<br>http://factordb.com/index.php?id=1100000000808118212&open=prime<br>http://factordb.com/index.php?id=1100000004163040839&open=prime<br>http://factordb.com/index.php?id=1100000003998413751&open=prime<br>http://factordb.com/index.php?id=1100000000808118332&open=prime<br>http://factordb.com/index.php?id=1100000003949188041&open=prime<br>http://factordb.com/index.php?id=1100000003949189035&open=prime<nowiki/>||http://factordb.com/index.php?showid=1100000001582289581&base=19<br>http://factordb.com/index.php?showid=1100000008755307222&base=19<br>http://factordb.com/index.php?showid=1100000005513825027&base=19<br>http://factordb.com/index.php?showid=1100000008755311453&base=19<br>http://factordb.com/index.php?showid=1100000000808118212&base=19<br>http://factordb.com/index.php?showid=1100000004163040839&base=19<br>http://factordb.com/index.php?showid=1100000003998413751&base=19<br>http://factordb.com/index.php?showid=1100000000808118332&base=19<br>http://factordb.com/index.php?showid=1100000003949188041&base=19<br>http://factordb.com/index.php?showid=1100000003949189035&base=19<nowiki/>||17||200000|| |- ||20||3314||G0₆₂₆₉D<br>CD₂₄₄₉<br>50₁₁₆₃AJ<br>J₆₅₅05J<br>JCJ₆₂₉<br>E₅₆₆C7<br>3A₅₂₇3<br>G₄₄₇99<br>EC0₄₂₉7<br>40₃₈₇404B||6271<br>2450<br>1166<br>658<br>631<br>568<br>529<br>449<br>432<br>392||8159<br>3188<br>1517<br>857<br>821<br>739<br>688<br>585<br>562<br>510||16×20⁶²⁷⁰+13<br>(241×20²⁴⁴⁹−13)/19<br>5×20¹¹⁶⁵+219<br>20⁶⁵⁸−7881<br>393×20⁶²⁹−1<br>(14×20⁵⁶⁸−907)/19<br>(67×20⁵²⁸−143)/19<br>(16×20⁴⁴⁹−2809)/19<br>292×20⁴³⁰+7<br>4×20³⁹¹+32091||http://factordb.com/index.php?id=1100000003590539457&open=prime<br>http://factordb.com/index.php?id=1100000002325393915&open=prime<br>http://factordb.com/index.php?id=1100000003590502412&open=prime<br>http://factordb.com/index.php?id=1100000003590502490&open=prime<br>http://factordb.com/index.php?id=1100000001559454258&open=prime<br>http://factordb.com/index.php?id=1100000003590502516&open=prime<br>http://factordb.com/index.php?id=1100000003590502531&open=prime<br>http://factordb.com/index.php?id=1100000000840126753&open=prime<br>http://factordb.com/index.php?id=1100000002633348702&open=prime<br>http://factordb.com/index.php?id=1100000003590502563&open=prime<nowiki/>||http://factordb.com/index.php?showid=1100000003590539457&base=20<br>http://factordb.com/index.php?showid=1100000002325393915&base=20<br>http://factordb.com/index.php?showid=1100000003590502412&base=20<br>http://factordb.com/index.php?showid=1100000003590502490&base=20<br>http://factordb.com/index.php?showid=1100000001559454258&base=20<br>http://factordb.com/index.php?showid=1100000003590502516&base=20<br>http://factordb.com/index.php?showid=1100000003590502531&base=20<br>http://factordb.com/index.php?showid=1100000000840126753&base=20<br>http://factordb.com/index.php?showid=1100000002633348702&base=20<br>http://factordb.com/index.php?showid=1100000003590502563&base=20<nowiki/>||0||–|| |- ||21||13386~13394||27₁₈₄₄₉₉9D<br>F9₁₇₈₇₇₁D<br>2FC₁₁₂₀₂₂A<br>7₁₀₈₄₅₀ID<br>40₄₇₃₃₃9G<br>B90₄₅₀₁₉E5<br>HD₃₇₄₁₄<br>BD₃₅₀₂₇B<br>990₃₃₂₃₉99H<br>5₃₀₆₀₆FEK||184502<br>178773<br>112025<br>108452<br>47336<br>45023<br>37415<br>35029<br>33244<br>30609||243952<br>236377<br>148121<br>143397<br>62588<br>59531<br>49471<br>46316<br>43956<br>40472||(47×21¹⁸⁴⁵⁰¹+953)/20<br>(309×21¹⁷⁸⁷⁷²+71)/20<br>(288×21¹¹²⁰²³−13)/5<br>(7×21¹⁰⁸⁴⁵²+4733)/20<br>4×21⁴⁷³³⁵+205<br>240×21⁴⁵⁰²¹+299<br>(353×21³⁷⁴¹⁴−13)/20<br>(233×21³⁵⁰²⁸−53)/20<br>198×21³³²⁴²+4175<br>(21³⁰⁶⁰⁹+18455)/4||http://factordb.com/index.php?id=1100000008700600990&open=prime<br>http://factordb.com/index.php?id=1100000008700596669&open=prime<br>http://factordb.com/index.php?id=1100000008700593358&open=prime<br>http://factordb.com/index.php?id=1100000008700586183&open=prime<br>http://factordb.com/index.php?id=1100000000808118331&open=prime<br>http://factordb.com/index.php?id=1100000003996110311&open=prime<br>http://factordb.com/index.php?id=1100000003996110479&open=prime<br>http://factordb.com/index.php?id=1100000003996110718&open=prime<br>http://factordb.com/index.php?id=1100000003996110944&open=prime<br>http://factordb.com/index.php?id=1100000003996111130&open=prime<nowiki/>||http://factordb.com/index.php?showid=1100000008700600990&base=21<br>http://factordb.com/index.php?showid=1100000008700596669&base=21<br>http://factordb.com/index.php?showid=1100000008700593358&base=21<br>http://factordb.com/index.php?showid=1100000008700586183&base=21<br>http://factordb.com/index.php?showid=1100000000808118331&base=21<br>http://factordb.com/index.php?showid=1100000003996110311&base=21<br>http://factordb.com/index.php?showid=1100000003996110479&base=21<br>http://factordb.com/index.php?showid=1100000003996110718&base=21<br>http://factordb.com/index.php?showid=1100000003996110944&base=21<br>http://factordb.com/index.php?showid=1100000003996111130&base=21<nowiki/>||8||200000|| |- ||22||8003||BK₂₂₀₀₁5<br>7₃₈₁₅2L<br>L₂₃₈₅KE7<br>7₉₅₉K7<br>J0₇₆₇IGGJ<br>K0₇₆₀EC1<br>I₆₂₆AF<br>E60₄₉₆L<br>L₄₈₃G3<br>L0₄₅₄B63||22003<br>3817<br>2388<br>961<br>772<br>764<br>628<br>499<br>485<br>458||29538<br>5124<br>3206<br>1290<br>1037<br>1026<br>843<br>670<br>652<br>615||(251×22²²⁰⁰²−335)/21<br>(22³⁸¹⁷−289)/3<br>22²³⁸⁸−653<br>(22⁹⁶¹+857)/3<br>19×22⁷⁷¹+199779<br>20×22⁷⁶³+7041<br>(6×22⁶²⁸−1259)/7<br>314×22⁴⁹⁷+21<br>22⁴⁸⁵−129<br>21×22⁴⁵⁷+5459||http://factordb.com/index.php?id=1100000003594696838&open=prime<br>http://factordb.com/index.php?id=1100000003591359839&open=prime<br>http://factordb.com/index.php?id=1100000003591360774&open=prime<br>http://factordb.com/index.php?id=1100000003591361817&open=prime<br>http://factordb.com/index.php?id=1100000003591362567&open=prime<br>http://factordb.com/index.php?id=1100000000632724415&open=prime<br>http://factordb.com/index.php?id=1100000000632724334&open=prime<br>http://factordb.com/index.php?id=1100000000632703239&open=prime<br>http://factordb.com/index.php?id=1100000003591364730&open=prime<br>http://factordb.com/index.php?id=1100000003591365331&open=prime<nowiki/>||http://factordb.com/index.php?showid=1100000003594696838&base=22<br>http://factordb.com/index.php?showid=1100000003591359839&base=22<br>http://factordb.com/index.php?showid=1100000003591360774&base=22<br>http://factordb.com/index.php?showid=1100000003591361817&base=22<br>http://factordb.com/index.php?showid=1100000003591362567&base=22<br>http://factordb.com/index.php?showid=1100000000632724415&base=22<br>http://factordb.com/index.php?showid=1100000000632724334&base=22<br>http://factordb.com/index.php?showid=1100000000632703239&base=22<br>http://factordb.com/index.php?showid=1100000003591364730&base=22<br>http://factordb.com/index.php?showid=1100000003591365331&base=22<nowiki/>||0||–|| |- ||23||65178~65265||B0₉₃₀₄₆FB<br>L₈₆₄₄₄D<br>AJ₈₁₀₆₅4<br>20₇₃₅₆₀98<br>J₆₈₂₁₇G4<br>D70₆₆₇₇₀B<br>5F₆₂₃₄₀6<br>A7M7₆₁₅₃₂<br>B30₆₁₁₃₆5<br>EJ₅₂₁₆₉||93049<br>86445<br>81067<br>73563<br>68219<br>66773<br>62342<br>61535<br>61139<br>52170||126708<br>117715<br>110391<br>100172<br>92896<br>90927<br>84893<br>83794<br>83255<br>71042||11×23⁹³⁰⁴⁸+356<br>(21×23⁸⁶⁴⁴⁵−197)/22<br>(239×23⁸¹⁰⁶⁶−349)/22<br>2×23⁷³⁵⁶²+215<br>(19×23⁶⁸²¹⁹−1867)/22<br>306×23⁶⁶⁷⁷¹+11<br>(125×23⁶²³⁴¹−213)/22<br>(120413×23⁶¹⁵³²−7)/22<br>256×23⁶¹¹³⁷+5<br>(327×23⁵²¹⁶⁹−19)/22||http://factordb.com/index.php?id=1100000004691540361&open=prime<br>http://factordb.com/index.php?id=1100000004691546739&open=prime<br>http://factordb.com/index.php?id=1100000004691548070&open=prime<br>http://factordb.com/index.php?id=1100000004691548569&open=prime<br>http://factordb.com/index.php?id=1100000004691549462&open=prime<br>http://factordb.com/index.php?id=1100000004691549803&open=prime<br>http://factordb.com/index.php?id=1100000004691551005&open=prime<br>http://factordb.com/index.php?id=1100000004691556967&open=prime<br>http://factordb.com/index.php?id=1100000004691557254&open=prime<br>http://factordb.com/index.php?id=1100000004691557548&open=prime<nowiki/>||http://factordb.com/index.php?showid=1100000004691540361&base=23<br>http://factordb.com/index.php?showid=1100000004691546739&base=23<br>http://factordb.com/index.php?showid=1100000004691548070&base=23<br>http://factordb.com/index.php?showid=1100000004691548569&base=23<br>http://factordb.com/index.php?showid=1100000004691549462&base=23<br>http://factordb.com/index.php?showid=1100000004691549803&base=23<br>http://factordb.com/index.php?showid=1100000004691551005&base=23<br>http://factordb.com/index.php?showid=1100000004691556967&base=23<br>http://factordb.com/index.php?showid=1100000004691557254&base=23<br>http://factordb.com/index.php?showid=1100000004691557548&base=23<nowiki/>||87||100000|| |- ||24||3409||N00N₈₁₂₉LN<br>88N₅₉₅₁<br>A0₂₉₅₁8ID<br>D₂₆₉₈LD<br>N₂₆₄₄LLN<br>BC0₃₃₁B<br>20₃₁₃7<br>C7₂₉₈<br>D0₂₅₉KKD<br>I0₂₄₁I5||8134<br>5953<br>2955<br>2700<br>2647<br>334<br>315<br>299<br>263<br>244||11227<br>8216<br>4079<br>3727<br>3654<br>461<br>434<br>413<br>363<br>337||13249×24⁸¹³¹−49<br>201×24⁵⁹⁵¹−1<br>10×24²⁹⁵⁴+5053<br>(13×24²⁷⁰⁰+4403)/23<br>24²⁶⁴⁷−1201<br>276×24³³²+11<br>2×24³¹⁴+7<br>(283×24²⁹⁸−7)/23<br>13×24²⁶²+12013<br>18×24²⁴³+437||http://factordb.com/index.php?id=1100000003593391606&open=prime<br>http://factordb.com/index.php?id=1100000003593275880&open=prime<br>http://factordb.com/index.php?id=1100000003593269654&open=prime<br>http://factordb.com/index.php?id=1100000003593269876&open=prime<br>http://factordb.com/index.php?id=1100000003593270089&open=prime<br>http://factordb.com/index.php?id=1100000002633359842&open=prime<br>http://factordb.com/index.php?id=1100000002355610241&open=prime<br>http://factordb.com/index.php?id=1100000002326181235&open=prime<br>http://factordb.com/index.php?id=1100000003593270725&open=prime<br>http://factordb.com/index.php?id=1100000002633360037&open=prime<nowiki/>||http://factordb.com/index.php?showid=1100000003593391606&base=24<br>http://factordb.com/index.php?showid=1100000003593275880&base=24<br>http://factordb.com/index.php?showid=1100000003593269654&base=24<br>http://factordb.com/index.php?showid=1100000003593269876&base=24<br>http://factordb.com/index.php?showid=1100000003593270089&base=24<br>http://factordb.com/index.php?showid=1100000002633359842&base=24<br>http://factordb.com/index.php?showid=1100000002355610241&base=24<br>http://factordb.com/index.php?showid=1100000002326181235&base=24<br>http://factordb.com/index.php?showid=1100000003593270725&base=24<br>http://factordb.com/index.php?showid=1100000002633360037&base=24<nowiki/>||0||–|| |- ||25||133639~133724||E₉₈₃₉₆FOO<br>1J710₉₆₂₇₂1<br>NB0₈₅₅₉₈5NH<br>D70₈₁₅₈₁JJ7<br>F0₈₀₀₅₄HL<br>J010₇₅₉₄₃E7<br>K₆₇₇₇₁5I<br>LO₆₆₃₇₇KC<br>KJD0₆₃₃₉₉1<br>70₆₀₈₉₂D711||98399<br>96277<br>85603<br>81586<br>80057<br>75948<br>67773<br>66380<br>63403<br>60897||137556<br>134589<br>119668<br>114053<br>111915<br>106171<br>94743<br>92796<br>88634<br>85130||(7×25⁹⁸³⁹⁹+10613)/12<br>27676×25⁹⁶²⁷³+1<br>586×25⁸⁵⁶⁰¹+3717<br>332×25⁸¹⁵⁸⁴+12357<br>15×25⁸⁰⁰⁵⁶+446<br>11876×25⁷⁵⁹⁴⁵+357<br>(5×25⁶⁷⁷⁷³−2267)/6<br>22×25⁶⁶³⁷⁹−113<br>12988×25⁶³⁴⁰⁰+1<br>7×25⁶⁰⁸⁹⁶+207526||http://factordb.com/index.php?id=1100000000808118215&open=prime<br>http://factordb.com/index.php?id=1100000003983674902&open=prime<br>http://factordb.com/index.php?id=1100000004909706420&open=prime<br>http://factordb.com/index.php?id=1100000004909733266&open=prime<br>http://factordb.com/index.php?id=1100000004909750102&open=prime<br>http://factordb.com/index.php?id=1100000004909770736&open=prime<br>http://factordb.com/index.php?id=1100000004586986394&open=prime<br>http://factordb.com/index.php?id=1100000000808118270&open=prime<br>http://factordb.com/index.php?id=1100000004586986664&open=prime<br>http://factordb.com/index.php?id=1100000004586986798&open=prime<nowiki/>||http://factordb.com/index.php?showid=1100000000808118215&base=25<br>http://factordb.com/index.php?showid=1100000003983674902&base=25<br>http://factordb.com/index.php?showid=1100000004909706420&base=25<br>http://factordb.com/index.php?showid=1100000004909733266&base=25<br>http://factordb.com/index.php?showid=1100000004909750102&base=25<br>http://factordb.com/index.php?showid=1100000004909770736&base=25<br>http://factordb.com/index.php?showid=1100000004586986394&base=25<br>http://factordb.com/index.php?showid=1100000000808118270&base=25<br>http://factordb.com/index.php?showid=1100000004586986664&base=25<br>http://factordb.com/index.php?showid=1100000004586986798&base=25<nowiki/>||85||100000|| |- ||26||25256~25259||85M₁₉₇₀₆₀B<br>M0₆₁₁₈₆2BB<br>J0₄₄₃₀₃KCB<br>6K₂₃₃₀₀5<br>LD0₂₀₉₇₅7<br>7₂₀₂₇₉OL<br>5₁₉₃₉₁6F<br>9GDK₁₅₉₂₀P<br>M₈₇₇₂P<br>K0₄₃₆₄I5||197063<br>61190<br>44307<br>23302<br>20978<br>20281<br>19393<br>15924<br>8773<br>4367||278839<br>86583<br>62694<br>32972<br>29684<br>28697<br>27440<br>22532<br>12414<br>6180||(5347×26¹⁹⁷⁰⁶¹−297)/25<br>22×26⁶¹¹⁸⁹+1649<br>19×26⁴⁴³⁰⁶+13843<br>(34×26²³³⁰¹−79)/5<br>559×26²⁰⁹⁷⁶+7<br>(7×26²⁰²⁸¹+11393)/25<br>(26¹⁹³⁹³+179)/5<br>(32569×26¹⁵⁹²¹+21)/5<br>(22×26⁸⁷⁷³+53)/25<br>20×26⁴³⁶⁶+473||http://factordb.com/index.php?id=1100000008573990023&open=prime<br>http://factordb.com/index.php?id=1100000003968169875&open=prime<br>http://factordb.com/index.php?id=1100000003968156595&open=prime<br>http://factordb.com/index.php?id=1100000003892628745&open=prime<br>http://factordb.com/index.php?id=1100000003892628658&open=prime<br>http://factordb.com/index.php?id=1100000003892628605&open=prime<br>http://factordb.com/index.php?id=1100000003850151202&open=prime<br>http://factordb.com/index.php?id=1100000003850155316&open=prime<br>http://factordb.com/index.php?id=1100000000758011195&open=prime<br>http://factordb.com/index.php?id=1100000002634136508&open=prime<nowiki/>||http://factordb.com/index.php?showid=1100000008573990023&base=26<br>http://factordb.com/index.php?showid=1100000003968169875&base=26<br>http://factordb.com/index.php?showid=1100000003968156595&base=26<br>http://factordb.com/index.php?showid=1100000003892628745&base=26<br>http://factordb.com/index.php?showid=1100000003892628658&base=26<br>http://factordb.com/index.php?showid=1100000003892628605&base=26<br>http://factordb.com/index.php?showid=1100000003850151202&base=26<br>http://factordb.com/index.php?showid=1100000003850155316&base=26<br>http://factordb.com/index.php?showid=1100000000758011195&base=26<br>http://factordb.com/index.php?showid=1100000002634136508&base=26<nowiki/>||3||200000|| |- ||27||102852~102896||CA0F₈₈₈₈₃A<br>GNN0₇₈₇₉₅N<br>O44L₆₆₀₁₆7<br>NJ0₆₄₃₆₉H<br>ME₄₉₆₄₀9G<br>PH0₄₇₈₉₀1<br>QF₄₇₁₆₅AF5<br>J0₄₀₇₉₁PD<br>510₃₉₁₆₄I07<br>NGN0₃₆₃₂₉N||88887<br>78799<br>66020<br>64372<br>49643<br>47893<br>47169<br>40794<br>39169<br>36333||127230<br>112790<br>94499<br>92140<br>71058<br>68553<br>67516<br>58391<br>56065<br>52006||(234483×27⁸⁸⁸⁸⁴−145)/26<br>12308×27⁷⁸⁷⁹⁶+23<br>(457829×27⁶⁶⁰¹⁷−385)/26<br>640×27⁶⁴³⁷⁰+17<br>(293×27⁴⁹⁶⁴²−1736)/13<br>692×27⁴⁷⁸⁹¹+1<br>(691×27⁴⁷¹⁶⁸−95045)/26<br>19×27⁴⁰⁷⁹³+688<br>136×27³⁹¹⁶⁷+13129<br>17222×27³⁶³³⁰+23||http://factordb.com/index.php?id=1100000000808118233&open=prime<br>http://factordb.com/index.php?id=1100000004681348398&open=prime<br>http://factordb.com/index.php?id=1100000004374140861&open=prime<br>http://factordb.com/index.php?id=1100000004374138999&open=prime<br>http://factordb.com/index.php?id=1100000000819229859&open=prime<br>http://factordb.com/index.php?id=1100000004102754118&open=prime<br>http://factordb.com/index.php?id=1100000004102755880&open=prime<br>http://factordb.com/index.php?id=1100000004102758254&open=prime<br>http://factordb.com/index.php?id=1100000004102875088&open=prime<br>http://factordb.com/index.php?id=1100000004103372866&open=prime<nowiki/>||http://factordb.com/index.php?showid=1100000000808118233&base=27<br>http://factordb.com/index.php?showid=1100000004681348398&base=27<br>http://factordb.com/index.php?showid=1100000004374140861&base=27<br>http://factordb.com/index.php?showid=1100000004374138999&base=27<br>http://factordb.com/index.php?showid=1100000000819229859&base=27<br>http://factordb.com/index.php?showid=1100000004102754118&base=27<br>http://factordb.com/index.php?showid=1100000004102755880&base=27<br>http://factordb.com/index.php?showid=1100000004102758254&base=27<br>http://factordb.com/index.php?showid=1100000004102875088&base=27<br>http://factordb.com/index.php?showid=1100000004103372866&base=27<nowiki/>||44||100000|| |- ||28||25528~25529||O4O₉₄₅₃₅9<br>5OA₃₁₂₃₈F<br>N6₂₄₀₅₁LR<br>D0₅₂₆₇77D<br>QO₄₂₃₉69<br>5₃₇₄₆8P<br>G0₁₈₉₉AN<br>A₁₄₂₃6F<br>5I₁₃₇₀F<br>5₁₃₃₂P8P||94538<br>31241<br>24054<br>5271<br>4242<br>3748<br>1902<br>1425<br>1372<br>1335||136812<br>45210<br>34810<br>7628<br>6139<br>5424<br>2753<br>2062<br>1985<br>1932||(6092×28⁹⁴⁵³⁶−143)/9<br>(4438×28³¹²³⁹+125)/27<br>(209×28²⁴⁰⁵³+3967)/9<br>13×28⁵²⁷⁰+5697<br>(242×28⁴²⁴¹−4679)/9<br>(5×28³⁷⁴⁸+2803)/27<br>16×28¹⁹⁰¹+303<br>(10×28¹⁴²⁵−2899)/27<br>(17×28¹³⁷¹−11)/3<br>(5×28¹³³⁵+426163)/27||http://factordb.com/index.php?id=1100000000808118231&open=prime<br>http://factordb.com/index.php?id=1100000003880455200&open=prime<br>http://factordb.com/index.php?id=1100000003879667576&open=prime<br>http://factordb.com/index.php?id=1100000003850151420&open=prime<br>http://factordb.com/index.php?id=1100000000840839934&open=prime<br>http://factordb.com/index.php?id=1100000003850161974&open=prime<br>http://factordb.com/index.php?id=1100000003850161973&open=prime<br>http://factordb.com/index.php?id=1100000000840839947&open=prime<br>http://factordb.com/index.php?id=1100000003850161972&open=prime<br>http://factordb.com/index.php?id=1100000003850161965&open=prime<nowiki/>||http://factordb.com/index.php?showid=1100000000808118231&base=28<br>http://factordb.com/index.php?showid=1100000003880455200&base=28<br>http://factordb.com/index.php?showid=1100000003879667576&base=28<br>http://factordb.com/index.php?showid=1100000003850151420&base=28<br>http://factordb.com/index.php?showid=1100000000840839934&base=28<br>http://factordb.com/index.php?showid=1100000003850161974&base=28<br>http://factordb.com/index.php?showid=1100000003850161973&base=28<br>http://factordb.com/index.php?showid=1100000000840839947&base=28<br>http://factordb.com/index.php?showid=1100000003850161972&base=28<br>http://factordb.com/index.php?showid=1100000003850161965&base=28<nowiki/>||1||900000|| |- ||29||355242~355367||830₉₉₃₇₇4<br>GP5J₉₄₉₃₅<br>P05J₉₀₂₈₉<br>BBD0₈₈₈₈₈PB<br>8B₈₅₃₃₃G<br>L0₈₁₅₇₁5955<br>E0₇₇₃₇₂L7B<br>LPC₇₅₁₅₁9<br>JR0₇₄₆₂₂7<br>B₇₄₅₀₁0RP||99380<br>94938<br>90292<br>88893<br>85335<br>81576<br>77376<br>75154<br>74625<br>74504||145333<br>138837<br>132043<br>129997<br>124794<br>119297<br>113155<br>109905<br>109132<br>108955||235×29⁹⁹³⁷⁸+4<br>(397227×29⁹⁴⁹³⁵−19)/28<br>(588859×29⁹⁰²⁸⁹−19)/28<br>9583×29⁸⁸⁸⁹⁰+736<br>(235×29⁸⁵³³⁴+129)/14<br>21×29⁸¹⁵⁷⁵+129664<br>14×29⁷⁷³⁷⁵+17875<br>(4441×29⁷⁵¹⁵²−24)/7<br>578×29⁷⁴⁶²³+7<br>(11×29⁷⁴⁵⁰⁴−245655)/28||http://factordb.com/index.php?id=1100000008253882372&open=prime<br>http://factordb.com/index.php?id=1100000008253893542&open=prime<br>http://factordb.com/index.php?id=1100000008253899083&open=prime<br>http://factordb.com/index.php?id=1100000008253909183&open=prime<br>http://factordb.com/index.php?id=1100000008253921388&open=prime<br>http://factordb.com/index.php?id=1100000008253925955&open=prime<br>http://factordb.com/index.php?id=1100000008253931446&open=prime<br>http://factordb.com/index.php?id=1100000000808118236&open=prime<br>http://factordb.com/index.php?id=1100000008253934219&open=prime<br>http://factordb.com/index.php?id=1100000008253936120&open=prime<nowiki/>||http://factordb.com/index.php?showid=1100000008253882372&base=29<br>http://factordb.com/index.php?showid=1100000008253893542&base=29<br>http://factordb.com/index.php?showid=1100000008253899083&base=29<br>http://factordb.com/index.php?showid=1100000008253909183&base=29<br>http://factordb.com/index.php?showid=1100000008253921388&base=29<br>http://factordb.com/index.php?showid=1100000008253925955&base=29<br>http://factordb.com/index.php?showid=1100000008253931446&base=29<br>http://factordb.com/index.php?showid=1100000000808118236&base=29<br>http://factordb.com/index.php?showid=1100000008253934219&base=29<br>http://factordb.com/index.php?showid=1100000008253936120&base=29<nowiki/>||125||100000|| |- ||30||2619||OT₃₄₂₀₅<br>I0₂₄₆₀₈D<br>5₄₈₈₂J<br>C0₁₀₂₂1<br>M0₅₄₇SS7<br>M₂₄₁QB<br>AN₂₀₆<br>50₁₆₄B<br>J₁₅₃QJ<br>J₉₄QQJ||34206<br>24610<br>4883<br>1024<br>551<br>243<br>207<br>166<br>155<br>97||50527<br>36352<br>7213<br>1513<br>814<br>359<br>306<br>245<br>229<br>144||25×30³⁴²⁰⁵−1<br>18×30²⁴⁶⁰⁹+13<br>(5×30⁴⁸⁸³+401)/29<br>12×30¹⁰²³+1<br>22×30⁵⁵⁰+26047<br>(22×30²⁴³+3139)/29<br>(313×30²⁰⁶−23)/29<br>5×30¹⁶⁵+11<br>(19×30¹⁵⁵+6071)/29<br>(19×30⁹⁷+188771)/29||http://factordb.com/index.php?id=1100000000800812865&open=prime<br>http://factordb.com/index.php?id=1100000003593967511&open=prime<br>http://factordb.com/index.php?id=1100000002327649423&open=prime<br>http://factordb.com/index.php?id=1100000000785448736&open=prime<br>http://factordb.com/index.php?id=1100000003593407988&open=prime<br>http://factordb.com/index.php?id=1100000003593408295&open=prime<br>http://factordb.com/index.php?id=1100000002327651073&open=prime<br>http://factordb.com/index.php?id=1100000002356282476&open=ecm<br>http://factordb.com/index.php?id=1100000003593409109&open=ecm<br>http://factordb.com/index.php?id=1100000003593409165&open=ecm<nowiki/>||http://factordb.com/index.php?showid=1100000000800812865&base=30<br>http://factordb.com/index.php?showid=1100000003593967511&base=30<br>http://factordb.com/index.php?showid=1100000002327649423&base=30<br>http://factordb.com/index.php?showid=1100000000785448736&base=30<br>http://factordb.com/index.php?showid=1100000003593407988&base=30<br>http://factordb.com/index.php?showid=1100000003593408295&base=30<br>http://factordb.com/index.php?showid=1100000002327651073&base=30<br>http://factordb.com/index.php?showid=1100000002356282476&base=30<br>http://factordb.com/index.php?showid=1100000003593409109&base=30<br>http://factordb.com/index.php?showid=1100000003593409165&base=30<nowiki/>||0||–|| |- ||31||569323~569400||2IIF₉₁₈₀₅<br>B0₈₈₃₀₉APO9<br>J0T₇₇₅₁₆<br>J090₇₇₁₂₈NNN<br>D₆₉₈₆₁QO<br>9MH0₆₈₆₃₇D<br>J₆₇₁₆₂D<br>N0₆₆₉₇₁32P<br>DDDQ0₆₄₀₈₈TD<br>U₆₃₈₆₁CM3||91808<br>88314<br>77518<br>77134<br>69863<br>68641<br>67163<br>66975<br>64094<br>63864||136918<br>131708<br>115608<br>115035<br>104191<br>102369<br>100165<br>99884<br>95587<br>95245||(4997×31⁹¹⁸⁰⁵−1)/2<br>11×31⁸⁸³¹³+322688<br>(17699×31⁷⁷⁵¹⁶−29)/30<br>18268×31⁷⁷¹³¹+22839<br>(13×31⁶⁹⁸⁶³+12407)/30<br>9348×31⁶⁸⁶³⁸+13<br>(19×31⁶⁷¹⁶³−199)/30<br>23×31⁶⁶⁹⁷⁴+2970<br>400205×31⁶⁴⁰⁹⁰+912<br>31⁶³⁸⁶⁴−17574||http://factordb.com/index.php?id=1100000007050395732&open=prime<br>http://factordb.com/index.php?id=1100000007050397309&open=prime<br>http://factordb.com/index.php?id=1100000007050398940&open=prime<br>http://factordb.com/index.php?id=1100000007050400178&open=prime<br>http://factordb.com/index.php?id=1100000006965878559&open=prime<br>http://factordb.com/index.php?id=1100000006965875678&open=prime<br>http://factordb.com/index.php?id=1100000006965873668&open=prime<br>http://factordb.com/index.php?id=1100000006965870538&open=prime<br>http://factordb.com/index.php?id=1100000006965868103&open=prime<br>http://factordb.com/index.php?id=1100000006965865343&open=prime<nowiki/>||http://factordb.com/index.php?showid=1100000007050395732&base=31<br>http://factordb.com/index.php?showid=1100000007050397309&base=31<br>http://factordb.com/index.php?showid=1100000007050398940&base=31<br>http://factordb.com/index.php?showid=1100000007050400178&base=31<br>http://factordb.com/index.php?showid=1100000006965878559&base=31<br>http://factordb.com/index.php?showid=1100000006965875678&base=31<br>http://factordb.com/index.php?showid=1100000006965873668&base=31<br>http://factordb.com/index.php?showid=1100000006965870538&base=31<br>http://factordb.com/index.php?showid=1100000006965868103&base=31<br>http://factordb.com/index.php?showid=1100000006965865343&base=31<nowiki/>||77||100000|| |- ||32||168882~169002||V₉₉₅₈₃63<br>6₈₉₀₇₄AF<br>8₇₇₇₀₀H<br>Q₇₇₄₀₁EQQQ3<br>8₇₇₂₄₉3<br>JM₇₆₀₂₈L<br>E₇₂₉₁₉IL<br>B0₆₇₆₈₀CB<br>GK₆₆₀₇₆F<br>KN₆₅₀₂₂||99585<br>89076<br>77701<br>77406<br>77250<br>76030<br>72921<br>67683<br>66078<br>65023||149891<br>134073<br>116952<br>116508<br>116273<br>114437<br>109757<br>101873<br>99458<br>97870||32⁹⁹⁵⁸⁵−829<br>(6×32⁸⁹⁰⁷⁶+4241)/31<br>(8×32⁷⁷⁷⁰¹+271)/31<br>(26×32⁷⁷⁴⁰⁶−390071011)/31<br>(8×32⁷⁷²⁵⁰−163)/31<br>(611×32⁷⁶⁰²⁹−53)/31<br>(14×32⁷²⁹²¹+4171)/31<br>11×32⁶⁷⁶⁸²+395<br>(516×32⁶⁶⁰⁷⁷−175)/31<br>(643×32⁶⁵⁰²²−23)/31||http://factordb.com/index.php?id=1100000005514892191&open=prime<br>http://factordb.com/index.php?id=1100000005514897129&open=prime<br>http://factordb.com/index.php?id=1100000005514901700&open=prime<br>http://factordb.com/index.php?id=1100000005514915338&open=prime<br>http://factordb.com/index.php?id=1100000005514918574&open=prime<br>http://factordb.com/index.php?id=1100000005514922523&open=prime<br>http://factordb.com/index.php?id=1100000004591654373&open=prime<br>http://factordb.com/index.php?id=1100000004591654467&open=prime<br>http://factordb.com/index.php?id=1100000004591654632&open=prime<br>http://factordb.com/index.php?id=1100000004591654952&open=prime<nowiki/>||http://factordb.com/index.php?showid=1100000005514892191&base=32<br>http://factordb.com/index.php?showid=1100000005514897129&base=32<br>http://factordb.com/index.php?showid=1100000005514901700&base=32<br>http://factordb.com/index.php?showid=1100000005514915338&base=32<br>http://factordb.com/index.php?showid=1100000005514918574&base=32<br>http://factordb.com/index.php?showid=1100000005514922523&base=32<br>http://factordb.com/index.php?showid=1100000004591654373&base=32<br>http://factordb.com/index.php?showid=1100000004591654467&base=32<br>http://factordb.com/index.php?showid=1100000004591654632&base=32<br>http://factordb.com/index.php?showid=1100000004591654952&base=32<nowiki/>||120||100000|| |- ||33||280012~280093||DP₉₅₀₉₃M5<br>HJ0₉₄₂₉₅J<br>90₉₃₅₉₇Q<br>9F0₉₃₁₅₇N<br>7₈₉₄₄₉333H<br>K3₈₀₇₅₁6K<br>D₈₀₁₀₇9UD<br>VFU₇₂₂₀₄FK<br>J₆₈₇₁₅2BJ<br>DF0₆₈₃₆₇J||95096<br>94298<br>93599<br>93160<br>89453<br>80754<br>80110<br>72208<br>68718<br>68370||144405<br>143193<br>142131<br>141465<br>135835<br>122626<br>121648<br>109649<br>104350<br>103821||(441×33⁹⁵⁰⁹⁵−3833)/32<br>580×33⁹⁴²⁹⁶+19<br>9×33⁹³⁵⁹⁸+26<br>312×33⁹³¹⁵⁸+23<br>(7×33⁸⁹⁴⁵³−4743239)/32<br>(643×33⁸⁰⁷⁵³+3709)/32<br>(13×33⁸⁰¹¹⁰−121453)/32<br>(16623×33⁷²²⁰⁶−8095)/16<br>(19×33⁶⁸⁷¹⁸−600883)/32<br>444×33⁶⁸³⁶⁸+19||http://factordb.com/index.php?id=1100000005652348775&open=prime<br>http://factordb.com/index.php?id=1100000005652362811&open=prime<br>http://factordb.com/index.php?id=1100000005652375073&open=prime<br>http://factordb.com/index.php?id=1100000005652389776&open=prime<br>http://factordb.com/index.php?id=1100000005652430746&open=prime<br>http://factordb.com/index.php?id=1100000005652446200&open=prime<br>http://factordb.com/index.php?id=1100000005652461592&open=prime<br>http://factordb.com/index.php?id=1100000004614764298&open=prime<br>http://factordb.com/index.php?id=1100000004614770536&open=prime<br>http://factordb.com/index.php?id=1100000004614784274&open=prime<nowiki/>||http://factordb.com/index.php?showid=1100000005652348775&base=33<br>http://factordb.com/index.php?showid=1100000005652362811&base=33<br>http://factordb.com/index.php?showid=1100000005652375073&base=33<br>http://factordb.com/index.php?showid=1100000005652389776&base=33<br>http://factordb.com/index.php?showid=1100000005652430746&base=33<br>http://factordb.com/index.php?showid=1100000005652446200&base=33<br>http://factordb.com/index.php?showid=1100000005652461592&base=33<br>http://factordb.com/index.php?showid=1100000004614764298&base=33<br>http://factordb.com/index.php?showid=1100000004614770536&base=33<br>http://factordb.com/index.php?showid=1100000004614784274&base=33<nowiki/>||81||100000|| |- ||34||184785~184832||GFGC₉₉₉₉₆5<br>90₉₇₉₅₀FJ<br>NM0₈₅₂₁₈KX<br>F₈₃₁₈₉H2HP<br>P₇₉₄₄₁444P<br>6₇₇₀₂₇8X<br>XQIQ₇₂₂₄₁D<br>T₆₆₅₃₀IF<br>4₆₆₁₅₂B<br>2EEC₆₆₀₃₉7||100000<br>97953<br>85222<br>83193<br>79445<br>77029<br>72245<br>66532<br>66153<br>66043||153148<br>150013<br>130516<br>127408<br>121669<br>117968<br>110642<br>101893<br>101312<br>101143||(209246×34⁹⁹⁹⁹⁷−81)/11<br>9×34⁹⁷⁹⁵²+529<br>804×34⁸⁵²²⁰+713<br>(5×34⁸³¹⁹³+700233)/11<br>(25×34⁷⁹⁴⁴⁵−28062367)/33<br>(2×34⁷⁷⁰²⁹+1043)/11<br>(1288676×34⁷²²⁴²−455)/33<br>(29×34⁶⁶⁵³²−12833)/33<br>(4×34⁶⁶¹⁵³+227)/33<br>(30826×34⁶⁶⁰⁴⁰−59)/11||http://factordb.com/index.php?id=1100000004702891268&open=prime<br>http://factordb.com/index.php?id=1100000004702894713&open=prime<br>http://factordb.com/index.php?id=1100000004702900996&open=prime<br>http://factordb.com/index.php?id=1100000004702910376&open=prime<br>http://factordb.com/index.php?id=1100000004702913746&open=prime<br>http://factordb.com/index.php?id=1100000004702918600&open=prime<br>http://factordb.com/index.php?id=1100000004399656529&open=prime<br>http://factordb.com/index.php?id=1100000004399657696&open=prime<br>http://factordb.com/index.php?id=1100000004399658651&open=prime<br>http://factordb.com/index.php?id=1100000004399659716&open=prime<nowiki/>||http://factordb.com/index.php?showid=1100000004702891268&base=34<br>http://factordb.com/index.php?showid=1100000004702894713&base=34<br>http://factordb.com/index.php?showid=1100000004702900996&base=34<br>http://factordb.com/index.php?showid=1100000004702910376&base=34<br>http://factordb.com/index.php?showid=1100000004702913746&base=34<br>http://factordb.com/index.php?showid=1100000004702918600&base=34<br>http://factordb.com/index.php?showid=1100000004399656529&base=34<br>http://factordb.com/index.php?showid=1100000004399657696&base=34<br>http://factordb.com/index.php?showid=1100000004399658651&base=34<br>http://factordb.com/index.php?showid=1100000004399659716&base=34<nowiki/>||47||100000|| |- ||35||720002~720062||N0N₉₉₉₇₁9<br>V0₈₃₆₆₉E73<br>N₈₁₅₆₃K7N<br>BJ0₈₁₂₇₉N<br>J0₈₀₀₆₂FUH<br>43V₇₉₇₅₄<br>9₇₆₆₀₀K3<br>LB₇₁₃₆₆PB<br>Q₆₄₁₅₀H<br>50₆₃₃₉₇5R||99974<br>83673<br>81566<br>81282<br>80066<br>79756<br>76602<br>71369<br>64151<br>63400||154367<br>129197<br>125944<br>125505<br>123628<br>123148<br>118279<br>110199<br>99054<br>97894||(27393×35⁹⁹⁹⁷²−499)/34<br>31×35⁸³⁶⁷²+17398<br>(23×35⁸¹⁵⁶⁶−144013)/34<br>404×35⁸¹²⁸⁰+23<br>19×35⁸⁰⁰⁶⁵+19442<br>(4893×35⁷⁹⁷⁵⁴−31)/34<br>(9×35⁷⁶⁶⁰²+12877)/34<br>(725×35⁷¹³⁶⁸+16649)/34<br>(13×35⁶⁴¹⁵¹−166)/17<br>5×35⁶³³⁹⁹+202||http://factordb.com/index.php?id=1100000008248342445&open=prime<br>http://factordb.com/index.php?id=1100000008248353306&open=prime<br>http://factordb.com/index.php?id=1100000008248375642&open=prime<br>http://factordb.com/index.php?id=1100000008248397018&open=prime<br>http://factordb.com/index.php?id=1100000008248412468&open=prime<br>http://factordb.com/index.php?id=1100000008248418540&open=prime<br>http://factordb.com/index.php?id=1100000008248423670&open=prime<br>http://factordb.com/index.php?id=1100000008192119974&open=prime<br>http://factordb.com/index.php?id=1100000008192126630&open=prime<br>http://factordb.com/index.php?id=1100000008192129294&open=prime<nowiki/>||http://factordb.com/index.php?showid=1100000008248342445&base=35<br>http://factordb.com/index.php?showid=1100000008248353306&base=35<br>http://factordb.com/index.php?showid=1100000008248375642&base=35<br>http://factordb.com/index.php?showid=1100000008248397018&base=35<br>http://factordb.com/index.php?showid=1100000008248412468&base=35<br>http://factordb.com/index.php?showid=1100000008248418540&base=35<br>http://factordb.com/index.php?showid=1100000008248423670&base=35<br>http://factordb.com/index.php?showid=1100000008192119974&base=35<br>http://factordb.com/index.php?showid=1100000008192126630&base=35<br>http://factordb.com/index.php?showid=1100000008192129294&base=35<nowiki/>||60||100000|| |- ||36||35286~35290||P₈₁₉₉₃SZ<br>S0₇₅₀₀₇8H<br>7K₂₆₅₆₇Z<br>J₁₀₁₁₇LJ<br>VL0₇₂₅₈J<br>EO0₆₁₇₇V<br>FZ₅₇₇₇3P<br>T09₄₆₁₈1<br>RY₄₅₆₂H<br>OZ₃₉₃₂AZ||81995<br>75010<br>26569<br>10119<br>7261<br>6180<br>5780<br>4621<br>4564<br>3935||127609<br>116739<br>41349<br>15748<br>11301<br>9618<br>8996<br>7192<br>7103<br>6124||(5×36⁸¹⁹⁹⁵+821)/7<br>28×36⁷⁵⁰⁰⁹+305<br>(53×36²⁶⁵⁶⁸+101)/7<br>(19×36¹⁰¹¹⁹+2501)/35<br>1137×36⁷²⁵⁹+19<br>528×36⁶¹⁷⁸+31<br>16×36⁵⁷⁷⁹−1163<br>(36549×36⁴⁶¹⁹−289)/35<br>(979×36⁴⁵⁶³−629)/35<br>25×36³⁹³⁴−901||http://factordb.com/index.php?id=1100000002394962083&open=prime<br>http://factordb.com/index.php?id=1100000004020085177&open=prime<br>http://factordb.com/index.php?id=1100000003896952461&open=prime<br>http://factordb.com/index.php?id=1100000003807362491&open=prime<br>http://factordb.com/index.php?id=1100000003807362489&open=prime<br>http://factordb.com/index.php?id=1100000003807362488&open=prime<br>http://factordb.com/index.php?id=1100000003807362487&open=prime<br>http://factordb.com/index.php?id=1100000003807362486&open=prime<br>http://factordb.com/index.php?id=1100000003807362485&open=prime<br>http://factordb.com/index.php?id=1100000000840634476&open=prime<nowiki/>||http://factordb.com/index.php?showid=1100000002394962083&base=36<br>http://factordb.com/index.php?showid=1100000004020085177&base=36<br>http://factordb.com/index.php?showid=1100000003896952461&base=36<br>http://factordb.com/index.php?showid=1100000003807362491&base=36<br>http://factordb.com/index.php?showid=1100000003807362489&base=36<br>http://factordb.com/index.php?showid=1100000003807362488&base=36<br>http://factordb.com/index.php?showid=1100000003807362487&base=36<br>http://factordb.com/index.php?showid=1100000003807362486&base=36<br>http://factordb.com/index.php?showid=1100000003807362485&base=36<br>http://factordb.com/index.php?showid=1100000000840634476&base=36<nowiki/>||4||200000|| |} == The fully proof of Athena problem in decimal (base ''b'' = 10) == '''Bold''' for the Athena primes, ''x'' ◁ ''y'' means ''x'' is a subsequence of ''y''. Assume ''p'' is a prime > 10, and the last digit of ''p'' must lie in {1,3,7,9}. Case 1: ''p'' ends with 1. In this case we can write ''p'' = ''x''1. If ''x'' contains 1, 3, 4, 6, or 7, then (respectively) '''11''' ◁ ''p'', '''31''' ◁ ''p'', '''41''' ◁ ''p'', '''61''' ◁ ''p'', or '''71''' ◁ ''p''. Hence we may assume all digits of ''x'' are 0, 2, 5, 8, or 9. Case 1.1: ''p'' begins with 2. In this case we can write ''p'' = 2''y''1. If 5 ◁ ''y'', then '''251''' ◁ ''p''. If 8 ◁ ''y'', then '''281''' ◁ ''p''. If 9 ◁ ''y'', then 29 ◁ ''p''. Hence we may assume all digits of ''y'' are 0 or 2. If 22 ◁ ''y'', then '''2221''' ◁ ''p''. Hence we may assume ''y'' contains zero or one 2's. If ''y'' contains no 2's, then ''p'' ∈ 2{0}1. But then, since the sum of the digits of ''p'' is 3, ''p'' is divisible by 3, so ''p'' cannot be prime. If ''y'' contains exactly one 2, then we can write ''p'' = 2''z''2''w''1, where ''z'',''w'' ∈ {0}. If 0 ◁ ''z'' and 0 ◁ ''w'', then '''20201''' ◁ ''p''. Hence we may assume either ''z'' or ''w'' is empty. If ''z'' is empty, then ''p'' ∈ 22{0}1, and the smallest prime ''p'' ∈ 22{0}1 is '''22000001'''. If ''w'' is empty, then ''p'' ∈ 2{0}21, and the smallest prime ''p'' ∈ 2{0}21 is '''20021'''. Case 1.2: ''p'' begins with 5. In this case we can write ''p'' = 5''y''1. If 2 ◁ ''y'', then '''521''' ◁ ''p''. If 9 ◁ ''y'', then 59 ◁ ''p''. Hence we may assume all digits of ''y'' are 0, 5, or 8. If 05 ◁ ''y'', then '''5051''' ◁ ''p''. If 08 ◁ ''y'', then '''5081''' ◁ ''p''. If 50 ◁ ''y'', then '''5501''' ◁ ''p''. If 58 ◁ ''y'', then '''5581''' ◁ ''p''. If 80 ◁ ''y'', then '''5801''' ◁ ''p''. If 85 ◁ ''y'', then '''5851''' ◁ ''p''. Hence we may assume ''y'' ∈ {0} ∪ {5} ∪ {8}. If ''y'' ∈ {0}, then ''p'' ∈ 5{0}1. But then, since the sum of the digits of ''p'' is 6, ''p'' is divisible by 3, so ''p'' cannot be prime. If ''y'' ∈ {5}, then ''p'' ∈ 5{5}1, and the smallest prime ''p'' ∈ 5{5}1 is '''555555555551'''. If ''y'' ∈ {8}, since if 88 ◁ ''y'', then 881 ◁ ''p'', hence we may assume ''y'' ∈ {''𝜆'',8}, and thus ''p'' ∈ {51,581}, but 51 and 581 are both composite. Case 1.3: ''p'' begins with 8. In this case we can write p = 8''y''1. If 2 ◁ ''y'', then '''821''' ◁ ''p''. If 8 ◁ ''y'', then '''881''' ◁ ''p''. If 9 ◁ ''y'', then 89 ◁ ''p''. Hence we may assume all digits of ''y'' are 0 or 5. If 50 ◁ ''y'', then '''8501''' ◁ ''p''. Hence we may assume y ∈ {0}{5}. If 005 ◁ ''y'', then '''80051''' ◁ p. Hence we may assume y ∈ {0} ∪ {5} ∪ 0{5}. If y ∈ {0}, then ''p'' ∈ 8{0}1. But then, since the sum of the digits of ''p'' is 9, ''p'' is divisible by 3, so ''p'' cannot be prime. If y ∈ {5}, since if 55555555555 ◁ ''y'', then 555555555551 ◁ ''p'', hence we may assume ''y'' ∈ {''𝜆'', 5, 55, 555, 5555, 55555, 555555, 5555555, 55555555, 555555555, 5555555555}, and thus ''p'' ∈ {81, 851, 8551, 85551, 855551, 8555551, 85555551, 855555551, 8555555551, 85555555551, 855555555551}, but all of these numbers are composite. If y ∈ 0{5}, since if 55555555555 ◁ ''y'', then 555555555551 ◁ ''p'', hence we may assume ''y'' ∈ {0, 05, 055, 0555, 05555, 055555, 0555555, 05555555, 055555555, 0555555555, 05555555555}, and thus ''p'' ∈ {801, 8051, 80551, 805551, 8055551, 80555551, 805555551, 8055555551, 80555555551, 805555555551, 8055555555551}, and of these numbers only 80555551 and 8055555551 are primes, but 80555551 ◁ 8055555551, thus only '''80555551''' is a minimal element. Case 1.4: ''p'' begins with 9. In this case we can write p = 9''y''1. If 9 ◁ ''y'', then '''991''' ◁ ''p''. Hence we may assume all digits of ''y'' are 0, 2, 5, or 8. If 00 ◁ ''y'', then '''9001''' ◁ ''p''. If 22 ◁ ''y'', then '''9221''' ◁ ''p''. If 55 ◁ ''y'', then '''9551''' ◁ ''p''. If 88 ◁ ''y'', then 881 ◁ ''p''. Hence we may assume ''y'' contains at most one 0, at most one 2, at most one 5, and at most one 8. If ''y'' only contains at most one 0 and does not contain any of {2,5,8}, then ''y'' ∈ {''𝜆'',0}, and thus ''p'' ∈ {91,901}, but 91 and 901 are both composite. If ''y'' only contains at most one 0 and only one of {2,5,8}, then the sum of the digits of ''p'' is divisible by 3, ''p'' is divisible by 3, so ''p'' cannot be prime. Hence we may assume ''y'' contains at least two of {2,5,8}. If 25 ◁ ''y'', then 251 ◁ ''p''. If 28 ◁ ''y'', then 281 ◁ ''p''. If 52 ◁ ''y'', then 521 ◁ ''p''. If 82 ◁ ''y'', then 821 ◁ ''p''. Hence we may assume ''y'' contains no 2's (since if ''y'' contains 2, then ''y'' cannot contain either 5's or 8's, which is a contradiction). If 85 ◁ ''y'', then '''9851''' ◁ ''p''. Hence we may assume ''y'' ∈ {58,580,508,058}, and thus ''p'' ∈ {9581,95801,95081,90581}, and of these numbers only 95801 is prime, but 95801 is not a minimal element since 5801 ◁ 95801. Case 2: ''p'' ends with 3. In this case we can write p = ''x''3. If ''x'' contains 1, 2, 4, 5, 7, or 8, then (respectively) '''13''' ◁ ''p'', '''23''' ◁ ''p'', '''43''' ◁ ''p'', '''53''' ◁ ''p'', '''73''' ◁ ''p'', or '''83''' ◁ ''p''. Hence we may assume all digits of ''x'' are 0, 3, 6, or 9, and thus all digits of ''p'' are 0, 3, 6, or 9. But then, since the digits of ''p'' all have a common factor 3, ''p'' is divisible by 3, so ''p'' cannot be prime. Case 3: ''p'' ends with 7. In this case we can write ''p'' = ''x''7. If ''x'' contains 1, 3, 4, 6, or 9, then (respectively) '''17''' ◁ ''p'', '''37''' ◁ ''p'', '''47''' ◁ ''p'', '''67''' ◁ ''p'', or '''97''' ◁ ''p''. Hence we may assume all digits of ''x'' are 0, 2, 5, 7, or 8. Case 3.1: ''p'' begins with 2. In this case we can write ''p'' = 2''y''7. If 2 ◁ ''y'', then '''227''' ◁ ''p''. If 5 ◁ ''y'', then '''257''' ◁ ''p''. If 7 ◁ ''y'', then '''277''' ◁ ''p''. Hence we may assume all digits of ''y'' are 0 or 8. If 08 ◁ ''y'', then '''2087''' ◁ ''p''. If 88 ◁ ''y'', then 887 ◁ ''p''. Hence we may assume ''y'' ∈ {0} ∪ 8{0}. If ''y'' ∈ {0}, then ''p'' ∈ 2{0}7. But then, since the sum of the digits of ''p'' is 9, ''p'' is divisible by 3, so ''p'' cannot be prime. If y ∈ 8{0}, then ''p'' ∈ 28{0}7. But then ''p'' is divisible by 7, since for ''n'' ≥ 0 we have 7 × 40_''n''1 = 280_''n''7. Case 3.2: ''p'' begins with 5. In this case we can write ''p'' = 5''y''7. If 5 ◁ ''y'', then '''557''' ◁ ''p''. If 7 ◁ ''y'', then '''577''' ◁ ''p''. If 8 ◁ ''y'', then '''587''' ◁ ''p''. Hence we may assume all digits of ''y'' are 0 or 2. If 22 ◁ ''y'', then 227 ◁ ''p''. Hence we may assume ''y'' contains zero or one 2's. If ''y'' contains no 2's, then ''p'' ∈ 5{0}7. But then, since the sum of the digits of ''p'' is 12, ''p'' is divisible by 3, so ''p'' cannot be prime. If ''y'' contains exactly one 2, then we can write ''p'' = 5''z''2''w''7, where ''z'',''w'' ∈ {0}. If 0 ◁ ''z'' and 0 ◁ ''w'', then '''50207''' ◁ ''p''. Hence we may assume either ''z'' or ''w'' is empty. If ''z'' is empty, then ''p'' ∈ 52{0}7, and the smallest prime ''p'' ∈ 52{0}7 is '''5200007'''. If ''w'' is empty, then ''p'' ∈ 5{0}27, and the smallest prime ''p'' ∈ 5{0}27 is '''5000000000000000000000000000027'''. Case 3.3: ''p'' begins with 7. In this case we can write ''p'' = 7''y''7. If 2 ◁ ''y'', then '''727''' ◁ ''p''. If 5 ◁ ''y'', then '''757''' ◁ ''p''. If 8 ◁ ''y'', then '''787''' ◁ ''p''. Hence we may assume all digits of ''y'' are 0 or 7, and thus all digits of ''p'' are 0 or 7. But then, since the digits of ''p'' all have a common factor 7, ''p'' is divisible by 7, so ''p'' cannot be prime. Case 3.4: ''p'' begins with 8. In this case we can write ''p'' = 8''y''7. If 2 ◁ ''y'', then '''827''' ◁ ''p''. If 5 ◁ ''y'', then '''857''' ◁ ''p''. If 7 ◁ ''y'', then '''877''' ◁ ''p''. If 8 ◁ ''y'', then '''887''' ◁ ''p''. Hence we may assume ''y'' ∈ {0}, and thus ''p'' ∈ 8{0}7. But then, since the sum of the digits of ''p'' is 15, ''p'' is divisible by 3, so ''p'' cannot be prime. Case 4: ''p'' ends with 9. In this case we can write ''p'' = ''x''9. If ''x'' contains 1, 2, 5, 7, or 8, then (respectively) '''19''' ◁ ''p'', '''29''' ◁ ''p'', '''59''' ◁ ''p'', '''79''' ◁ ''p'', or '''89''' ◁ ''p''. Hence we may assume all digits of ''x'' are 0, 3, 4, 6, or 9. If 44 ◁ ''x'', then '''449''' ◁ ''p''. Hence we may assume ''x'' contains zero or one 4's. If x contains no 4's, then all digits of ''x'' are 0, 3, 6, or 9, and thus all digits of ''p'' are 0, 3, 6, or 9. But then, since the digits of ''p'' all have a common factor 3, ''p'' is divisible by 3, so ''p'' cannot be prime. Hence we may assume that ''x'' contains exactly one 4. Case 4.1: ''p'' begins with 3. In this case we can write ''p'' = 3''y''4''z''9, where all digits of ''y'', ''z'' are 0, 3, 6, or 9. We must have '''349''' ◁ ''p''. Case 4.2: ''p'' begins with 4. In this case we can write ''p'' = 4''y''9, where all digits of ''y'' are 0, 3, 6, or 9. If 0 ◁ ''y'', then '''409''' ◁ ''p''. If 3 ◁ ''y'', then 43 ◁ ''p''. If 9 ◁ ''y'', then '''499''' ◁ ''p''. Hence we may assume ''y'' ∈ {6}, and thus ''p'' ∈ 4{6}9. But then ''p'' is divisible by 7, since for ''n'' ≥ 0 we have 7 × 6_''n''7 = 46_''n''9. Case 4.3: ''p'' begins with 6. In this case we can write p = 6''y''4''z''9, where all digits of ''y'', ''z'' are 0, 3, 6, or 9. If 0 ◁ ''z'', then 409 ◁ ''p''. If 3 ◁ ''z'', then 43 ◁ ''p''. If 6 ◁ ''z'', then '''6469''' ◁ ''p''. If 9 ◁ ''z'', then 499 ◁ ''p''. Hence we may assume ''z'' is empty. If 3 ◁ ''y'', then 349 ◁ ''p''. If 9 ◁ ''y'', then '''6949''' ◁ ''p''. Hence we may assume all digits of ''y'' are 0 or 6. If 06 ◁ ''y'', then '''60649''' ◁ ''p''. Hence we may assume ''y'' ∈ {6}{0}. If 666 ◁ ''y'', then '''666649''' ◁ ''p''. If 00000 ◁ ''y'', then '''60000049''' ◁ ''p''. Hence we may assume ''y'' ∈ {''𝜆'', 0, 00, 000, 0000, 6, 60, 600, 6000, 60000, 66, 660, 6600, 66000, 660000}, and thus ''p'' ∈ {649, 6049, 60049, 600049, 6000049, 6649, 66049, 660049, 6600049, 66000049, 66649, 666049, 6660049, 66600049, 666000049}, and of these numbers only '''66000049''' and '''66600049''' are primes. Case 4.4: ''p'' begins with 9. In this case we can write p = 9''y''4''z''9, where all digits of ''y'', ''z'' are 0, 3, 6, or 9. If 0 ◁ ''y'', then '''9049''' ◁ ''p''. If 3 ◁ ''y'', then 349 ◁ ''p''. If 6 ◁ ''y'', then '''9649''' ◁ ''p''. If 9 ◁ ''y'', then '''9949''' ◁ ''p''. Hence we may assume ''y'' is empty. If 0 ◁ ''z'', then 409 ◁ ''p''. If 3 ◁ ''z'', then 43 ◁ ''p''. If 9 ◁ ''z'', then 499 ◁ ''p''. Hence we may assume ''z'' ∈ {6}, and thus ''p'' ∈ 94{6}9, and the smallest prime ''p'' ∈ 94{6}9 is 946669. [[Category:Number theory]] 6m7ul9rnquva7x5b0nrn9oq2g33dl43 0 330078 2823799 2823493 2026-08-21T03:12:48Z Ckopplemann 3108346 scenario box 2823799 wikitext text/x-wiki {{METP}} {{title|Pleasure anticipation and dopamine :<br> How does the brains reward system generate motivation through expected rather than experienced pleasure? }} <div align=center>Edit above to match the wording (and [[w:Stylistic or specialised usage|casing]]) in the [[Motivation and emotion/Book/2026|2026 list of topics]].<br>[[Motivation and emotion/About/Staff|Seek approval]] for any changes.<br>Do not include your name (authorship is as per the [[Special:History/{{PAGENAME}}|page's history]]).</div> __TOC__ ==Overview== {{RoundBoxTop|theme=3}}SCENARIO - WANTING WITHOUT LIKING A university student is up late studying for their final exam, they're under considerable stress and are experiencing a strong desire to use their vape. They anticipate that using their vape will feel satisfying and rewarding as they can not focus on anything else. Eventually they use their vape, however the experience is disappointing and uncomfortable. The taste is unpleasant and they now feel nauseas, the expected satisfaction is breif. Despite this, the craving later returns. Why can the anticipation of a experience create such a strong motivation when the experience itself involves little pleasure? {{RoundBoxBottom}} * {{RoundBoxTop|theme=3}} '''Focus questions''' Break the sub-title down into three to five [[Motivation and emotion/Assessment/Chapter/Focus questions|focus questions]]. Align the top-level headings with these focus questions. * What is the first focus question? * What is the second focus question? * What is the third focus question? Ask [[w:Open-ended question|open-ended]] questions. For example: {{cross}} Is there a relationship between weather and criminal behaviour? (closed-ended)<br>{{tick}} What is the relationship between weather and criminal behaviour? (open-ended) {{RoundBoxBottom}} ==Pleasure anticipation and motivation == === Anticipatory and consummatory pleasure === === Pleasure and motivated behaviour === == Dopamine and reward anticipation == === The dopamine reward system === === Reward prediction and learning === == Wanting, liking and incentive salience == === Wanting versus liking === === Incentive salience theory === == Pleasure anticipation and human behaviour == === Sexual desire and pleasure === === Gambling, reward, and uncertainty === === Substance use and addiction === ==Key points== * For the topic development, provide at least three bullet-points for each heading and sub-heading, including the Overview and Conclusion * Include key citations ==Figures== [[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]] * For the book chapter, use several figures to illustrate concepts, add interest, and to serve as examples * For the topic development, use at least one figure (even if not ideal) to show that you know how to embed, caption, and cite a figure * Figures can show any kind of media such as photos, diagrams, graphs, video, audio, and so on * Embed figures throughout the chapter, starting with the scenario in the Overview section * Provide descriptive figure captions (use '''Figure #''' and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== Learning features help to bring book chapters to life and can be embedded throughout the chapter. Here are some options: {{anchor|Scenarios}} ;Scenarios * Scenarios, case studies, or examples that illustrate concepts in action * Present using [[#Feature boxes|feature boxes]]; can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Can be real or fictional; if real, provide citation(s) {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted '''Table 1''' A Descriptive Caption Explains The Table Contents and its Relevance to the Text e.g., The 2 x 2 Johari Window Model Showing the Relationship Between Known/Unknown and Self/Other {| class="wikitable" style="margin: auto; |- ! !! Known to self !! Not known to self |- | '''Known to others''' || Open area || Blind spot |- | '''Not known to others''' || Hidden area || Unknown |} ;Quizzes * One or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as the take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] Example simple quiz questions. Choose your answers and click "Submit": <quiz display=simple> {The purpose of quizzes is to provide an interactive learning feature: |type="()"} + True - False {Long and complex quiz questions are recommended: |type="()"} - True + False </quiz> ==Conclusion== * Arguably the most important section * Provide at least three bullet-points for this section even at the topic development stage, based on preliminary thinking * For the book chapter, develop clear take-home message(s) that address the focus questions based on psychological theory and research * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing this problem * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== [[Help:Contents/Links#Interwiki_links|Internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) * [[w:Self determination theory|Self determination theory]] (Wikipedia) {{tip|Suggestions for this section: * Link to the most relevant internal resources about the topic * Include the source in parentheses }} ==References== Provide the references for all citations in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. Alternatively, you can use wiki style (as used on Wikipedia), as long as the information is complete and the formatting is consistent. APA style example: {{Hanging indent|1= Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091 Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper & Row. }} {{tip|Suggestions for this section: * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) ** Hanging indent: Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: *** Use "Edit source" *** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== [[Help:Contents/Links#External_links|External links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Link to the most relevant external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Neurotransmitters/Dopamine]] [[Category:Motivation and emotion/Book/Pleasure]] 0xclfqqst19n89grddgzeu3v17u6akz 2823800 2823799 2026-08-21T03:16:28Z Ckopplemann 3108346 scenario box 2823800 wikitext text/x-wiki {{METP}} {{title|Pleasure anticipation and dopamine :<br> How does the brains reward system generate motivation through expected rather than experienced pleasure? }} __TOC__ ==Overview== {{RoundBoxTop|theme=3}}SCENARIO - WANTING WITHOUT LIKING A university student is up late studying for their final exam, they're under considerable stress and are experiencing a strong desire to use their vape. They anticipate that using their vape will feel satisfying and rewarding as they can not focus on anything else. Eventually they use their vape, however the experience is disappointing and uncomfortable. The taste is unpleasant and they now feel nauseas, the expected satisfaction is breif. Despite this, the craving later returns. Why can the anticipation of a experience create such a strong motivation when the experience itself involves little pleasure? {{RoundBoxBottom}} * {{RoundBoxTop|theme=3}} '''Focus questions''' Break the sub-title down into three to five [[Motivation and emotion/Assessment/Chapter/Focus questions|focus questions]]. Align the top-level headings with these focus questions. * What is the first focus question? * What is the second focus question? * What is the third focus question? Ask [[w:Open-ended question|open-ended]] questions. For example: {{cross}} Is there a relationship between weather and criminal behaviour? (closed-ended)<br>{{tick}} What is the relationship between weather and criminal behaviour? (open-ended) {{RoundBoxBottom}} ==Pleasure anticipation and motivation == === Anticipatory and consummatory pleasure === === Pleasure and motivated behaviour === == Dopamine and reward anticipation == === The dopamine reward system === === Reward prediction and learning === == Wanting, liking and incentive salience == === Wanting versus liking === === Incentive salience theory === == Pleasure anticipation and human behaviour == === Sexual desire and pleasure === === Gambling, reward, and uncertainty === === Substance use and addiction === ==Key points== * For the topic development, provide at least three bullet-points for each heading and sub-heading, including the Overview and Conclusion * Include key citations ==Figures== [[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]] * For the book chapter, use several figures to illustrate concepts, add interest, and to serve as examples * For the topic development, use at least one figure (even if not ideal) to show that you know how to embed, caption, and cite a figure * Figures can show any kind of media such as photos, diagrams, graphs, video, audio, and so on * Embed figures throughout the chapter, starting with the scenario in the Overview section * Provide descriptive figure captions (use '''Figure #''' and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== Learning features help to bring book chapters to life and can be embedded throughout the chapter. Here are some options: {{anchor|Scenarios}} ;Scenarios * Scenarios, case studies, or examples that illustrate concepts in action * Present using [[#Feature boxes|feature boxes]]; can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Can be real or fictional; if real, provide citation(s) {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted '''Table 1''' A Descriptive Caption Explains The Table Contents and its Relevance to the Text e.g., The 2 x 2 Johari Window Model Showing the Relationship Between Known/Unknown and Self/Other {| class="wikitable" style="margin: auto; |- ! !! Known to self !! Not known to self |- | '''Known to others''' || Open area || Blind spot |- | '''Not known to others''' || Hidden area || Unknown |} ;Quizzes * One or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as the take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] Example simple quiz questions. Choose your answers and click "Submit": <quiz display=simple> {The purpose of quizzes is to provide an interactive learning feature: |type="()"} + True - False {Long and complex quiz questions are recommended: |type="()"} - True + False </quiz> ==Conclusion== * Arguably the most important section * Provide at least three bullet-points for this section even at the topic development stage, based on preliminary thinking * For the book chapter, develop clear take-home message(s) that address the focus questions based on psychological theory and research * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing this problem * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== [[Help:Contents/Links#Interwiki_links|Internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) * [[w:Self determination theory|Self determination theory]] (Wikipedia) {{tip|Suggestions for this section: * Link to the most relevant internal resources about the topic * Include the source in parentheses }} ==References== Provide the references for all citations in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. Alternatively, you can use wiki style (as used on Wikipedia), as long as the information is complete and the formatting is consistent. APA style example: {{Hanging indent|1= Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091 Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper & Row. }} {{tip|Suggestions for this section: * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) ** Hanging indent: Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: *** Use "Edit source" *** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== [[Help:Contents/Links#External_links|External links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Link to the most relevant external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Neurotransmitters/Dopamine]] [[Category:Motivation and emotion/Book/Pleasure]] oatjn731n9ludt0vufbo6y6efilft42 2823801 2823800 2026-08-21T03:23:03Z Ckopplemann 3108346 2823801 wikitext text/x-wiki {{METP}} {{title|Pleasure anticipation and dopamine :<br> How does the brains reward system generate motivation through expected rather than experienced pleasure? }} __TOC__ ==Overview== {{RoundBoxTop|theme=3}}SCENARIO - WANTING WITHOUT LIKING [[File:Cartoon describing the vaporization process of e-cigarette.webp|thumb|right|120px|Figure 1. Illustration of the vaporisation process of an electronic cigarette.]] A university student is up late studying for their final exam, they're under considerable stress and are experiencing a strong desire to use their vape. They anticipate that using their vape will feel satisfying and rewarding as they can not focus on anything else. Eventually they use their vape, however the experience is disappointing and uncomfortable. The taste is unpleasant and they now feel nauseous, the expected satisfaction is breif. Despite this, the craving later returns. Why can the anticipation of a experience create such a strong motivation when the experience itself involves little pleasure? {{RoundBoxBottom}} * {{RoundBoxTop|theme=3}} '''Focus questions''' Break the sub-title down into three to five [[Motivation and emotion/Assessment/Chapter/Focus questions|focus questions]]. Align the top-level headings with these focus questions. * What is the first focus question? * What is the second focus question? * What is the third focus question? Ask [[w:Open-ended question|open-ended]] questions. For example: {{cross}} Is there a relationship between weather and criminal behaviour? (closed-ended)<br>{{tick}} What is the relationship between weather and criminal behaviour? (open-ended) {{RoundBoxBottom}} ==Pleasure anticipation and motivation == === Anticipatory and consummatory pleasure === === Pleasure and motivated behaviour === == Dopamine and reward anticipation == === The dopamine reward system === === Reward prediction and learning === == Wanting, liking and incentive salience == === Wanting versus liking === === Incentive salience theory === == Pleasure anticipation and human behaviour == === Sexual desire and pleasure === === Gambling, reward, and uncertainty === === Substance use and addiction === ==Key points== * For the topic development, provide at least three bullet-points for each heading and sub-heading, including the Overview and Conclusion * Include key citations ==Figures== [[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]] * For the book chapter, use several figures to illustrate concepts, add interest, and to serve as examples * For the topic development, use at least one figure (even if not ideal) to show that you know how to embed, caption, and cite a figure * Figures can show any kind of media such as photos, diagrams, graphs, video, audio, and so on * Embed figures throughout the chapter, starting with the scenario in the Overview section * Provide descriptive figure captions (use '''Figure #''' and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== Learning features help to bring book chapters to life and can be embedded throughout the chapter. Here are some options: {{anchor|Scenarios}} ;Scenarios * Scenarios, case studies, or examples that illustrate concepts in action * Present using [[#Feature boxes|feature boxes]]; can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Can be real or fictional; if real, provide citation(s) {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted '''Table 1''' A Descriptive Caption Explains The Table Contents and its Relevance to the Text e.g., The 2 x 2 Johari Window Model Showing the Relationship Between Known/Unknown and Self/Other {| class="wikitable" style="margin: auto; |- ! !! Known to self !! Not known to self |- | '''Known to others''' || Open area || Blind spot |- | '''Not known to others''' || Hidden area || Unknown |} ;Quizzes * One or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as the take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] Example simple quiz questions. Choose your answers and click "Submit": <quiz display=simple> {The purpose of quizzes is to provide an interactive learning feature: |type="()"} + True - False {Long and complex quiz questions are recommended: |type="()"} - True + False </quiz> ==Conclusion== * Arguably the most important section * Provide at least three bullet-points for this section even at the topic development stage, based on preliminary thinking * For the book chapter, develop clear take-home message(s) that address the focus questions based on psychological theory and research * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing this problem * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== [[Help:Contents/Links#Interwiki_links|Internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) * [[w:Self determination theory|Self determination theory]] (Wikipedia) {{tip|Suggestions for this section: * Link to the most relevant internal resources about the topic * Include the source in parentheses }} ==References== Provide the references for all citations in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. Alternatively, you can use wiki style (as used on Wikipedia), as long as the information is complete and the formatting is consistent. APA style example: {{Hanging indent|1= Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091 Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper & Row. }} {{tip|Suggestions for this section: * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) ** Hanging indent: Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: *** Use "Edit source" *** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== [[Help:Contents/Links#External_links|External links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Link to the most relevant external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Neurotransmitters/Dopamine]] [[Category:Motivation and emotion/Book/Pleasure]] 1qnlkijw5jg2mc8p0d8ydxof1dgogm4 0 330079 2823648 2823542 2026-08-20T13:43:40Z Amyuniversity 3106627 more drafting 2823648 wikitext text/x-wiki {{METP}} {{title|Body neutrality and emotional well-being:<br>How a body-neutral perspective can affect emotional well-being}} <div align=center>Edit above to match the wording (and [[w:Stylistic or specialised usage|casing]]) in the [[Motivation and emotion/Book/2026|2026 list of topics]].<br>[[Motivation and emotion/About/Staff|Seek approval]] for any changes.<br>Do not include your name (authorship is as per the [[Special:History/{{PAGENAME}}|page's history]]).</div> __TOC__ ==Overview== {{RoundBoxTop|theme=3}} [[File:A picture is worth a thousand words.jpg|right|thumb|150px|'''Figure 1'''. Use a captioned image to illustrate the scenario]] ; Imagine this ... or Scenario ... or Case study or ... ?) Start with an engaging [[#Scenarios|scenario, example, or case study]] which illustrates the problem and engages reader interest. Present the scenario in a [[#Feature box|feature box]]. To change the box colour: # Edit source # Change "theme=3" to another number Include an image and cite it (e.g., see Figure 1). {{RoundBoxBottom}} The Overview section should provide: # '''Scenario''': A short, engaging case study or real-world example in a feature box, with an accompanying image (see above) # '''Explanation of the problem, issue, or topc''': Briefly explain the problem, why it is important, and outline how psychological science can help # '''Focus questions''': Unpack the sub-title into focus questions in a feature box Recommended length: 180 to 330 words. This template provides key headings, examples, and tips for each section. Gradually remove this generic information as the chapter develops. It is OK to retain some template material for the topic development, but it should all be removed from the book chapter. Key resources: * [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] explains how to edit * [[Motivation and emotion/Assessment/Topic|Topic development guidelines]] * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] {{RoundBoxTop|theme=3}} '''Focus questions''' Break the sub-title down into three to five [[Motivation and emotion/Assessment/Chapter/Focus questions|focus questions]]. Align the top-level headings with these focus questions. * What is the first focus question? * What is the second focus question? * What is the third focus question? Ask [[w:Open-ended question|open-ended]] questions. For example: {{cross}} Is there a relationship between weather and criminal behaviour? (closed-ended)<br>{{tick}} What is the relationship between weather and criminal behaviour? (open-ended) {{RoundBoxBottom}} ==Headings== Use this heading structure: * [[#Overview|Overview]] * 3 to 6 major headings tailored to the topic; can have sub-headings: ** avoid sections with only one sub-heading (use 0 or 2+ sub-headings) ** provide an introductory paragraph before breaking into sub-sections * [[#Conclusion|Conclusion]] * [[#See also|See also]] * [[#References|References]] * [[#External links|External links]] ==Key points== * For the topic development, provide at least three bullet-points for each heading and sub-heading, including the Overview and Conclusion * Include key citations == Understanding Body Neutrality == === Body Image === * What is body image? * Explain how people develop perception of their bodies * introduce ideal standards === From Body Negativity to Body Positivity to Body Neutrality === * What is body positivity and how did it emerge? * Benefits of positive body image * Limitations in the expectation that people SHOULD love their bodies * Body neutrality as an alternative? - Acceptance without requiring positive feelings === Body Neutrality === * Finally explain body neutrality * How is it different to body positivity/dissatisfaction * Body functionality rather than acceptance * Reducing appearance-based view * Acknowledging negative body-related thoughts without acting on them * How is body neutrality different from simply "not caring" about one's body == Emotional Elements of Body Neutrality == === Negative Emotions === * Shame * Anxiety === Self-Esteem and Self-Worth === === Psychological Effects === * Psychological disorders? * Distorted self-image? ==Figures== [[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]] * For the book chapter, use several figures to illustrate concepts, add interest, and to serve as examples * For the topic development, use at least one figure (even if not ideal) to show that you know how to embed, caption, and cite a figure * Figures can show any kind of media such as photos, diagrams, graphs, video, audio, and so on * Embed figures throughout the chapter, starting with the scenario in the Overview section * Provide descriptive figure captions (use '''Figure #''' and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== Learning features help to bring book chapters to life and can be embedded throughout the chapter. Here are some options: {{anchor|Scenarios}} ;Scenarios * Scenarios, case studies, or examples that illustrate concepts in action * Present using [[#Feature boxes|feature boxes]]; can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Can be real or fictional; if real, provide citation(s) {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted '''Table 1''' A Descriptive Caption Explains The Table Contents and its Relevance to the Text e.g., The 2 x 2 Johari Window Model Showing the Relationship Between Known/Unknown and Self/Other {| class="wikitable" style="margin: auto; |- ! !! Known to self !! Not known to self |- | '''Known to others''' || Open area || Blind spot |- | '''Not known to others''' || Hidden area || Unknown |} ;Quizzes * One or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as the take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] Example simple quiz questions. Choose your answers and click "Submit": <quiz display=simple> {The purpose of quizzes is to provide an interactive learning feature: |type="()"} + True - False {Long and complex quiz questions are recommended: |type="()"} - True + False </quiz> ==Conclusion== * Arguably the most important section * Provide at least three bullet-points for this section even at the topic development stage, based on preliminary thinking * For the book chapter, develop clear take-home message(s) that address the focus questions based on psychological theory and research * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing this problem * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== [[Help:Contents/Links#Interwiki_links|Internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/2025/Body neutrality and emotional well-being|Body neutrality and emotional well-being]] (Book chapter, 2025) * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) * [[w:Self determination theory|Self determination theory]] (Wikipedia) {{tip|Suggestions for this section: * Link to the most relevant internal resources about the topic * Include the source in parentheses }} ==References== Provide the references for all citations in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. Alternatively, you can use wiki style (as used on Wikipedia), as long as the information is complete and the formatting is consistent. APA style example: {{Hanging indent|1= Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091 Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper & Row. }} {{tip|Suggestions for this section: * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) ** Hanging indent: Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: *** Use "Edit source" *** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== [[Help:Contents/Links#External_links|External links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Link to the most relevant external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Body image]] [[Category:Motivation and emotion/Book/Emotion]] b2vf8ervr64j26wfl10a8bj4e8rblig 2823838 2823648 2026-08-21T06:06:13Z ~2026-45566-86 3108810 /* Understanding Body Neutrality */ 2823838 wikitext text/x-wiki {{METP}} {{title|Body neutrality and emotional well-being:<br>How a body-neutral perspective can affect emotional well-being}} <div align=center>Edit above to match the wording (and [[w:Stylistic or specialised usage|casing]]) in the [[Motivation and emotion/Book/2026|2026 list of topics]].<br>[[Motivation and emotion/About/Staff|Seek approval]] for any changes.<br>Do not include your name (authorship is as per the [[Special:History/{{PAGENAME}}|page's history]]).</div> __TOC__ ==Overview== {{RoundBoxTop|theme=3}} [[File:A picture is worth a thousand words.jpg|right|thumb|150px|'''Figure 1'''. Use a captioned image to illustrate the scenario]] ; Imagine this ... or Scenario ... or Case study or ... ?) Start with an engaging [[#Scenarios|scenario, example, or case study]] which illustrates the problem and engages reader interest. Present the scenario in a [[#Feature box|feature box]]. To change the box colour: # Edit source # Change "theme=3" to another number Include an image and cite it (e.g., see Figure 1). {{RoundBoxBottom}} The Overview section should provide: # '''Scenario''': A short, engaging case study or real-world example in a feature box, with an accompanying image (see above) # '''Explanation of the problem, issue, or topc''': Briefly explain the problem, why it is important, and outline how psychological science can help # '''Focus questions''': Unpack the sub-title into focus questions in a feature box Recommended length: 180 to 330 words. This template provides key headings, examples, and tips for each section. Gradually remove this generic information as the chapter develops. It is OK to retain some template material for the topic development, but it should all be removed from the book chapter. Key resources: * [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] explains how to edit * [[Motivation and emotion/Assessment/Topic|Topic development guidelines]] * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] {{RoundBoxTop|theme=3}} '''Focus questions''' Break the sub-title down into three to five [[Motivation and emotion/Assessment/Chapter/Focus questions|focus questions]]. Align the top-level headings with these focus questions. * What is the first focus question? * What is the second focus question? * What is the third focus question? Ask [[w:Open-ended question|open-ended]] questions. For example: {{cross}} Is there a relationship between weather and criminal behaviour? (closed-ended)<br>{{tick}} What is the relationship between weather and criminal behaviour? (open-ended) {{RoundBoxBottom}} ==Headings== Use this heading structure: * [[#Overview|Overview]] * 3 to 6 major headings tailored to the topic; can have sub-headings: ** avoid sections with only one sub-heading (use 0 or 2+ sub-headings) ** provide an introductory paragraph before breaking into sub-sections * [[#Conclusion|Conclusion]] * [[#See also|See also]] * [[#References|References]] * [[#External links|External links]] ==Key points== * For the topic development, provide at least three bullet-points for each heading and sub-heading, including the Overview and Conclusion * Include key citations == Understanding Body Neutrality == === Body Image === * What is body image? Grogan, S. (2016). ''Body image: Understanding body dissatisfaction in men, women and children'' (3rd ed.). Routledge. * Explain how people develop perception of their bodies Shontz, F. C. (1989). [Rev. of ''Development and Structure of the Body Image, Volumes 1 and 2'']. ''Psychoanalytic Psychology'', ''6''(4), 503–507. <nowiki>https://doi.org/10.1037/0736-9735.6.4.503</nowiki> * introduce ideal standards === From Body Negativity to Body Positivity to Body Neutrality === * What is body positivity and how did it emerge? * Benefits of positive body image * Limitations in the expectation that people SHOULD love their bodies * Body neutrality as an alternative? - Acceptance without requiring positive feelings === Body Neutrality === * Finally explain body neutrality * How is it different to body positivity/dissatisfaction * Body functionality rather than acceptance * Reducing appearance-based view * Acknowledging negative body-related thoughts without acting on them * How is body neutrality different from simply "not caring" about one's body == Emotional Elements of Body Neutrality == === Negative Emotions === * Shame * Anxiety === Self-Esteem and Self-Worth === === Psychological Effects === * Psychological disorders? * Distorted self-image? ==Figures== [[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]] * For the book chapter, use several figures to illustrate concepts, add interest, and to serve as examples * For the topic development, use at least one figure (even if not ideal) to show that you know how to embed, caption, and cite a figure * Figures can show any kind of media such as photos, diagrams, graphs, video, audio, and so on * Embed figures throughout the chapter, starting with the scenario in the Overview section * Provide descriptive figure captions (use '''Figure #''' and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== Learning features help to bring book chapters to life and can be embedded throughout the chapter. Here are some options: {{anchor|Scenarios}} ;Scenarios * Scenarios, case studies, or examples that illustrate concepts in action * Present using [[#Feature boxes|feature boxes]]; can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Can be real or fictional; if real, provide citation(s) {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted '''Table 1''' A Descriptive Caption Explains The Table Contents and its Relevance to the Text e.g., The 2 x 2 Johari Window Model Showing the Relationship Between Known/Unknown and Self/Other {| class="wikitable" style="margin: auto; |- ! !! Known to self !! Not known to self |- | '''Known to others''' || Open area || Blind spot |- | '''Not known to others''' || Hidden area || Unknown |} ;Quizzes * One or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as the take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] Example simple quiz questions. Choose your answers and click "Submit": <quiz display=simple> {The purpose of quizzes is to provide an interactive learning feature: |type="()"} + True - False {Long and complex quiz questions are recommended: |type="()"} - True + False </quiz> ==Conclusion== * Arguably the most important section * Provide at least three bullet-points for this section even at the topic development stage, based on preliminary thinking * For the book chapter, develop clear take-home message(s) that address the focus questions based on psychological theory and research * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing this problem * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== [[Help:Contents/Links#Interwiki_links|Internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/2025/Body neutrality and emotional well-being|Body neutrality and emotional well-being]] (Book chapter, 2025) * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) * [[w:Self determination theory|Self determination theory]] (Wikipedia) {{tip|Suggestions for this section: * Link to the most relevant internal resources about the topic * Include the source in parentheses }} ==References== Provide the references for all citations in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. Alternatively, you can use wiki style (as used on Wikipedia), as long as the information is complete and the formatting is consistent. APA style example: {{Hanging indent|1= Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091 Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper & Row. }} {{tip|Suggestions for this section: * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) ** Hanging indent: Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: *** Use "Edit source" *** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== [[Help:Contents/Links#External_links|External links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Link to the most relevant external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Body image]] [[Category:Motivation and emotion/Book/Emotion]] os0lpmf2jljxdc6uenocpbmuegr7gv0 2823840 2823838 2026-08-21T06:11:57Z Amyuniversity 3106627 /* Understanding Body Neutrality */ 2823840 wikitext text/x-wiki {{METP}} {{title|Body neutrality and emotional well-being:<br>How a body-neutral perspective can affect emotional well-being}} <div align=center>Edit above to match the wording (and [[w:Stylistic or specialised usage|casing]]) in the [[Motivation and emotion/Book/2026|2026 list of topics]].<br>[[Motivation and emotion/About/Staff|Seek approval]] for any changes.<br>Do not include your name (authorship is as per the [[Special:History/{{PAGENAME}}|page's history]]).</div> __TOC__ ==Overview== {{RoundBoxTop|theme=3}} [[File:A picture is worth a thousand words.jpg|right|thumb|150px|'''Figure 1'''. Use a captioned image to illustrate the scenario]] ; Imagine this ... or Scenario ... or Case study or ... ?) Start with an engaging [[#Scenarios|scenario, example, or case study]] which illustrates the problem and engages reader interest. Present the scenario in a [[#Feature box|feature box]]. To change the box colour: # Edit source # Change "theme=3" to another number Include an image and cite it (e.g., see Figure 1). {{RoundBoxBottom}} The Overview section should provide: # '''Scenario''': A short, engaging case study or real-world example in a feature box, with an accompanying image (see above) # '''Explanation of the problem, issue, or topc''': Briefly explain the problem, why it is important, and outline how psychological science can help # '''Focus questions''': Unpack the sub-title into focus questions in a feature box Recommended length: 180 to 330 words. This template provides key headings, examples, and tips for each section. Gradually remove this generic information as the chapter develops. It is OK to retain some template material for the topic development, but it should all be removed from the book chapter. Key resources: * [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] explains how to edit * [[Motivation and emotion/Assessment/Topic|Topic development guidelines]] * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] {{RoundBoxTop|theme=3}} '''Focus questions''' Break the sub-title down into three to five [[Motivation and emotion/Assessment/Chapter/Focus questions|focus questions]]. Align the top-level headings with these focus questions. * What is the first focus question? * What is the second focus question? * What is the third focus question? Ask [[w:Open-ended question|open-ended]] questions. For example: {{cross}} Is there a relationship between weather and criminal behaviour? (closed-ended)<br>{{tick}} What is the relationship between weather and criminal behaviour? (open-ended) {{RoundBoxBottom}} ==Headings== Use this heading structure: * [[#Overview|Overview]] * 3 to 6 major headings tailored to the topic; can have sub-headings: ** avoid sections with only one sub-heading (use 0 or 2+ sub-headings) ** provide an introductory paragraph before breaking into sub-sections * [[#Conclusion|Conclusion]] * [[#See also|See also]] * [[#References|References]] * [[#External links|External links]] ==Key points== * For the topic development, provide at least three bullet-points for each heading and sub-heading, including the Overview and Conclusion * Include key citations == Understanding Body Neutrality == === Body Image === * What is body image? Grogan, S. (2016). ''Body image: Understanding body dissatisfaction in men, women and children'' (3rd ed.). Routledge. * Explain how people develop perception of their bodies Shontz, F. C. (1989). [Rev. of ''Development and Structure of the Body Image, Volumes 1 and 2'']. ''Psychoanalytic Psychology'', ''6''(4), 503–507. <nowiki>https://doi.org/10.1037/0736-9735.6.4.503</nowiki> * introduce ideal standards === From Body Negativity to Body Positivity to Body Neutrality === * What is body positivity and how did it emerge? - social media? * Benefits of positive body image * Limitations in the expectation that people SHOULD love their bodies * Body neutrality as an alternative? - Acceptance without requiring positive feelings === Body Neutrality === * Finally explain body neutrality * How is it different to body positivity/dissatisfaction * Body functionality rather than acceptance * Reducing appearance-based view * Acknowledging negative body-related thoughts without acting on them * How is body neutrality different from simply "not caring" about one's body == Emotional Elements of Body Neutrality == === Negative Emotions === * Shame * Anxiety === Self-Esteem and Self-Worth === === Psychological Effects === * Psychological disorders? * Distorted self-image? ==Figures== [[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]] * For the book chapter, use several figures to illustrate concepts, add interest, and to serve as examples * For the topic development, use at least one figure (even if not ideal) to show that you know how to embed, caption, and cite a figure * Figures can show any kind of media such as photos, diagrams, graphs, video, audio, and so on * Embed figures throughout the chapter, starting with the scenario in the Overview section * Provide descriptive figure captions (use '''Figure #''' and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== Learning features help to bring book chapters to life and can be embedded throughout the chapter. Here are some options: {{anchor|Scenarios}} ;Scenarios * Scenarios, case studies, or examples that illustrate concepts in action * Present using [[#Feature boxes|feature boxes]]; can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Can be real or fictional; if real, provide citation(s) {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted '''Table 1''' A Descriptive Caption Explains The Table Contents and its Relevance to the Text e.g., The 2 x 2 Johari Window Model Showing the Relationship Between Known/Unknown and Self/Other {| class="wikitable" style="margin: auto; |- ! !! Known to self !! Not known to self |- | '''Known to others''' || Open area || Blind spot |- | '''Not known to others''' || Hidden area || Unknown |} ;Quizzes * One or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as the take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] Example simple quiz questions. Choose your answers and click "Submit": <quiz display=simple> {The purpose of quizzes is to provide an interactive learning feature: |type="()"} + True - False {Long and complex quiz questions are recommended: |type="()"} - True + False </quiz> ==Conclusion== * Arguably the most important section * Provide at least three bullet-points for this section even at the topic development stage, based on preliminary thinking * For the book chapter, develop clear take-home message(s) that address the focus questions based on psychological theory and research * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing this problem * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== [[Help:Contents/Links#Interwiki_links|Internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/2025/Body neutrality and emotional well-being|Body neutrality and emotional well-being]] (Book chapter, 2025) * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) * [[w:Self determination theory|Self determination theory]] (Wikipedia) {{tip|Suggestions for this section: * Link to the most relevant internal resources about the topic * Include the source in parentheses }} ==References== Provide the references for all citations in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. Alternatively, you can use wiki style (as used on Wikipedia), as long as the information is complete and the formatting is consistent. APA style example: {{Hanging indent|1= Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091 Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper & Row. }} {{tip|Suggestions for this section: * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) ** Hanging indent: Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: *** Use "Edit source" *** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== [[Help:Contents/Links#External_links|External links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Link to the most relevant external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Body image]] [[Category:Motivation and emotion/Book/Emotion]] dk0ayyh429whfgn3qse9dwj0aytrxnn 2823842 2823840 2026-08-21T06:22:18Z Amyuniversity 3106627 /* Understanding Body Neutrality */ 2823842 wikitext text/x-wiki {{METP}} {{title|Body neutrality and emotional well-being:<br>How a body-neutral perspective can affect emotional well-being}} <div align=center>Edit above to match the wording (and [[w:Stylistic or specialised usage|casing]]) in the [[Motivation and emotion/Book/2026|2026 list of topics]].<br>[[Motivation and emotion/About/Staff|Seek approval]] for any changes.<br>Do not include your name (authorship is as per the [[Special:History/{{PAGENAME}}|page's history]]).</div> __TOC__ ==Overview== {{RoundBoxTop|theme=3}} [[File:A picture is worth a thousand words.jpg|right|thumb|150px|'''Figure 1'''. Use a captioned image to illustrate the scenario]] ; Imagine this ... or Scenario ... or Case study or ... ?) Start with an engaging [[#Scenarios|scenario, example, or case study]] which illustrates the problem and engages reader interest. Present the scenario in a [[#Feature box|feature box]]. To change the box colour: # Edit source # Change "theme=3" to another number Include an image and cite it (e.g., see Figure 1). {{RoundBoxBottom}} The Overview section should provide: # '''Scenario''': A short, engaging case study or real-world example in a feature box, with an accompanying image (see above) # '''Explanation of the problem, issue, or topc''': Briefly explain the problem, why it is important, and outline how psychological science can help # '''Focus questions''': Unpack the sub-title into focus questions in a feature box Recommended length: 180 to 330 words. This template provides key headings, examples, and tips for each section. Gradually remove this generic information as the chapter develops. It is OK to retain some template material for the topic development, but it should all be removed from the book chapter. Key resources: * [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] explains how to edit * [[Motivation and emotion/Assessment/Topic|Topic development guidelines]] * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] {{RoundBoxTop|theme=3}} '''Focus questions''' Break the sub-title down into three to five [[Motivation and emotion/Assessment/Chapter/Focus questions|focus questions]]. Align the top-level headings with these focus questions. * What is the first focus question? * What is the second focus question? * What is the third focus question? Ask [[w:Open-ended question|open-ended]] questions. For example: {{cross}} Is there a relationship between weather and criminal behaviour? (closed-ended)<br>{{tick}} What is the relationship between weather and criminal behaviour? (open-ended) {{RoundBoxBottom}} ==Headings== Use this heading structure: * [[#Overview|Overview]] * 3 to 6 major headings tailored to the topic; can have sub-headings: ** avoid sections with only one sub-heading (use 0 or 2+ sub-headings) ** provide an introductory paragraph before breaking into sub-sections * [[#Conclusion|Conclusion]] * [[#See also|See also]] * [[#References|References]] * [[#External links|External links]] ==Key points== * For the topic development, provide at least three bullet-points for each heading and sub-heading, including the Overview and Conclusion * Include key citations == Understanding Body Neutrality == === Body Image === * What is body image? Grogan, S. (2016). ''Body image: Understanding body dissatisfaction in men, women and children'' (3rd ed.). Routledge. * Explain how people develop perception of their bodies Shontz, F. C. (1989). [Rev. of ''Development and Structure of the Body Image, Volumes 1 and 2'']. ''Psychoanalytic Psychology'', ''6''(4), 503–507. <nowiki>https://doi.org/10.1037/0736-9735.6.4.503</nowiki> * introduce ideal standards: Frederick, D. A., Forbes, M., Gentle, B., Reynolds, T. A., & Walters, T. (2012). Beauty standards. In ''Encyclopedia of human sexuality''. Wiley-Blackwell. === From Body Negativity to Body Positivity to Body Neutrality === * What is body positivity and how did it emerge? - social media? * Benefits of positive body image * Limitations in the expectation that people SHOULD love their bodies * Body neutrality as an alternative? - Acceptance without requiring positive feelings === Body Neutrality === * Finally explain body neutrality * How is it different to body positivity/dissatisfaction * Body functionality rather than acceptance * Reducing appearance-based view * Acknowledging negative body-related thoughts without acting on them * How is body neutrality different from simply "not caring" about one's body == Emotional Elements of Body Neutrality == === Negative Emotions === * Shame * Anxiety === Self-Esteem and Self-Worth === === Psychological Effects === * Psychological disorders? * Distorted self-image? ==Figures== [[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]] * For the book chapter, use several figures to illustrate concepts, add interest, and to serve as examples * For the topic development, use at least one figure (even if not ideal) to show that you know how to embed, caption, and cite a figure * Figures can show any kind of media such as photos, diagrams, graphs, video, audio, and so on * Embed figures throughout the chapter, starting with the scenario in the Overview section * Provide descriptive figure captions (use '''Figure #''' and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== Learning features help to bring book chapters to life and can be embedded throughout the chapter. Here are some options: {{anchor|Scenarios}} ;Scenarios * Scenarios, case studies, or examples that illustrate concepts in action * Present using [[#Feature boxes|feature boxes]]; can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Can be real or fictional; if real, provide citation(s) {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted '''Table 1''' A Descriptive Caption Explains The Table Contents and its Relevance to the Text e.g., The 2 x 2 Johari Window Model Showing the Relationship Between Known/Unknown and Self/Other {| class="wikitable" style="margin: auto; |- ! !! Known to self !! Not known to self |- | '''Known to others''' || Open area || Blind spot |- | '''Not known to others''' || Hidden area || Unknown |} ;Quizzes * One or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as the take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] Example simple quiz questions. Choose your answers and click "Submit": <quiz display=simple> {The purpose of quizzes is to provide an interactive learning feature: |type="()"} + True - False {Long and complex quiz questions are recommended: |type="()"} - True + False </quiz> ==Conclusion== * Arguably the most important section * Provide at least three bullet-points for this section even at the topic development stage, based on preliminary thinking * For the book chapter, develop clear take-home message(s) that address the focus questions based on psychological theory and research * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing this problem * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== [[Help:Contents/Links#Interwiki_links|Internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/2025/Body neutrality and emotional well-being|Body neutrality and emotional well-being]] (Book chapter, 2025) * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) * [[w:Self determination theory|Self determination theory]] (Wikipedia) {{tip|Suggestions for this section: * Link to the most relevant internal resources about the topic * Include the source in parentheses }} ==References== Provide the references for all citations in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. Alternatively, you can use wiki style (as used on Wikipedia), as long as the information is complete and the formatting is consistent. APA style example: {{Hanging indent|1= Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091 Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper & Row. }} {{tip|Suggestions for this section: * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) ** Hanging indent: Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: *** Use "Edit source" *** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== [[Help:Contents/Links#External_links|External links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Link to the most relevant external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Body image]] [[Category:Motivation and emotion/Book/Emotion]] p2467nme0uz9nmgvg84dpwkmcs18urn 0 330426 2823804 2818124 2026-08-21T04:10:58Z James500 297601 /* */ Add 2823804 wikitext text/x-wiki {{Bibliography}} This page is part of [[Universal Bibliography/Languages|bibliography of languages]]. This part of the [[Universal Bibliography]] is a bibliography of Japanese. Bibliography *Harald Suppanschitsch and Jürgen Stalph. Japanische Sprache und Schrift: eine Bibliographie des in deutscher Sprache veröffentlichten Schrifttums. 2001. [https://books.google.co.uk/books?id=7tBw_wLMOagC&pg=PR1#v=onepage&q&f=false] *Oskar Nachod. "Linguistics". Bibliography of the Japanese Empire 1906-1926. 1928. vol 2. Chapter XII. pp [https://archive.org/details/bibliographyofja0002oska/page/613/mode/1up 613] to 628, 753 and 754. *Wenckstern. "Philology: The Japanese Language". A Bibliography of the Japanese Empire. Chapter VI. vol 1, pp [https://books.google.co.uk/books?id=dcVAAAAAYAAJ&pg=PA74#v=onepage&q&f=false 74] to 88. vol 2, pp [https://archive.org/details/bibliographyofja0002frvo/page/74/mode/1up 74] to 89. General *Haruhiko Kindaichi. The Japanese Language. Tuttle. 1978. [https://books.google.co.uk/books?id=s_UZAQAAIAAJ] 1989. [https://books.google.co.uk/books?id=PdzkyasVMMoC] 2010. [https://books.google.co.uk/books?id=dAbRAgAAQBAJ&pg=PA1#v=onepage&q&f=false] *Osamu Mizutani. Japanese: The Spoken Language in Japanese Life. Japan Times. 1981. [https://books.google.co.uk/books?id=jZsPAAAAYAAJ] *Charles Berlitz. Passport to Japanese. 1985. [https://books.google.co.uk/books?id=MSQ04TeVfWYC] Periodicals *Japanese Language and Literature. (Journal of the Association of Teachers of Japanese.) [https://books.google.co.uk/books?&id=QpkmAQAAIAAJ] Periodical columns *[https://www.japantimes.co.jp/life/language/ Language]. [https://www.japantimes.co.jp/tag/bilingual/?type=column Bilingual]. [https://www.japantimes.co.jp/tag/vocabulary-boost/?type=column Vocabulary Boost]. The Japan Times. Kokugo *Paul H Clark. The Kokugo Revolution: Education, Identity, and Language Policy in Imperial Japan. (Japan Research Monograph 16). [https://books.google.co.uk/books?id=F6jSEQAAQBAJ&pg=PP1#v=onepage&q&f=false] *Yeounsuk Lee. The Ideology of Kokugo: Nationalizing Language in Modern Japan. University of Hawaii Press. 2010. [https://books.google.co.uk/books?id=54wBEAAAQBAJ&pg=PP1#v=onepage&q&f=false] **Kokugo To Iu Shisō: Kindai Nihon No Gengo Ninshiki. (Japanese: 「国語」という思想: 近代日本の言語認識). Iwanami Shoten. Tokyo. 1996. Nihongo *Makoto Sugawara. Nihongo: A Japanese Approach to Japanese. East Publications. [https://books.google.co.uk/books?id=fKkPAAAAYAAJ] *Roy Andrew Miller. Nihongo: In Defence of Japanese. The Athlone Press. 1986. [https://books.google.co.uk/books?id=oRxkAAAAMAAJ] *Nihongo Notes. The Japan Times. [https://books.google.co.uk/books?id=LdkpAQAAIAAJ] *Yutaka Sato and Margaret Y. Yamashita. Nihongo: Introductory Japanese. 1994. vol 2. [https://books.google.co.uk/books?id=ptACuS6HnpUC&pg=PP1#v=onepage&q&f=false] *Minna No Nihongo I. 3A Corporation. (スリーエーネットワーク). 1998. [https://books.google.co.uk/books?id=G-bl2P5lRl4C&pg=PP1#v=onepage&q&f=false] **Minna No Nihongo II. [https://books.google.co.uk/books?id=4nHnMa4Zw-MC&pg=PP1#v=onepage&q&f=false] Introductions *A E Backhouse. The Japanese Language: An Introduction. Oxford University Press. 1993. [https://books.google.co.uk/books?id=vawPAAAAYAAJ] *Richard Bowring and Haruko Uryū Laurie. An Introduction to Modern Japanese. 1992. [https://books.google.co.uk/books?id=Gu3k3eiOXWAC&pg=PP1#v=onepage&q&f=false] Understanding *Yasuko Obana. Understanding Japanese: A Handbook for Learners and Teachers. 2000. [https://books.google.co.uk/books?id=I9IPAAAAYAAJ] Learn *Yuko Fukuroi. Learn Japanese. Institute of Asian Studies. 1997. [https://books.google.co.uk/books?id=0SJkAAAAMAAJ] *John Young and Kimiko Nakajima-Okano. Learn Japanese: New College Text: Volume IV. 1985. [https://books.google.co.uk/books?id=rxwxLVwW2t0C&pg=PP1#v=onepage&q&f=false] *John Young and Kimiko Nakajima-Okano. Learn Japanese: Pattern Approach. University of Maryland. 1963. [https://books.google.co.uk/books?id=pG1AsovGf3AC] *Nobuko Mizutani. Let's Learn Japanese. (Radio Japan). 1993. [https://books.google.co.uk/books?id=4urrPQAACAAJ] *Senko K Maynard. Learning Japanese for Real: A Guide to Grammar, Use, and Genres of the Nihongo World. University of Hawaii Press. 2011. [https://books.google.co.uk/books?id=QF4EEAAAQBAJ&pg=PP1#v=onepage&q&f=false] *Muneo Kimura. Learning Japanese: Techniques for Intermediate and Advanced Student. (Orientation Seminars on Japan, number 23). Office for the Japanese Studies Center, The Japan Foundation. 1986. [https://books.google.co.uk/books?id=ZyUHAQAAIAAJ] *Miwa Kai. Listen & Learn Japanese. 1959. Reprinted 1986. [https://books.google.co.uk/books?id=wBrYftZU6z4C&pg=PR1#v=onepage&q&f=false] Study *Jun Maeda. Let's Study Japanese. (Tuttle Language Library). 1st Ed: 1965. [https://books.google.co.uk/books?id=itdGCgAAQBAJ&pg=PP1#v=onepage&q&f=false] Courses *Fudeko Obazawa Reekie. A First Course in Japanese. 2007. [https://books.google.co.uk/books?id=VvmrFBsaXOkC&pg=PR3#v=onepage&q&f=false] *Intensive Course in Japanese. Language Services Co Ltd. [https://books.google.co.uk/books?id=SRhIAAAAMAAJ] [https://books.google.co.uk/books?id=0ytIAAAAMAAJ] *Akiyama. Nucleus Course in Japanese. Institute of Modern Languages. [https://books.google.co.uk/books?id=iGw-AAAAIAAJ] *Oreste Vaccari and Enko Elisa Vaccari. Complete Course of Japanese Conversation-Grammar. [https://books.google.co.uk/books?id=x9MTAQAAMAAJ] *Clay MacCauley. An Introductory Course in Japanese. 1897. [https://books.google.co.uk/books?id=Hmvl19e6ld4C&pg=PP5#v=onepage&q&f=false] Fundamentals *Toyoaki Uehara and Gisaburo N Kiyose. Fundamentals of Japanese. Indiana University Press. Bloomington and London. Tenri University Press. Tenri 1974. Reviews: [https://www.jstor.org/stable/598969] and Hiroshi Miyaji, "Book Reviews" (1976) [https://books.google.co.uk/books?id=EilkAAAAMAAJ 11] The Journal of the Association of Teachers of Japanese 106 (No 1: January 1976) Essential *Essential Japanese: Speak Japanese with Confidence. Tuttle. 2012. [https://books.google.co.uk/books?id=aJzTAgAAQBAJ&pg=PA1#v=onepage&q&f=false] *Lynne Strugnell. Essential Japanese. Berlitz. [https://books.google.co.uk/books?id=2vxBU3vjytQC] *Samuel E Martin. Essential Japanese: An Introduction to the Standard Colloquial Language. 1954. [https://books.google.co.uk/books?id=rx5kAAAAMAAJ] *Helmut Morsbach and Kazue Kurebayashi. Essential Japanese: A Guidebook to Language and Culture. Penguin Books.1990. ISBN 9780140101881. [https://books.google.co.uk/books?id=3rqgQ7zW3AsC] Ultimate *Ultimate Japanese **Suguru Akutsu. Ultimate Japanese: Advanced. 1998. [https://books.google.co.uk/books?id=7VV4RAAACAAJ]. Review: [https://books.google.co.uk/books?id=GnMqAQAAIAAJ 33] The Journal of the Association of Teachers of Japanese 111 (No 2: October 1999) Easy *Samuel E Martin. Easy Japanese: A Direct Learning Approach for Immediate Communication. 1st Ed: 1957. 2nd Ed: 1959. 3rd Ed: 1962. 4th Ed: 2006: [https://books.google.co.uk/books?id=CKHTAgAAQBAJ&pg=PP1#v=onepage&q&f=false] *Jack Seward. Easy Japanese. 1992. [https://books.google.co.uk/books?id=jQIraVXUxN0C] *Fumiko Koide. Easy Japanese. Nippon Kyooiku Kiki Fukyu Center Company. 1971. [https://books.google.co.uk/books?id=Q4JEAQAAMAAJ] *Emiko Konomi. Easy Japanese: Learn to Speak Japanese Quickly! [https://books.google.co.uk/books?id=mjtRDwAAQBAJ&pg=PP1#v=onepage&q&f=false] Basic *Eriko Sato. Basic Japanese. [Practice Makes Perfect]. Premium 3rd Ed: 2023.[https://books.google.co.uk/books?id=JmeYEAAAQBAJ] *NTC's Basic Japanese. [https://books.google.co.uk/books?id=hLyZCKpa8jMC] *Samuel E. Martin and Eriko Sato. Basic Japanese: Learn to Speak Japanese in 10 Easy Lessons. Tuttle. [https://books.google.co.uk/books?id=F1RSDwAAQBAJ&pg=PA1#v=onepage&q&f=false] *Shoko Hamano and Takae Tsujioka. Basic Japanese: A Grammar and Workbook. 2011. [https://books.google.co.uk/books?id=l0fJAwAAQBAJ&pg=PP1#v=onepage&q&f=false] Demystified, Dummies *Eriko Sato. Japanese Demystified. 2008. [https://books.google.co.uk/books?id=Ak7AlXKi3pYC&pg=PR3#v=onepage&q&f=false] *Eriko Sato. Japanese For Dummies. 2002. [https://books.google.co.uk/books?id=Oi6lpE_NC-wC] Hiroko Chiba and Erik Sato. 3rd Ed. [https://books.google.co.uk/books?id=Gql7DwAAQBAJ&pg=PP1#v=onepage&q&f=false] Intermediate *Michael L Kluemper and Lisa Berkson. Intermediate Japanese Textbook. 2022. [https://books.google.co.uk/books?id=7hl2EAAAQBAJ&pg=PP1#v=onepage&q&f=false] **Intermediate Japanese Workbook. [https://books.google.co.uk/books?id=4qB-EAAAQBAJ&pg=PP1#v=onepage&q&f=false] *Hiyaku: An Intermediate Japanese Course. 2011. [https://books.google.co.uk/books?id=9ZDtCQAAQBAJ&pg=PP1#v=onepage&q&f=false] *Haruko Laurie and Richard Bowring. Cambridge Intermediate Japanese. 2002. [https://books.google.co.uk/books?id=E1wLAQAAMAAJ] *Yasuko Ito Watt and Richard Rubinger. Readers Guide to Intermediate Japanese: A Quick Reference to Written Expressions. 1998. [https://books.google.co.uk/books?id=S8ACEQAAQBAJ&pg=PP1#v=onepage&q&f=false] Intermediate to advanced *The Routledge Intermediate to Advanced Japanese Reader. [https://books.google.co.uk/books?id=ZcMfEAAAQBAJ&pg=PP1#v=onepage&q&f=false] Advanced *Noriko Ishihara and Magara Maeda. Advanced Japanese: Communication in Context. 2010. [https://books.google.co.uk/books?id=gmBQDwAAQBAJ&pg=PP1#v=onepage&q&f=false] *An Introduction to Advanced Spoken Japanese. Inter-university Center for Japanese Language Studies. Delmer M Brown. 1987. [https://books.google.com/books?id=Og96QDPsx18C] For high school students; High school programs *Esther M T Sato, Loren I Shishido and Masako Sakihara. Japanese Now. 1982. [https://books.google.co.uk/books?id=k17cHllNfTAC&pg=PP1#v=onepage&q&f=false vol 1] **Esther M T Sato and Masako Sakihara. 1990. [https://books.google.co.uk/books?id=vufHtRpVZt4C&pg=PP1#v=onepage&q&f=false vol 4]. For scientists and engineers *Edward E. Daub, R Byron Bird and Nobuo Inoue. Basic Technical Japanese. 科学技術日本語の基礎. University of Wisconsin Press. 1990. [https://books.google.co.uk/books?id=oN23JJhjFpwC&pg=PP1#v=onepage&q&f=false] Readings *Joseph K Yamagiwa (ed). Readings in Japanese Language and Linguistics. University of Michigan Press. [https://books.google.co.uk/books?id=76wPAAAAYAAJ] Dictionaries See also [[w:en:Japanese dictionary]] and [[w:en:Category:Japanese dictionaries]] Vocabulary *Akira Miura. Essential Japanese Vocabulary. Tuttle. [https://books.google.co.uk/books?id=ZZvTAgAAQBAJ&pg=PA1#v=onepage&q&f=false] *Schaum's Outline of Japanese Vocabulary [https://books.google.co.uk/books?id=fV0NAAAACAAJ] *Carol and Nobuo Akiyama. Japanese Vocabulary. Barron's. 1991. [https://books.google.co.uk/books?id=7Aa6PAAACAAJ] Words *Akira Miura. Japanese Words & Their Uses. Charles E Tuttle. 1983. [https://books.google.co.uk/books?id=MVVzBgAAQBAJ&pg=PP1#v=onepage&q&f=false] Verbs *Complete Japanese Verb Guide. Tuttle. 1989. [https://books.google.co.uk/books?id=I_EPCwAAQBAJ&pg=PP1#v=onepage&q&f=false] *P Suski. Japanese Verbs. (Super Review). Research & Education Association. 2002. [https://books.google.co.uk/books?id=9t6oHZh5gecC&pg=PP1#v=onepage&q&f=false] *Naoko Chino. Japanese Verbs at a Glance. Kodansha International. 1996. [https://books.google.co.uk/books?id=-8AjAQAAIAAJ] *600 Basic Japanese Verbs. Tuttle. [https://books.google.co.uk/books?id=wZgdBAAAQBAJ&pg=PP1#v=onepage&q&f=false] *Roland A Lange. 501 Japanese Verbs. Barron's. 1988. [https://books.google.co.uk/books?id=ANQXAAAAIAAJ] **201 Japanese Verbs. 1971. [https://books.google.co.uk/books?id=Dve2QgAACAAJ] *Rita Lampkin. Japanese Verbs and Essentials of Grammar: A Practical Guide to the Mastery of Japanese. 1995. [https://books.google.co.uk/books?id=P_CyQgAACAAJ] *Suski. Conjugation of Japanese Verbs in the Modern Spoken Japanese. 1942. [https://books.google.co.uk/books?id=SZIPAAAAYAAJ] *G F Verbeck. A Synopsis of All the Conjugations of the Japanese Verbs. 1887. [https://books.google.co.uk/books?id=jEJlAAAAIAAJ&pg=PA1#v=onepage&q&f=false] *Ready Conjugator of Japanese Verbs and Adjectives [https://books.google.co.uk/books?id=jrNDAQAAIAAJ] *Tadao Miyamoto. The Light Verb Construction in Japanese: The Role of the Verbal Noun. 1999. [https://books.google.co.uk/books?id=pHKVTctA-WwC&pg=PP1#v=onepage&q&f=false] Adjectives *Ann Tarumoto. Complete Japanese Adjective Guide. Tuttle. 2001. [https://books.google.co.uk/books?id=SIC4CgAAQBAJ&pg=PP1#v=onepage&q&f=false] Copula *Tomiko Narahara. The Japanese Copula: Forms and Functions. 2002: [https://books.google.co.uk/books?id=UKOHDAAAQBAJ&pg=PP1#v=onepage&q&f=false]. Reviews: [https://www.jstor.org/stable/25064474] [https://www.jstor.org/stable/44486751] [https://www.jstor.org/stable/4176893] Idioms *Kodansha's Dictionary of Basic Japanese Idioms. 2002. [https://books.google.co.uk/books?id=mQ5gyagWePMC&pg=PP1#v=onepage&q&f=false] *Nobuo Akiyama and Carol Akiyama. Japanese Idioms. Barron's. 1996. [https://books.google.co.uk/books?id=V5YPAAAAYAAJ] *Michael L Maynard and Senko K Maynard. 101 Japanese Idioms: Understanding Japanese Language and Culture Through Popular Phrases. 1993. [https://books.google.co.uk/books?id=HXI-Xvv5dMYC] Grammar *Stefan Kaiser, Yasuko Ichikawa, Noriko Kobayashi and Hilofumi Yamamoto. Japanese: A Comprehensive Grammar. 2001. 2nd Ed: 2013: [https://books.google.co.uk/books?id=vJH3CumpiZEC&pg=PP1#v=onepage&q&f=false]. *Naomi H McGloin, Mutsuko Endo Hudson, Fumiko Nazikian and Tomomi Kakegawa. Modern Japanese Grammar: A Practical Guide. 2014. [https://books.google.co.uk/books?id=qcdBDgAAQBAJ&pg=PA11#v=onepage&q&f=false] *Yuki Johnson. Fundamentals of Japanese Grammar. [https://books.google.co.uk/books?id=keIZAQAAIAAJ] *Kazuhiro Teruya. A Systemic Functional Grammar of Japanese. 2007. [https://books.google.co.uk/books?id=SJcqAQAAIAAJ] *Kimihiko Nomura. Japanese Grammar: The Connecting Point. 2010. [https://books.google.co.uk/books?id=I913EQAAQBAJ&pg=PP1#v=onepage&q&f=false] *Schaum's Outline of Japanese Grammar [https://books.google.com/books?id=oZMYsHvuhXIC] *Masahiro Tanimori and Eriko Sato. Essential Japanese Grammar. Tuttle. [https://books.google.co.uk/books?id=CUXRAgAAQBAJ&pg=PP1#v=onepage&q&f=false] *Zeljko Cipris and Shoko Hamano. Making Sense of Japanese Grammar: A Clear Guide through Common Problems. 2002. [https://books.google.co.uk/books?id=GZ0BEAAAQBAJ&pg=PP1#v=onepage&q&f=false] *Carol Akiyama and Nobuo Akiyama. Pocket Japanese Grammar. 4th Ed: 2020: [https://books.google.co.uk/books?id=aga9DwAAQBAJ&pg=PP1#v=onepage&q&f=false] **Japanese Grammar. 3rd Ed. [https://books.google.co.uk/books?id=cO5wDwAAQBAJ&pg=PP1#v=onepage&q&f=false] *Harold G Henderson. Handbook of Japanese Grammar. 1945. 2011. [https://books.google.co.uk/books?id=NYEBAwAAQBAJ&pg=PP1#v=onepage&q&f=false] *W P Lehmann and Lloyd Faust. A Grammar of Formal Written Japanese. (Harvard-Yenching Institute Studies, vol 5). 1951. [https://books.google.co.uk/books?id=50s0AAAAIAAJ] Read; Reading *[[w:en:Eleanor Jorden|Eleanor Harz Jorden]] and Hamako Ito Chaplin. Reading Japanese. Yale University Press. 1976. [https://books.google.co.uk/books?id=1MF6kCogEx0C&pg=PP1#v=onepage&q&f=false] *Jiří Jelínek and Patricia A Heron. Reading Japanese: A self-instructional manual for beginners, leading to independent translating ability. University of Sheffield, Centre of Japanese Studies. 1975. [https://books.google.co.uk/books?id=IKQPAAAAYAAJ] *Dale P Crowley, with the assistance of Yoshiyuki Kawata and Yoko Kawata. Manual for Reading Japanese. University Press of Hawaii. Honolulu. 1972. [https://books.google.co.uk/books?id=nK0PAAAAYAAJ] *John Braden. Read Practical Japanese. Kenkyusha. 1976. [https://books.google.co.uk/books?id=3MAPAAAAYAAJ] *Setsuko Aihara, with Graham Parkes. Strategies for Reading Japanese: A Rational Approach to the Japanese Sentence. Japan Publications Trading Company. Tokyo. 1992. [https://books.google.co.uk/books?id=tMs_AQAAIAAJ] *Len Walsh. Read Japanese Today: The Easy Way to Learn Hiragana, Katakana and Kanji. Tuttle. [https://books.google.co.uk/books?id=1hjBEQAAQBAJ&pg=PP1#v=onepage&q&f=false]. Read Japanese Today: The Easy Way to Learn 400 Practical Kanji. [https://books.google.co.uk/books?id=QcrXBQAAQBAJ&pg=PP1#v=onepage&q&f=false] *Arthur Rose-Innes. Japanese Reading for Beginners. K Yoshikawa & Co. [https://books.google.co.uk/books?id=cP1z4IcbiO4C] See also *[[w:en:Category:Japanese language learning resources]] ==Writing== Written; Writing *David Ashworth and Ikumi Hitosugi. Written Japanese: An Introduction. 1993. [https://books.google.co.uk/books?id=fLDhgDHj7_EC&pg=PP1#v=onepage&q&f=false] *Heath Rose. The Japanese Writing System: Challenges, Strategies and Self-regulation for Learning Kanji. 2017. [https://books.google.co.uk/books?id=ZDU8DwAAQBAJ&pg=PA1924#v=onepage&q&f=false] *Basil Hall Chamberlain. A Practical Introduction to the Study of Japanese Writing. 1899. [https://books.google.co.uk/books?id=-SWFGQkuJN8C&pg=PP5#v=onepage&q&f=false] Handwritten *P G O'Neill. A Reader of Handwritten Japanese. Kodansha International. 1984. [https://books.google.co.uk/books?id=r-MZAQAAIAAJ] ==Characters and syllabaries== *Andrew N Nelson. Modern Reader's Japanese-English Character Dictionary. 1962. 1st Revised Ed: 1966. 2nd Revised Ed: 1974. Classic Ed: 1995. [https://books.google.co.uk/books?id=fKuHCgAAQBAJ&pg=PP1#v=onepage&q&f=false]. Review: The Incorporated Linguist, [https://books.google.co.uk/books?id=E2MtAQAAMAAJ vol 5], no 1, p 24. **John H Haig. The Compact Nelson: Japanese - English Character Dictionary. Tuttle. 1999. [https://books.google.co.uk/books?id=3bzewAEACAAJ] *Mark Spahn and Wolfgang Hadamitzky. Japanese Character Dictionary: With Compound Lookup via Any Kanji. 漢英熟語リバ一ス字典. Nichigai Associates. 1989. [https://books.google.co.uk/books?id=RqEPAAAAYAAJ] *NTC's New Japanese-English Character Dictionary. 1993. ISBN 0844284343. [https://books.google.co.uk/books?id=rZoFwQEACAAJ] **New Japanese-English Character Dictionary. Kenyusha. Tokyo. 1990. ISBN 4767490405. Hiragana and katakana *Timothy G Stout. Japanese Hiragana & Katakana for Beginners. 2011. [https://books.google.co.uk/books?id=ZPs8BAAAQBAJ&pg=PP1#v=onepage&q&f=false] *Kenneth G Henshall and Tetsuo Takagaki. Learning Japanese Hiragana and Katakana. Revised 2nd Ed. [https://books.google.co.uk/books?id=QyfRAgAAQBAJ&pg=PP1#v=onepage&q&f=false] **Guide to Learning Hiragana & Katakana. Tuttle. 1990. [https://books.google.com/books?id=18i1QgAACAAJ] *Glen McCabe. Japanese Hiragana and Katakana Flash Cards. 2012. [https://books.google.co.uk/books?id=aSFFBAAAQBAJ&pg=PA34#v=onepage&q&f=false] *Richard S Keirstead. Japanese Hiragana & Katakana: Language Practice Pad. 2016. [https://books.google.co.uk/books?id=yPxHDgAAQBAJ&pg=PP1#v=onepage&q&f=false] Hiragana *Fujihiko Kaneda. Easy Hiragana. Passport Books. 1989. [https://books.google.com/books?id=CvQZAQAAIAAJ] *James W Heisig. Remembering the Hiragana: a complete course on how to teach yourself the Japanese syllabary in 3 hours. Japan Publications Trading Co. 1987. [https://books.google.co.uk/books?id=VdEPAAAAYAAJ] *Timothy G Stout. Japanese Hiragana for Beginners. 2007. [https://books.google.co.uk/books?id=dR_RAgAAQBAJ&pg=PP1#v=onepage&q&f=false] *Jim Gleeson. Writing Japanese Hiragana: An Introductory Japanese Language Workbook. 1996. Revised Ed: 2015: [https://books.google.co.uk/books?id=YtZGCgAAQBAJ&pg=PP1#v=onepage&q&f=false]. *Yuko Green. My First Hiragana Activity Book. 2000. [https://books.google.co.uk/books?id=C-OKxX_cdpgC&pg=PP1#v=onepage&q&f=false] Katakana *Tina Wells. Easy Katakana: How to Read and Write English Words Used in Japanese. Passport Books. 1989. [https://books.google.co.uk/books?id=-ZSDP-9i9oUC] *Helmut Morsbach, Kazue Kurebayashi and James W. Heisig. Remembering the Katakana. Japan Publications Trading Co. 1990. [https://books.google.co.uk/books?id=HeAPAAAAYAAJ] *Jim Gleeson. Writing Japanese Katakana: An Introductory Japanese Language Workbook. 1996. Revised Ed: 2015: [https://books.google.co.uk/books?id=rNZGCgAAQBAJ&pg=PP1#v=onepage&q&f=false] *Timothy G Stout. Japanese Katakana for Beginners: First Steps to Mastering the Japanese Writing System. 2007. [https://books.google.co.uk/books?id=W5sdBAAAQBAJ&pg=PP1#v=onepage&q&f=false] Kanji and kana *Wolfgang Hadamitzky and Mark Spahn. Japanese Kanji and Kana: A Complete Guide to the Japanese Writing System. 1981. 2nd Ed: 1997. 3rd Ed: 2011. [https://books.google.co.uk/books?id=3w7QAgAAQBAJ&pg=PP1#v=onepage&q&f=false] Kanji *James W Heisig. Remembering the Kanji. 1977. 5th Ed: 2007. [https://books.google.co.uk/books?id=TtEaylKrGaMC&pg=PP1#v=onepage&q&f=false vol 1]. Remembering the Kanji 1. [https://books.google.co.uk/books?id=PYOUEAAAQBAJ&pg=PP1#v=onepage&q&f=false] **James W Heisig. Remembering the Kanji: A systematic guide to reading Japanese characters. 1987. [https://books.google.co.uk/books?id=IKQPAAAAYAAJ] *James W Heisig and Tanya Sienko. Remembering the Kanji 3. 1994. 2nd Ed: 2008. [https://books.google.co.uk/books?id=wTZ4x_BHe5EC&pg=PP1#v=onepage&q&f=false] *Editorial staff of The East magazine. Kanji Kanji. The East Publications Inc. Tokyo. 1972: [https://books.google.co.uk/books?id=HcYPAAAAYAAJ]. Revised Ed: 1983: [https://books.google.co.uk/books?id=T8YPAAAAYAAJ]. *Andrew Dykstra. Kanji 1-2-3. Kanji Press. [https://books.google.co.uk/books?id=SnBWAAAAYAAJ] *The Learner's Japanese Kanji Dictionary. Tuttle. *Naoomi Kuratani, Akemi Kobayashi and Shunsuke Okunishi (eds). A New Dictionary of Kanji Usage あたらしい漢字用法辞典. Gakken. 1982. [https://books.google.co.uk/books?id=5-C4AAAAIAAJ]. Review: "The Slimline Kanji Dictionaries" (1996) 9 International Journal of Lexicography 132 (No 2: June). Abstracts: [https://books.google.co.uk/books?id=2vYPAQAAMAAJ] [https://academic.oup.com/ijl/article-abstract/9/2/132/930154] *Jack Halpern. The Kodansha Kanji Usage Guide: An A to Z of Kun Homophones. [https://books.google.co.uk/books?id=qgWQEAAAQBAJ] *Laurence Matthews. Kanji Fast Finder 漢字早引き辞典. Tuttle. [https://books.google.co.uk/books?id=7SdpPwAACAAJ] *Glen Nolan Grant. Mastering Japanese Kanji. Tuttle. 2009. [https://books.google.co.uk/books?id=0L1GCgAAQBAJ&pg=PP1#v=onepage&q&f=false vol 1]. *John Millen. Kanji Power: A Workbook for Mastering Japanese Characters. Tuttle Publishing. 1993. [https://books.google.co.uk/books?id=uPu4AAAAIAAJ] *Oreste Vaccari. Standard Kanji. Revised Ed. 1949. [https://books.google.co.uk/books?id=b1Q98sCcgV0C] *P G O'Neill. Essential Kanji. Weatherhill. 1973 [https://books.google.co.uk/books?id=VYadVK-DqSYC]. Paperback Ed: 1987: [https://books.google.co.uk/books?id=dQ25AAAAIAAJ]. *Essential Japanese Kanji. Tuttle. 2015. [https://books.google.co.uk/books?id=Gr5GCgAAQBAJ&pg=PP1#v=onepage&q&f=false vol 1]. 2016. [https://books.google.co.uk/books?id=F8A0DwAAQBAJ&pg=PP1#v=onepage&q&f=false vol 2]. *Kodansha's Compact Kanji Guide: A new character dictionary for students and professionals. Kodansha International. 1991. Review: Gerald B Mathias and Timothy J Vance (1992) [https://books.google.co.uk/books?id=2loLAQAAMAAJ 26] The Journal of the Association of Teachers of Japanese 47 (No 1: April 1992) *Fujihiko Kaneda. Easy Kanji. Passport Books. 1996. [https://books.google.co.uk/books?id=R7ZM9Dao7NMC] *Erik Sato. Learning Japanese Kanji: Practice Book. Tuttle. [https://books.google.co.uk/books?id=IcA0DwAAQBAJ&pg=PP1#v=onepage&q&f=false vol 2]. *The Second 100 Japanese Kanji. Tuttle. [https://books.google.co.uk/books?id=gUjRAgAAQBAJ&pg=PP1#v=onepage&q&f=false] *Yasuko Kosaka Mitamura and Joyce Yumi Mitamura. Let's Learn Kanji: An Introduction to Radicals, Components and 250 Very Basic Kanji. Kodansha International. 1997. [https://books.google.co.uk/books?id=khnrnBXLciIC&pg=PP1#v=onepage&q&f=false] **Richard Glenn Covington, Yasuko Kosaka Mitamura and Joyce Yumi Mitamura. Let's Learn More Kanji: Family Groups, Learning Strategies, and 300 Complex Kanji. [https://books.google.co.uk/books?id=HLEOAAAACAAJ] ==Linguistics== *Yoko Hasegawa (ed). The Cambridge Handbook of Japanese Linguistics. 2018. [https://books.google.co.uk/books?id=CC5RDwAAQBAJ&pg=PP1#v=onepage&q&f=false] Reviews: [https://www.jstor.org/stable/48828212] [https://online.ucpress.edu/jjs/article-abstract/46/2/536/210735/Review-The-Cambridge-Handbook-of-Japanese] *Shigeru Miyagawa and Mamoru Saito (eds). The Oxford Handbook of Japanese Linguistics. 2008. [https://books.google.co.uk/books?id=4CS07LRO8O8C&pg=PP1#v=onepage&q&f=false] *Natsuko Tsujimura. An Introduction to Japanese Linguistics. 1996. Reviews: [https://www.jstor.org/stable/489672] [https://www.jstor.org/stable/417343]. 3rd Ed. [https://books.google.co.uk/books?id=LdaYAAAAQBAJ&pg=PP1#v=onepage&q&f=false] *Yoko Hasegawa. Japanese: A Linguistic Introduction. 2015. [https://books.google.co.uk/books?id=gpeiBQAAQBAJ&pg=PP1#v=onepage&q&f=false] *Toshiko Yamaguchi. Japanese Linguistics in Use: An Introduction for Language Learners. 2025. [https://books.google.co.uk/books?id=QP-YEQAAQBAJ&pg=PP1#v=onepage&q&f=false] **Japanese Linguistics: An Introduction. 2007. Review: [https://www.jstor.org/stable/25173131] **Japanese Language in Use: An Introduction. 2007. *Natsuko Tsujimura. Japanese Linguistics. 2005. [https://books.google.com/books?id=bgJ8PgAACAAJ] *Tetsuo Harada. Outlines of Modern Japanese Linguistics. Tateshina Print Company. 1966. [https://books.google.co.uk/books?id=jTcHAQAAIAAJ] Periodicals, Linguistics *Papers in Japanese Linguistics [https://books.google.co.uk/books?id=iZomAQAAIAAJ] *Journal of Japanese Linguistics [https://books.google.co.uk/books?id=458mAQAAIAAJ] Issues *Takashi Imai and Mamoru Saito (eds). Issues in Japanese Linguistics. (Studies in Generative Grammar 29). Foris Publications. Dordrecht, Holland. 1987. ISBN 90-6765-284-9. [https://books.google.co.uk/books?id=bYiFEAAAQBAJ&pg=PP1#v=onepage&q&f=false] *Yukio Otsu and Ann Farmer (eds). Theoretical Issues in Japanese Linguistics. (MIT Working Papers in Linguistics 2). 1980. [https://books.google.com/books?id=RDeBAAAAIAAJ] Kokugogaku and nihongogaku *Lidia Tanaka. "Japanese language studies: Kokugo as an ideology, nihongo as an autonomous and global scholarship?". Kaori Okano and Yoshio Sugimoto (eds). Rethinking Japanese Studies: Eurocentrism and the Asia-Pacific Region. Routledge Contemporary Japan Series. 2018.Chapter 3. pp [https://books.google.co.uk/books?id=sEcrDwAAQBAJ&pg=PA32#v=onepage&q&f=false 32] to 52. Nihongogaku (Japanese: [[w:ja:日本語学|日本語学]]) (English: Japanese linguistics; Japanese language studies) *[https://ndlsearch.ndl.go.jp/rnavi/humanities/post_198 日本語学に関する文献を探すには（主題書誌）]. [[w:en:National Diet Library|NDL]]. Cf. Kokugogaku (Japanese: [[en:wikt:国語学|国語学]]) (English: national language studies) Syntax and semantics *Masayoshi Shibatani. Syntax and Semantics. Japanese Generative Grammar 5. Academic Press. 1976. [https://books.google.co.uk/books?id=sPJZEQAAQBAJ&pg=PP1#v=onepage&q&f=false] *Kuroda. Japanese Syntax and Semantics: Collected Papers. 1992. [https://books.google.co.uk/books?id=OXnrCAAAQBAJ&pg=PP1#v=onepage&q&f=false] *John Hinds and Irwin Howard (eds). Problems in Japanese Syntax and Semantics. Kaitakusha Co Ltd. 1978. [https://books.google.co.uk/books?id=_yBkAAAAMAAJ] Semantics and pragmatics *Wesley M Jacobsen and Yukinori Takubo (eds). Handbook of Japanese Semantics and Pragmatics. 2020. [https://books.google.co.uk/books?id=wUUCEAAAQBAJ&pg=PR3#v=onepage&q&f=false] *Elin McCready, Katsuhiko Yabushita and Kei Yoshimoto (eds). Formal Approaches to Semantics and Pragmatics: Japanese and Beyond. 2014. 2020. [https://books.google.co.uk/books?id=ZeBcBAAAQBAJ&pg=PR4#v=onepage&q&f=false] Morphology and phonology *Jeroen Maarten van de Weijer and Tetsuo Nishihara (eds). Issues in Japanese Phonology and Morphology. (Studies in Generative Grammar 51).  2001. [https://books.google.co.uk/books?id=G4p_t7jy28AC&pg=PP1#v=onepage&q&f=false] Phonetics and Phonology *Haruo Kubozono (ed). Handbook of Japanese Phonetics and Phonology. 2015. [https://books.google.co.uk/books?id=8vFeCAAAQBAJ&pg=PR3#v=onepage&q&f=false] *Hiromi Otaka. Phonetics and Phonology of Moras, Feet and Geminate Consonants in Japanese. 2009. [https://books.google.co.uk/books?id=39Q_AQAAIAAJ] *James D McCawley. The Phonological Component of a Grammar of Japanese. Mouton & Co NV. The Hague. 1968. [https://books.google.co.uk/books?id=3JoPAAAAYAAJ] Syntax *Masayoshi Shibatani, Shigeru Miyagawa and Hisashi Noda (eds). Handbook of Japanese Syntax. 2017. [https://books.google.co.uk/books?id=tk8_DwAAQBAJ&pg=PA1#v=onepage&q&f=false] *Nobuko Hasegawa. Japanese Syntax in Comparative Grammar. Kuroshio Publishers. Tokyo. 1993. [https://books.google.co.uk/books?id=ztApAQAAIAAJ] Phonetics *Daniel Lepetit and Reiko Makino. Japanese Phonetics: A Thematic Bibliography. Canadian Scholars. 1996. ISBN 1551300923. Catalogue: Canadian Books in Print: Author and Title Index 2005. [https://books.google.co.uk/books?id=q2WLJa9rY5MC&pg=PA1063#v=onepage&q&f=false p 1063]. *Society Newsletter. 1926 to 1996. [[w:ja:日本音声学会|The Phonetic Society of Japan]]. [https://www.psj.gr.jp/eng/publication/society-newsletter] **Journal of the Phonetic Society of Japan. 1997 onwards. [https://www.psj.gr.jp/eng/publication] *Tsutomu Akamatsu. Japanese Phonetics: Theory and Practice. Lincom Europa. 1997. [https://books.google.com/books?id=guUZAQAAIAAJ] *P M Suski. The Phonetics of Japanese Language: With Reference to Japanese Script. 1931: [https://books.google.co.uk/books?id=gpthAAAAMAAJ]. 2011: [https://books.google.co.uk/books?id=9DuiAwAAQBAJ&pg=PP1#v=onepage&q&f=false]. Phonology *Laurence Labrune. The Phonology of Japanese. 2012. [https://books.google.co.uk/books?id=ix9r6CbEl6IC&pg=PR3#v=onepage&q&f=false] *Tsutomu Akamatsu. Japanese Phonology: A Functional Approach. Lincom Europa. 2000. [https://books.google.com/books?id=R-QZAQAAIAAJ] *Mieko Shimizu Han. Japanese Phonology: An Analysis Based on Sound Spectrograms. Kenkyusha. 1962. [https://books.google.co.uk/books?id=T3Xl7SviXB4C] Pragmatics *Mutsuko Endo Hudson, Yoshiko Matsumoto, Junko Mori (eds). Pragmatics of Japanese: Perspectives on grammar, interaction and culture. 2018. [https://books.google.co.uk/books?id=2wZTDwAAQBAJ&pg=PP1#v=onepage&q&f=false] *Gabriele Kasper. Pragmatics of Japanese as Native and Target Language. Second Language Teaching & Curriculum Center, University of Hawaiʼi at Mānoa. 1992. [https://books.google.co.uk/books?id=2_8ifcjhpYQC] *Naoko Taguchi. Pragmatic Competence. (Mouton Series in Pragmatics). 2009. [https://books.google.co.uk/books?id=14dEa1EZm4oC&pg=PP1#v=onepage&q&f=false] Sociolinguistics *Roy Andrew Miller. The Japanese Language in Contemporary Japan: Some Sociolinguistic Observations. 1977. [https://books.google.co.uk/books?id=9RxkAAAAMAAJ] ==Translation== *Yoko Hasegawa. The Routledge Course in Japanese Translation. 2012. [https://books.google.co.uk/books?id=5kX1O4bCx_oC&pg=PP1#v=onepage&q&f=false]. Review: [https://www.jstor.org/stable/24394410] *Judy Wakabayashi. Japanese–English Translation: An Advanced Guide. 2021. [https://books.google.co.uk/books?id=Nqf7DwAAQBAJ&pg=PA1#v=onepage&q&f=false] ==Dialects and regions== Dialects *Nobuko Kibe, Tetsuo Nitta and Kan Sasaki (eds). Handbook of Japanese Dialects. 2025. [https://books.google.co.uk/books?id=8_Y9EQAAQBAJ&pg=PR1#v=onepage&q&f=false] Kansai *Peter Tse. Kansai Japanese: The Language of Osaka, Kyoto, and Western Japan. (Tuttle Language Library). 1993. Reprinted 2002. [https://books.google.co.uk/books?id=FvVkCwAAQBAJ&pg=PP1#v=onepage&q&f=false] *DC Palter and Kaoru Slotsve. Colloquial Kansai Japanese: The Dialects and Culture of the Kansai Region. 1995. [https://books.google.co.uk/books?id=rJEdBAAAQBAJ&pg=PP1#v=onepage&q&f=false] ==History== *Bjarke Frellesvig. A History of the Japanese Language. 2010. [https://books.google.co.uk/books?id=v1FcAgiAC9IC&pg=PP1#v=onepage&q&f=false] *Lone Takeuchi. The Structure and History of Japanese: From Yamatokotoba to Nihongo. 1999. [https://books.google.co.uk/books?id=sr8PAAAAYAAJ] *Ohno Susumu. The Origin of the Japanese Language. Kokusai Bunka Shinkokai. Tokyo. 1970. [https://books.google.co.uk/books?id=pqcPAAAAYAAJ] *N A Syromiatnikov. The Ancient Japanese Language. Nauka Publishing House. 1981. [https://books.google.co.uk/books?id=OB5kAAAAMAAJ] *Yaeko Sato Habein. The History of the Japanese Written Language. University of Tokyo Press. 1984. [https://books.google.co.uk/books?id=xh1kAAAAMAAJ] ==Old Japanese== *John R Bentley. A Descriptive Grammar of Early Old Japanese Prose. 2001. [https://books.google.co.uk/books?id=Eoqv_NcLJ4gC&pg=PP1#v=onepage&q&f=false] *Alexander Vovin. A Descriptive and Comparative Grammar of Western Old Japanese. 2005. [https://books.google.co.uk/books?id=Ba1xEQAAQBAJ&pg=PR1#v=onepage&q&f=false] 2nd Ed: 2020. [https://books.google.co.uk/books?id=xfP_DwAAQBAJ&pg=PR3#v=onepage&q&f=false vol 1]. ==Classical Japanese== Introduction *Akira Komai and Thomas H Rohlich. An Introduction to Classical Japanese. Bonjinsha. Tokyo. 1991. Review: "Textbook Review by Questionnaire" (1992) [https://books.google.co.uk/books?id=tClnAAAAMAAJ 26] The Journal of the Association of Teachers of Japanese 50 (No 1: April 1992) Grammar *Noriko Katsuki-Pestemer. A Grammar of Classical Japanese. Lincom Europa. 2009. [https://books.google.co.uk/books?id=PHoLAQAAMAAJ] *Haruo Shirane. Classical Japanese: A Grammar. 2005. [https://books.google.co.uk/books?id=M5-vVlcVEDkC&pg=PP1#v=onepage&q&f=false]. Review: [https://muse.jhu.edu/article/209495/summary] *Alexander Vovin. A Reference Grammar of Classical Japanese Prose. 2003. [https://books.google.co.uk/books?id=24GTVscUCX0C&pg=PP1#v=onepage&q&f=false] *Akira Komai. A Grammar of Classical Japanese. Culver Publishing. 1979. [https://books.google.co.uk/books?id=sL0PAAAAYAAJ] *Tadashi Ikeda. Classical Japanese Grammar Illustrated with Texts. The Toho Gakkai (The Institute of Eastern Culture). 1980. [https://books.google.co.uk/books?id=jQjUAAAAMAAJ] Dictionary *Ivan Morris. Dictionary of Selected Forms in Classical Japanese Literature. Columbia University Press. 1966. [https://books.google.co.uk/books?id=O70PAAAAYAAJ] *Jiří Jelínek. Classical Japanese-English Grammar Dictionary. University of Sheffield, Centre of Japanese Studies. 1976. [https://books.google.co.uk/books?id=qOEPAAAAYAAJ] Clauses *Stefan Kaiser. Circumnominal Relative Clauses in Classical Japanese: An Historical Study. Otto Harrassowitz. Wiesbaden. 1991. ISBN 344703212X. [https://books.google.co.uk/books?id=GHsPAAAAYAAJ] [[Category:Japanese]] e3j0aztp0fjwzzctoq6syo75nw2sssj 0 330941 2823793 2822534 2026-08-21T02:54:14Z U3269672 3105208 2823793 wikitext text/x-wiki {{title|Akrasia:<br>Why do people act against their better judgement?}} __TOC__ ==Overview== {{RoundBoxTop|theme=3}}'''Consider this scenario''' [[File:Canva - Woman Feeling Emotional Stress.jpg|thumb|200px|'''Figure 1.''' A women feeling stressed]] Jordan signed up for a gym membership at the start of the year, determined to improve their physical and mental health. He bought new workout clothes, saved a list of routines and even told his friends he was committed to exercising. But when his alarm went off at 6:30am he hit snooze. Telling himself he will simply go after work instead but by 5:00pm he's to tired to go. The idea of lifting weights is to emotionally heavy and stress inducing for him, so Jordan chooses to stay home and watch a TV show. Each time Jordans alarm goes off and he ignores it, even while knowing going to the gym would be healthier and help him gain confidence, the short term comfort of staying home out ways those feelings. Jordan isn't lazy he his experiencing akrasia, a predictable motivational and emotional conflict between long term goals and short term impulses. {{RoundBoxBottom}} This Chapter will explain and explore why people act against their better judgement described by psychological explanations of self control and regulation, motivational deficits and emotional avoidance. * '''Explanation of the problem:''' akrasia is a problem because it affects many areas of persons life such as academics, health choices, financial decisions and relationships. People often intend to make choices that align with their values and goals, yet often make choices that are the opposite. this gap between intention and action can lead to issues with wellbeing and a sense of success in life ( reference) * introduce psychological importance:( why it matters) Akrasia matters because it undermines goal achievement, wellbeing, and personal growth. It reflects a tension between reflective, value based intensions and impulsive, emotionally driven tendencies. psychological science provides tools for understanding this conflict by examining self regulation, and cognitive biases (reference). * why the understanding of the psychological science can help provide ways to overcome actions of akrasia or the feelings left behind form failed long term goals.( Reference) * Introduce motivation in relation to topic * Introduce emotion in relation to topic Key resources: * [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 02]] explains about how to edit * [[Motivation and emotion/Assessment/Topic|Topic development guidelines]] * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] * {{RoundBoxTop|theme=3}} '''Focus questions''' # What is akrasia? # What psychological processes contribute to akrasia and the conflict between long term and short term impulses? # How do motivation and emotion interact to influence why people act against their better judgement ? # What evidence based strategies can help people reduce akrasia and act more consistently in line with their goals ? {{RoundBoxBottom}} ==Outline for chapter == Use this heading structure: * [[#Overview|Overview]] * 3 to 6 major headings tailored to the topic; can have sub-headings, but: ** avoid having only one sub-heading ** provide an introductory paragraph before breaking into sub-sections * [[#Conclusion|Conclusion]] * See also * References * External links == Akrasia == * General definition/introduction: acting against ones better judgement ect... "i know i shouldn't do this but" * Historical background: originates from ancient Greek philosophy. particularly Aristotle, who used the term akrasia to describe " weakness of will" ect.. Describe what he argued about failure to understand emotions and impulses.( reference (needs editing): Bobonich C., &  Destrée, P. (2007). Akrasia in Greek Philosophy: From Socrates to Plotinus. BRILL .106, 1-11. https://books.google.com.au/books?id=so097j_jPBsC&dq=akrasia+historical+background&lr=&source=gbs_navlinks_s) * Describe what the history laid a foundation for in modern explanations == Akrasia as a motivational and emotional conflict == '''Focus question''': what psychological processes contribute to akrasia and the conflict between long term and short term impulses? '''Overview/introduction to argument'''; Explain how akrasia arises from competing internal processes. Discuss the tension between long‑term goals and short‑term impulses. Introduce the idea that akrasia is not simply “laziness” but a predictable psychological phenomenon. describe long term and short term impulses/ goals are: ( I want to finish my degree vs I want to just relax right now) * immediate emotional or motivational states vs reflective value-based reasoning. * prioritisation of short term effective rewards even when they consciously prefer long term outcomes. this is especially true when tasks evoke discomfort. (reference) === Modelling the conceptual relationship === * Provide a model- if there is one '''Evidence of facilitative relationship''' == Self‑regulation and self‑control == Explain all in relation to behaviours of akrasia * failures in self‑regulation contribute to akrasia: Conflict of internal systems (Reference/ Edit: Bella, A. F. (2023). Psychological underpinnings of akrasia: A new integrative framework based on self-regulation vulnerabilities and failures. ''New Ideas in Psychology'', ''70'', Article 101027. https://doi.org/10.1016/j.newideapsych.2023.101027) * Discuss ego depletion: self control is a limited resource. ego depletion is the action of drawing on self control and will power from a limited source. (Reference: Baumeister, R. F., Bratslavsky, E., Muraven, M., & Tice, D. M. (1998). Ego Depletion: Is the Active Self a Limited Resource? ''Journal of Personality and Social Psychology'', ''74''(5), 1252–1265. https://doi.org/10.1037/0022-3514.74.5.12520. Inzlicht, M., & Schmeichel, B. J. (2012). What Is Ego Depletion? Toward a Mechanistic Revision of the Resource Model of Self-Control. ''Perspectives on Psychological Science'', ''7''(5), 450–463.)https://doi.org/10.1177/1745691612454134) * <u>(temporal discounting: disproportionate assessment of rewards and punishment)</u> potential topic unsure * implementation intentions. if - then * Provide examples of how these processes play out in everyday life. add figure / model == Motivational theories == * Explain how motivational deficits or conflicts lead to akrasia. [[File:Self-Determination-Theory-Visual 1.png|thumb|Figure 2: Self-Determination Theory visual diagram ]] Discuss self‑determination theory: * what is SDT? - autonomous, motivation vs controlled motivation, akrasia is more likely when motivation is controlled.(reference: Deci, E. L., & Ryan, R. M. (2000). The “What” and “Why” of Goal Pursuits: Human Needs and the Self-Determination of Behavior. ''Psychological Inquiry'', ''11''(4), 227–268. https://doi.org/10.1207/S15327965PLI1104-01) *expectancy‑value theory: actions based an appraisal of successes (reference: Wigfield, A., & Eccles, J. S. (2000). Expectancy–Value Theory of Achievement Motivation. ''Contemporary Educational Psychology'', ''25''(1), 68–81.https://doi.org/10.1006/ceps.1999.1015) * goal‑setting theory: challenging akrasia * Show how motivation quality affects the likelihood of acting in line with long‑term goals. add figure / model where possible == Emotion and akrasia == * Explain * emotional avoidance: tasks that evoke frustration are avoided * anxiety: high anxiety leads to task aversion * affect regulation: choice of immediate mood regulation over long term solutions * Discuss how people often choose short‑term emotional relief over long‑term outcomes. add figure / model == How does this understanding of the psychological science behind akrasia help those experiencing this ( write title to something more formal) == '''Focus question''': what strategies are there to reduce to act of akrasia and act more consciously in line with their goals? * Explain how empirical findings support, challenge, or refine theoretical models * Show how integrated knowledge helps explain akrasia more accurately. * Discuss implications for improving motivational and emotional lives. Present practical, research‑supported strategies for reducing akrasia, such as: * Implementation intentions * Emotion regulation techniques * Reducing cognitive load * Structuring environments to support long‑term goals * Enhancing autonomous motivation Explain why each strategy works and how individuals can apply it. ==Figures== [[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== Interactive learning features help to bring book chapters to life and can be embedded throughout the chapter. ;Scenarios * Scenarios, case studies, or examples describe concepts in action * Can be real or fictional; if real, provide citations * Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Present using [[#Feature boxes|feature boxes]] {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted '''Table 1''' A Descriptive Caption Which Explains The Table Contents and its Relevance to the Text e.g., The 2 x 2 Johari Window Model Showing Knowing x Self/Other {| class="wikitable" style="margin: auto; |- ! !! Known to self !! Not known to self |- | '''Known to others''' || Open area || Blind spot |- | '''Not known to others''' || Hidden area || Unknown |} ;Quizzes * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] Example simple quiz questions. Choose your answers and click "Submit": <quiz display=simple> {The purpose of quizzes is to provide an interactive learning feature: |type="()"} + True - False {Long and complex quiz questions are recommended: |type="()"} - True + False </quiz> ==Conclusion== * summarise the most important points in 3–5 sentences. * Align with subtitle and focus questions. * Highlight implications for personal growth and psychological wellbeing. * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) * [[w:Self determination theory|Self determination theory]] (Wikipedia) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses }} ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]].{{Hanging indent|1= Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091 Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper & Row. }}{{Hanging indent|1= References Bobonich C., & Destrée, P. (2007). Akrasia in Greek Philosophy: From Socrates to Plotinus. BRILL .106, 1-11. https://books.google.com.au/books?id=so097j_jPBsC&dq=akrasia+historical+background&lr=&source=gbs_navlinks_s Bella, A. F. (2023). Psychological underpinnings of akrasia: A new integrative framework based on self-regulation vulnerabilities and failures. New Ideas in Psychology, 70, Article 101027. https://doi.org/10.1016/j.newideapsych.2023.101027) Baumeister, R. F., et al. (1998). Ego depletion: Is the active self a limited resource? Journal of Personality and Social Psychology. DOI: https://doi.org/10.1037/0022-3514.74.5.1252 (doi.org in Bing) Deci, E. L., & Ryan, R. M. (2000). The “What” and “Why” of Goal Pursuits: Human Needs and the Self-Determination of Behavior. Psychological Inquiry, 11(4), 227–268. https://doi.org/10.1207/S15327965PLI1104-01 Inzlicht, M., & Schmeichel, B. J. (2012). What Is Ego Depletion? Toward a Mechanistic Revision of the Resource Model of Self-Control. Perspectives on Psychological Science, 7(5), 450–463. https://doi.org/10.1177/1745691612454134 Wigfield, A., & Eccles, J. S. (2000). Expectancy–Value Theory of Achievement Motivation. Contemporary Educational Psychology, 25(1), 68–81. https://doi.org/10.1006/ceps.1999.1015}} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Self-control]] . 6o6071escnun0zors56o9icw245d980 2823794 2823793 2026-08-21T02:54:33Z U3269672 3105208 /* Learning features */ 2823794 wikitext text/x-wiki {{title|Akrasia:<br>Why do people act against their better judgement?}} __TOC__ ==Overview== {{RoundBoxTop|theme=3}}'''Consider this scenario''' [[File:Canva - Woman Feeling Emotional Stress.jpg|thumb|200px|'''Figure 1.''' A women feeling stressed]] Jordan signed up for a gym membership at the start of the year, determined to improve their physical and mental health. He bought new workout clothes, saved a list of routines and even told his friends he was committed to exercising. But when his alarm went off at 6:30am he hit snooze. Telling himself he will simply go after work instead but by 5:00pm he's to tired to go. The idea of lifting weights is to emotionally heavy and stress inducing for him, so Jordan chooses to stay home and watch a TV show. Each time Jordans alarm goes off and he ignores it, even while knowing going to the gym would be healthier and help him gain confidence, the short term comfort of staying home out ways those feelings. Jordan isn't lazy he his experiencing akrasia, a predictable motivational and emotional conflict between long term goals and short term impulses. {{RoundBoxBottom}} This Chapter will explain and explore why people act against their better judgement described by psychological explanations of self control and regulation, motivational deficits and emotional avoidance. * '''Explanation of the problem:''' akrasia is a problem because it affects many areas of persons life such as academics, health choices, financial decisions and relationships. People often intend to make choices that align with their values and goals, yet often make choices that are the opposite. this gap between intention and action can lead to issues with wellbeing and a sense of success in life ( reference) * introduce psychological importance:( why it matters) Akrasia matters because it undermines goal achievement, wellbeing, and personal growth. It reflects a tension between reflective, value based intensions and impulsive, emotionally driven tendencies. psychological science provides tools for understanding this conflict by examining self regulation, and cognitive biases (reference). * why the understanding of the psychological science can help provide ways to overcome actions of akrasia or the feelings left behind form failed long term goals.( Reference) * Introduce motivation in relation to topic * Introduce emotion in relation to topic Key resources: * [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 02]] explains about how to edit * [[Motivation and emotion/Assessment/Topic|Topic development guidelines]] * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] * {{RoundBoxTop|theme=3}} '''Focus questions''' # What is akrasia? # What psychological processes contribute to akrasia and the conflict between long term and short term impulses? # How do motivation and emotion interact to influence why people act against their better judgement ? # What evidence based strategies can help people reduce akrasia and act more consistently in line with their goals ? {{RoundBoxBottom}} ==Outline for chapter == Use this heading structure: * [[#Overview|Overview]] * 3 to 6 major headings tailored to the topic; can have sub-headings, but: ** avoid having only one sub-heading ** provide an introductory paragraph before breaking into sub-sections * [[#Conclusion|Conclusion]] * See also * References * External links == Akrasia == * General definition/introduction: acting against ones better judgement ect... "i know i shouldn't do this but" * Historical background: originates from ancient Greek philosophy. particularly Aristotle, who used the term akrasia to describe " weakness of will" ect.. Describe what he argued about failure to understand emotions and impulses.( reference (needs editing): Bobonich C., &  Destrée, P. (2007). Akrasia in Greek Philosophy: From Socrates to Plotinus. BRILL .106, 1-11. https://books.google.com.au/books?id=so097j_jPBsC&dq=akrasia+historical+background&lr=&source=gbs_navlinks_s) * Describe what the history laid a foundation for in modern explanations == Akrasia as a motivational and emotional conflict == '''Focus question''': what psychological processes contribute to akrasia and the conflict between long term and short term impulses? '''Overview/introduction to argument'''; Explain how akrasia arises from competing internal processes. Discuss the tension between long‑term goals and short‑term impulses. Introduce the idea that akrasia is not simply “laziness” but a predictable psychological phenomenon. describe long term and short term impulses/ goals are: ( I want to finish my degree vs I want to just relax right now) * immediate emotional or motivational states vs reflective value-based reasoning. * prioritisation of short term effective rewards even when they consciously prefer long term outcomes. this is especially true when tasks evoke discomfort. (reference) === Modelling the conceptual relationship === * Provide a model- if there is one '''Evidence of facilitative relationship''' == Self‑regulation and self‑control == Explain all in relation to behaviours of akrasia * failures in self‑regulation contribute to akrasia: Conflict of internal systems (Reference/ Edit: Bella, A. F. (2023). Psychological underpinnings of akrasia: A new integrative framework based on self-regulation vulnerabilities and failures. ''New Ideas in Psychology'', ''70'', Article 101027. https://doi.org/10.1016/j.newideapsych.2023.101027) * Discuss ego depletion: self control is a limited resource. ego depletion is the action of drawing on self control and will power from a limited source. (Reference: Baumeister, R. F., Bratslavsky, E., Muraven, M., & Tice, D. M. (1998). Ego Depletion: Is the Active Self a Limited Resource? ''Journal of Personality and Social Psychology'', ''74''(5), 1252–1265. https://doi.org/10.1037/0022-3514.74.5.12520. Inzlicht, M., & Schmeichel, B. J. (2012). What Is Ego Depletion? Toward a Mechanistic Revision of the Resource Model of Self-Control. ''Perspectives on Psychological Science'', ''7''(5), 450–463.)https://doi.org/10.1177/1745691612454134) * <u>(temporal discounting: disproportionate assessment of rewards and punishment)</u> potential topic unsure * implementation intentions. if - then * Provide examples of how these processes play out in everyday life. add figure / model == Motivational theories == * Explain how motivational deficits or conflicts lead to akrasia. [[File:Self-Determination-Theory-Visual 1.png|thumb|Figure 2: Self-Determination Theory visual diagram ]] Discuss self‑determination theory: * what is SDT? - autonomous, motivation vs controlled motivation, akrasia is more likely when motivation is controlled.(reference: Deci, E. L., & Ryan, R. M. (2000). The “What” and “Why” of Goal Pursuits: Human Needs and the Self-Determination of Behavior. ''Psychological Inquiry'', ''11''(4), 227–268. https://doi.org/10.1207/S15327965PLI1104-01) *expectancy‑value theory: actions based an appraisal of successes (reference: Wigfield, A., & Eccles, J. S. (2000). Expectancy–Value Theory of Achievement Motivation. ''Contemporary Educational Psychology'', ''25''(1), 68–81.https://doi.org/10.1006/ceps.1999.1015) * goal‑setting theory: challenging akrasia * Show how motivation quality affects the likelihood of acting in line with long‑term goals. add figure / model where possible == Emotion and akrasia == * Explain * emotional avoidance: tasks that evoke frustration are avoided * anxiety: high anxiety leads to task aversion * affect regulation: choice of immediate mood regulation over long term solutions * Discuss how people often choose short‑term emotional relief over long‑term outcomes. add figure / model == How does this understanding of the psychological science behind akrasia help those experiencing this ( write title to something more formal) == '''Focus question''': what strategies are there to reduce to act of akrasia and act more consciously in line with their goals? * Explain how empirical findings support, challenge, or refine theoretical models * Show how integrated knowledge helps explain akrasia more accurately. * Discuss implications for improving motivational and emotional lives. Present practical, research‑supported strategies for reducing akrasia, such as: * Implementation intentions * Emotion regulation techniques * Reducing cognitive load * Structuring environments to support long‑term goals * Enhancing autonomous motivation Explain why each strategy works and how individuals can apply it. ==Figures== [[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== Interactive learning features help to bring book chapters to life and can be embedded throughout the chapter. {{RoundBoxTop|theme=3}} Your feature box text, scenario, or case study goes here. {{RoundBoxBottom}} ;Scenarios * Scenarios, case studies, or examples describe concepts in action * Can be real or fictional; if real, provide citations * Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Present using [[#Feature boxes|feature boxes]] {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted '''Table 1''' A Descriptive Caption Which Explains The Table Contents and its Relevance to the Text e.g., The 2 x 2 Johari Window Model Showing Knowing x Self/Other {| class="wikitable" style="margin: auto; |- ! !! Known to self !! Not known to self |- | '''Known to others''' || Open area || Blind spot |- | '''Not known to others''' || Hidden area || Unknown |} ;Quizzes * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] Example simple quiz questions. Choose your answers and click "Submit": <quiz display=simple> {The purpose of quizzes is to provide an interactive learning feature: |type="()"} + True - False {Long and complex quiz questions are recommended: |type="()"} - True + False </quiz> ==Conclusion== * summarise the most important points in 3–5 sentences. * Align with subtitle and focus questions. * Highlight implications for personal growth and psychological wellbeing. * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) * [[w:Self determination theory|Self determination theory]] (Wikipedia) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses }} ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]].{{Hanging indent|1= Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091 Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper & Row. }}{{Hanging indent|1= References Bobonich C., & Destrée, P. (2007). Akrasia in Greek Philosophy: From Socrates to Plotinus. BRILL .106, 1-11. https://books.google.com.au/books?id=so097j_jPBsC&dq=akrasia+historical+background&lr=&source=gbs_navlinks_s Bella, A. F. (2023). Psychological underpinnings of akrasia: A new integrative framework based on self-regulation vulnerabilities and failures. New Ideas in Psychology, 70, Article 101027. https://doi.org/10.1016/j.newideapsych.2023.101027) Baumeister, R. F., et al. (1998). Ego depletion: Is the active self a limited resource? Journal of Personality and Social Psychology. DOI: https://doi.org/10.1037/0022-3514.74.5.1252 (doi.org in Bing) Deci, E. L., & Ryan, R. M. (2000). The “What” and “Why” of Goal Pursuits: Human Needs and the Self-Determination of Behavior. Psychological Inquiry, 11(4), 227–268. https://doi.org/10.1207/S15327965PLI1104-01 Inzlicht, M., & Schmeichel, B. J. (2012). What Is Ego Depletion? Toward a Mechanistic Revision of the Resource Model of Self-Control. Perspectives on Psychological Science, 7(5), 450–463. https://doi.org/10.1177/1745691612454134 Wigfield, A., & Eccles, J. S. (2000). Expectancy–Value Theory of Achievement Motivation. Contemporary Educational Psychology, 25(1), 68–81. https://doi.org/10.1006/ceps.1999.1015}} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Self-control]] . il2ime5zr82c93ita25nlwe5gy4ldkk 2823795 2823794 2026-08-21T02:57:43Z U3269672 3105208 /* Learning features */ 2823795 wikitext text/x-wiki {{title|Akrasia:<br>Why do people act against their better judgement?}} __TOC__ ==Overview== {{RoundBoxTop|theme=5}}'''Consider this scenario''' [[File:Canva - Woman Feeling Emotional Stress.jpg|thumb|200px|'''Figure 1.''' A women feeling stressed]] Jordan signed up for a gym membership at the start of the year, determined to improve their physical and mental health. He bought new workout clothes, saved a list of routines and even told his friends he was committed to exercising. But when his alarm went off at 6:30am he hit snooze. Telling himself he will simply go after work instead but by 5:00pm he's to tired to go. The idea of lifting weights is to emotionally heavy and stress inducing for him, so Jordan chooses to stay home and watch a TV show. Each time Jordans alarm goes off and he ignores it, even while knowing going to the gym would be healthier and help him gain confidence, the short term comfort of staying home out ways those feelings. Jordan isn't lazy he his experiencing akrasia, a predictable motivational and emotional conflict between long term goals and short term impulses. {{RoundBoxBottom}} This Chapter will explain and explore why people act against their better judgement described by psychological explanations of self control and regulation, motivational deficits and emotional avoidance. * '''Explanation of the problem:''' akrasia is a problem because it affects many areas of persons life such as academics, health choices, financial decisions and relationships. People often intend to make choices that align with their values and goals, yet often make choices that are the opposite. this gap between intention and action can lead to issues with wellbeing and a sense of success in life ( reference) * introduce psychological importance:( why it matters) Akrasia matters because it undermines goal achievement, wellbeing, and personal growth. It reflects a tension between reflective, value based intensions and impulsive, emotionally driven tendencies. psychological science provides tools for understanding this conflict by examining self regulation, and cognitive biases (reference). * why the understanding of the psychological science can help provide ways to overcome actions of akrasia or the feelings left behind form failed long term goals.( Reference) * Introduce motivation in relation to topic * Introduce emotion in relation to topic Key resources: * [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 02]] explains about how to edit * [[Motivation and emotion/Assessment/Topic|Topic development guidelines]] * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] * {{RoundBoxTop|theme=5}} '''Focus questions''' # What is akrasia? # What psychological processes contribute to akrasia and the conflict between long term and short term impulses? # How do motivation and emotion interact to influence why people act against their better judgement ? # What evidence based strategies can help people reduce akrasia and act more consistently in line with their goals ? {{RoundBoxBottom}} ==Outline for chapter == Use this heading structure: * [[#Overview|Overview]] * 3 to 6 major headings tailored to the topic; can have sub-headings, but: ** avoid having only one sub-heading ** provide an introductory paragraph before breaking into sub-sections * [[#Conclusion|Conclusion]] * See also * References * External links == Akrasia == * General definition/introduction: acting against ones better judgement ect... "i know i shouldn't do this but" * Historical background: originates from ancient Greek philosophy. particularly Aristotle, who used the term akrasia to describe " weakness of will" ect.. Describe what he argued about failure to understand emotions and impulses.( reference (needs editing): Bobonich C., &  Destrée, P. (2007). Akrasia in Greek Philosophy: From Socrates to Plotinus. BRILL .106, 1-11. https://books.google.com.au/books?id=so097j_jPBsC&dq=akrasia+historical+background&lr=&source=gbs_navlinks_s) * Describe what the history laid a foundation for in modern explanations == Akrasia as a motivational and emotional conflict == '''Focus question''': what psychological processes contribute to akrasia and the conflict between long term and short term impulses? '''Overview/introduction to argument'''; Explain how akrasia arises from competing internal processes. Discuss the tension between long‑term goals and short‑term impulses. Introduce the idea that akrasia is not simply “laziness” but a predictable psychological phenomenon. describe long term and short term impulses/ goals are: ( I want to finish my degree vs I want to just relax right now) * immediate emotional or motivational states vs reflective value-based reasoning. * prioritisation of short term effective rewards even when they consciously prefer long term outcomes. this is especially true when tasks evoke discomfort. (reference) === Modelling the conceptual relationship === * Provide a model- if there is one '''Evidence of facilitative relationship''' == Self‑regulation and self‑control == Explain all in relation to behaviours of akrasia * failures in self‑regulation contribute to akrasia: Conflict of internal systems (Reference/ Edit: Bella, A. F. (2023). Psychological underpinnings of akrasia: A new integrative framework based on self-regulation vulnerabilities and failures. ''New Ideas in Psychology'', ''70'', Article 101027. https://doi.org/10.1016/j.newideapsych.2023.101027) * Discuss ego depletion: self control is a limited resource. ego depletion is the action of drawing on self control and will power from a limited source. (Reference: Baumeister, R. F., Bratslavsky, E., Muraven, M., & Tice, D. M. (1998). Ego Depletion: Is the Active Self a Limited Resource? ''Journal of Personality and Social Psychology'', ''74''(5), 1252–1265. https://doi.org/10.1037/0022-3514.74.5.12520. Inzlicht, M., & Schmeichel, B. J. (2012). What Is Ego Depletion? Toward a Mechanistic Revision of the Resource Model of Self-Control. ''Perspectives on Psychological Science'', ''7''(5), 450–463.)https://doi.org/10.1177/1745691612454134) * <u>(temporal discounting: disproportionate assessment of rewards and punishment)</u> potential topic unsure * implementation intentions. if - then * Provide examples of how these processes play out in everyday life. add figure / model == Motivational theories == * Explain how motivational deficits or conflicts lead to akrasia. [[File:Self-Determination-Theory-Visual 1.png|thumb|Figure 2: Self-Determination Theory visual diagram ]] Discuss self‑determination theory: * what is SDT? - autonomous, motivation vs controlled motivation, akrasia is more likely when motivation is controlled.(reference: Deci, E. L., & Ryan, R. M. (2000). The “What” and “Why” of Goal Pursuits: Human Needs and the Self-Determination of Behavior. ''Psychological Inquiry'', ''11''(4), 227–268. https://doi.org/10.1207/S15327965PLI1104-01) *expectancy‑value theory: actions based an appraisal of successes (reference: Wigfield, A., & Eccles, J. S. (2000). Expectancy–Value Theory of Achievement Motivation. ''Contemporary Educational Psychology'', ''25''(1), 68–81.https://doi.org/10.1006/ceps.1999.1015) * goal‑setting theory: challenging akrasia * Show how motivation quality affects the likelihood of acting in line with long‑term goals. add figure / model where possible == Emotion and akrasia == * Explain * emotional avoidance: tasks that evoke frustration are avoided * anxiety: high anxiety leads to task aversion * affect regulation: choice of immediate mood regulation over long term solutions * Discuss how people often choose short‑term emotional relief over long‑term outcomes. add figure / model == How does this understanding of the psychological science behind akrasia help those experiencing this ( write title to something more formal) == '''Focus question''': what strategies are there to reduce to act of akrasia and act more consciously in line with their goals? * Explain how empirical findings support, challenge, or refine theoretical models * Show how integrated knowledge helps explain akrasia more accurately. * Discuss implications for improving motivational and emotional lives. Present practical, research‑supported strategies for reducing akrasia, such as: * Implementation intentions * Emotion regulation techniques * Reducing cognitive load * Structuring environments to support long‑term goals * Enhancing autonomous motivation Explain why each strategy works and how individuals can apply it. ==Figures== [[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== {{RoundBoxTop|theme=5}} ADD scenario that follows up on jordans problem with a solutions based on principles discussed {{RoundBoxBottom}} ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted '''Table 1''' A Descriptive Caption Which Explains The Table Contents and its Relevance to the Text e.g., The 2 x 2 Johari Window Model Showing Knowing x Self/Other {| class="wikitable" style="margin: auto; |- ! !! Known to self !! Not known to self |- | '''Known to others''' || Open area || Blind spot |- | '''Not known to others''' || Hidden area || Unknown |} ;Quizzes * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] Example simple quiz questions. Choose your answers and click "Submit": <quiz display=simple> {The purpose of quizzes is to provide an interactive learning feature: |type="()"} + True - False {Long and complex quiz questions are recommended: |type="()"} - True + False </quiz> ==Conclusion== * summarise the most important points in 3–5 sentences. * Align with subtitle and focus questions. * Highlight implications for personal growth and psychological wellbeing. * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) * [[w:Self determination theory|Self determination theory]] (Wikipedia) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses }} ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]].{{Hanging indent|1= Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091 Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper & Row. }}{{Hanging indent|1= References Bobonich C., & Destrée, P. (2007). Akrasia in Greek Philosophy: From Socrates to Plotinus. BRILL .106, 1-11. https://books.google.com.au/books?id=so097j_jPBsC&dq=akrasia+historical+background&lr=&source=gbs_navlinks_s Bella, A. F. (2023). Psychological underpinnings of akrasia: A new integrative framework based on self-regulation vulnerabilities and failures. New Ideas in Psychology, 70, Article 101027. https://doi.org/10.1016/j.newideapsych.2023.101027) Baumeister, R. F., et al. (1998). Ego depletion: Is the active self a limited resource? Journal of Personality and Social Psychology. DOI: https://doi.org/10.1037/0022-3514.74.5.1252 (doi.org in Bing) Deci, E. L., & Ryan, R. M. (2000). The “What” and “Why” of Goal Pursuits: Human Needs and the Self-Determination of Behavior. Psychological Inquiry, 11(4), 227–268. https://doi.org/10.1207/S15327965PLI1104-01 Inzlicht, M., & Schmeichel, B. J. (2012). What Is Ego Depletion? Toward a Mechanistic Revision of the Resource Model of Self-Control. Perspectives on Psychological Science, 7(5), 450–463. https://doi.org/10.1177/1745691612454134 Wigfield, A., & Eccles, J. S. (2000). Expectancy–Value Theory of Achievement Motivation. Contemporary Educational Psychology, 25(1), 68–81. https://doi.org/10.1006/ceps.1999.1015}} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Self-control]] . dnzwt0xfn29us1yu8uzkqsh3e2ycqi2 2823821 2823795 2026-08-21T04:38:20Z Jtneill 10242 /* External links */ 2823821 wikitext text/x-wiki {{title|Akrasia:<br>Why do people act against their better judgement?}} __TOC__ ==Overview== {{RoundBoxTop|theme=5}}'''Consider this scenario''' [[File:Canva - Woman Feeling Emotional Stress.jpg|thumb|200px|'''Figure 1.''' A women feeling stressed]] Jordan signed up for a gym membership at the start of the year, determined to improve their physical and mental health. He bought new workout clothes, saved a list of routines and even told his friends he was committed to exercising. But when his alarm went off at 6:30am he hit snooze. Telling himself he will simply go after work instead but by 5:00pm he's to tired to go. The idea of lifting weights is to emotionally heavy and stress inducing for him, so Jordan chooses to stay home and watch a TV show. Each time Jordans alarm goes off and he ignores it, even while knowing going to the gym would be healthier and help him gain confidence, the short term comfort of staying home out ways those feelings. Jordan isn't lazy he his experiencing akrasia, a predictable motivational and emotional conflict between long term goals and short term impulses. {{RoundBoxBottom}} This Chapter will explain and explore why people act against their better judgement described by psychological explanations of self control and regulation, motivational deficits and emotional avoidance. * '''Explanation of the problem:''' akrasia is a problem because it affects many areas of persons life such as academics, health choices, financial decisions and relationships. People often intend to make choices that align with their values and goals, yet often make choices that are the opposite. this gap between intention and action can lead to issues with wellbeing and a sense of success in life ( reference) * introduce psychological importance:( why it matters) Akrasia matters because it undermines goal achievement, wellbeing, and personal growth. It reflects a tension between reflective, value based intensions and impulsive, emotionally driven tendencies. psychological science provides tools for understanding this conflict by examining self regulation, and cognitive biases (reference). * why the understanding of the psychological science can help provide ways to overcome actions of akrasia or the feelings left behind form failed long term goals.( Reference) * Introduce motivation in relation to topic * Introduce emotion in relation to topic Key resources: * [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 02]] explains about how to edit * [[Motivation and emotion/Assessment/Topic|Topic development guidelines]] * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] * {{RoundBoxTop|theme=5}} '''Focus questions''' # What is akrasia? # What psychological processes contribute to akrasia and the conflict between long term and short term impulses? # How do motivation and emotion interact to influence why people act against their better judgement ? # What evidence based strategies can help people reduce akrasia and act more consistently in line with their goals ? {{RoundBoxBottom}} ==Outline for chapter == Use this heading structure: * [[#Overview|Overview]] * 3 to 6 major headings tailored to the topic; can have sub-headings, but: ** avoid having only one sub-heading ** provide an introductory paragraph before breaking into sub-sections * [[#Conclusion|Conclusion]] * See also * References * External links == Akrasia == * General definition/introduction: acting against ones better judgement ect... "i know i shouldn't do this but" * Historical background: originates from ancient Greek philosophy. particularly Aristotle, who used the term akrasia to describe " weakness of will" ect.. Describe what he argued about failure to understand emotions and impulses.( reference (needs editing): Bobonich C., &  Destrée, P. (2007). Akrasia in Greek Philosophy: From Socrates to Plotinus. BRILL .106, 1-11. https://books.google.com.au/books?id=so097j_jPBsC&dq=akrasia+historical+background&lr=&source=gbs_navlinks_s) * Describe what the history laid a foundation for in modern explanations == Akrasia as a motivational and emotional conflict == '''Focus question''': what psychological processes contribute to akrasia and the conflict between long term and short term impulses? '''Overview/introduction to argument'''; Explain how akrasia arises from competing internal processes. Discuss the tension between long‑term goals and short‑term impulses. Introduce the idea that akrasia is not simply “laziness” but a predictable psychological phenomenon. describe long term and short term impulses/ goals are: ( I want to finish my degree vs I want to just relax right now) * immediate emotional or motivational states vs reflective value-based reasoning. * prioritisation of short term effective rewards even when they consciously prefer long term outcomes. this is especially true when tasks evoke discomfort. (reference) === Modelling the conceptual relationship === * Provide a model- if there is one '''Evidence of facilitative relationship''' == Self‑regulation and self‑control == Explain all in relation to behaviours of akrasia * failures in self‑regulation contribute to akrasia: Conflict of internal systems (Reference/ Edit: Bella, A. F. (2023). Psychological underpinnings of akrasia: A new integrative framework based on self-regulation vulnerabilities and failures. ''New Ideas in Psychology'', ''70'', Article 101027. https://doi.org/10.1016/j.newideapsych.2023.101027) * Discuss ego depletion: self control is a limited resource. ego depletion is the action of drawing on self control and will power from a limited source. (Reference: Baumeister, R. F., Bratslavsky, E., Muraven, M., & Tice, D. M. (1998). Ego Depletion: Is the Active Self a Limited Resource? ''Journal of Personality and Social Psychology'', ''74''(5), 1252–1265. https://doi.org/10.1037/0022-3514.74.5.12520. Inzlicht, M., & Schmeichel, B. J. (2012). What Is Ego Depletion? Toward a Mechanistic Revision of the Resource Model of Self-Control. ''Perspectives on Psychological Science'', ''7''(5), 450–463.)https://doi.org/10.1177/1745691612454134) * <u>(temporal discounting: disproportionate assessment of rewards and punishment)</u> potential topic unsure * implementation intentions. if - then * Provide examples of how these processes play out in everyday life. add figure / model == Motivational theories == * Explain how motivational deficits or conflicts lead to akrasia. [[File:Self-Determination-Theory-Visual 1.png|thumb|Figure 2: Self-Determination Theory visual diagram ]] Discuss self‑determination theory: * what is SDT? - autonomous, motivation vs controlled motivation, akrasia is more likely when motivation is controlled.(reference: Deci, E. L., & Ryan, R. M. (2000). The “What” and “Why” of Goal Pursuits: Human Needs and the Self-Determination of Behavior. ''Psychological Inquiry'', ''11''(4), 227–268. https://doi.org/10.1207/S15327965PLI1104-01) *expectancy‑value theory: actions based an appraisal of successes (reference: Wigfield, A., & Eccles, J. S. (2000). Expectancy–Value Theory of Achievement Motivation. ''Contemporary Educational Psychology'', ''25''(1), 68–81.https://doi.org/10.1006/ceps.1999.1015) * goal‑setting theory: challenging akrasia * Show how motivation quality affects the likelihood of acting in line with long‑term goals. add figure / model where possible == Emotion and akrasia == * Explain * emotional avoidance: tasks that evoke frustration are avoided * anxiety: high anxiety leads to task aversion * affect regulation: choice of immediate mood regulation over long term solutions * Discuss how people often choose short‑term emotional relief over long‑term outcomes. add figure / model == How does this understanding of the psychological science behind akrasia help those experiencing this ( write title to something more formal) == '''Focus question''': what strategies are there to reduce to act of akrasia and act more consciously in line with their goals? * Explain how empirical findings support, challenge, or refine theoretical models * Show how integrated knowledge helps explain akrasia more accurately. * Discuss implications for improving motivational and emotional lives. Present practical, research‑supported strategies for reducing akrasia, such as: * Implementation intentions * Emotion regulation techniques * Reducing cognitive load * Structuring environments to support long‑term goals * Enhancing autonomous motivation Explain why each strategy works and how individuals can apply it. ==Figures== [[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== {{RoundBoxTop|theme=5}} ADD scenario that follows up on jordans problem with a solutions based on principles discussed {{RoundBoxBottom}} ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted '''Table 1''' A Descriptive Caption Which Explains The Table Contents and its Relevance to the Text e.g., The 2 x 2 Johari Window Model Showing Knowing x Self/Other {| class="wikitable" style="margin: auto; |- ! !! Known to self !! Not known to self |- | '''Known to others''' || Open area || Blind spot |- | '''Not known to others''' || Hidden area || Unknown |} ;Quizzes * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] Example simple quiz questions. Choose your answers and click "Submit": <quiz display=simple> {The purpose of quizzes is to provide an interactive learning feature: |type="()"} + True - False {Long and complex quiz questions are recommended: |type="()"} - True + False </quiz> ==Conclusion== * summarise the most important points in 3–5 sentences. * Align with subtitle and focus questions. * Highlight implications for personal growth and psychological wellbeing. * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) * [[w:Self determination theory|Self determination theory]] (Wikipedia) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses }} ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]].{{Hanging indent|1= Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091 Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper & Row. }}{{Hanging indent|1= References Bobonich C., & Destrée, P. (2007). Akrasia in Greek Philosophy: From Socrates to Plotinus. BRILL .106, 1-11. https://books.google.com.au/books?id=so097j_jPBsC&dq=akrasia+historical+background&lr=&source=gbs_navlinks_s Bella, A. F. (2023). Psychological underpinnings of akrasia: A new integrative framework based on self-regulation vulnerabilities and failures. New Ideas in Psychology, 70, Article 101027. https://doi.org/10.1016/j.newideapsych.2023.101027) Baumeister, R. F., et al. (1998). Ego depletion: Is the active self a limited resource? Journal of Personality and Social Psychology. DOI: https://doi.org/10.1037/0022-3514.74.5.1252 (doi.org in Bing) Deci, E. L., & Ryan, R. M. (2000). The “What” and “Why” of Goal Pursuits: Human Needs and the Self-Determination of Behavior. Psychological Inquiry, 11(4), 227–268. https://doi.org/10.1207/S15327965PLI1104-01 Inzlicht, M., & Schmeichel, B. J. (2012). What Is Ego Depletion? Toward a Mechanistic Revision of the Resource Model of Self-Control. Perspectives on Psychological Science, 7(5), 450–463. https://doi.org/10.1177/1745691612454134 Wigfield, A., & Eccles, J. S. (2000). Expectancy–Value Theory of Achievement Motivation. Contemporary Educational Psychology, 25(1), 68–81. https://doi.org/10.1006/ceps.1999.1015}} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Self-control]] qw59isu8bdzwtyqr7fk114mchdb5jc2 828 331015 2823758 2823229 2026-08-20T23:59:25Z Helpme2222 3106525 2823758 Scribunto text/plain -- My function for teaching grammar local p = {}; local frame = mw.getCurrentFrame() local grammatical_moods = { "Jelen ido", "Mult ido", "Felszolito mod", "Felteteles mod" } local balls = { grammatical_moods } function p.title() local grammatical_cases = { ablative = 1, inessive = { ANCOVA = "ANCOVA" } } local cases2 = "ba" local cases3 = "ba" -- if grammatical_cases.inessive[frame:getParent():getTitle()] then cases2 = "true" else cases2 = "false" end -- if "ANCOVA" == frame:getParent():getTitle() then cases3 = "true" else cases3 = "false" end local detected = false detected = detected or true return mw.title.getCurrentTitle() end function p.ifexist() return tonumber(frame:expandTemplate{ title = "User:Helpme2222/Sandbox", args = {frame.args[1]} }) end function p.performance() for i = 1,1000000000 do local tense = "jelen" end return end function p.performance1() local var = "" for i = 1,100000000 do if var[1] then end end return end function p.performance2() local var = "" for i = 1,100000000 do if type(var) == "table" then end end return end function p.tableMake() local loady = require("Module:Sandbox/22/") local var = { keyword = {loady.tableBake()}, kljuczslovo = {loady.tableBake()}, yaoshiwenzi = {loady.tableBake()}, llavepalabra = {loady.tableBake()}, } return var end function p.expand() return frame:expandTemplate{ title = "User:Helpme2222/Sandbox" } end function p.title3() return mw.title.getCurrentTitle().fullText end function p.title2() local grammatical_cases = { ablative = 1, inessive = { ANCOVA = "ANCOVA", ["Module:Sandbox/22"] = "Module:Sandbox/22" } } local concepts = { grammatical_cases, } local PAGENAME = tostring(mw.title.getCurrentTitle()) local detected = false local out = {} local debugger = {} for i, group in ipairs(concepts) do if group.inessive[PAGENAME] then table.insert(debugger,"Okay, managed TRUE on "..i..":"..group.ablative) detected = detected or true local formattedGroup = {} for memberKey, memberRendervalue in pairs(group.inessive) do table.insert(formattedGroup, "<li>" .. memberRendervalue .. "</li>") end table.insert(out, "<h3>" .. group.ablative .. "</h3><ul>" .. table.concat( formattedGroup ) .. "</ul>" ) table.insert(out, "this sucks ass") return "this sucks ass" else table.insert(debugger,"Managed FALSE on "..i..":"..group.ablative..". Comparator: "..PAGENAME..", ") end end return debugger --[[ if detected then return tostring(detected) .. table.concat(out) end return --]] end function p.sanitizeChar(capture) -- If the set of likely illegal characters to appear in title expands, a rewrite of this as a table is merited if capture == "?" then return "" elseif capture == "#" then return "No. " end end function p.sanitizeTitle() local title = frame.args[1] return mw.ustring.gsub( title, "(?:\\?|\\#)", p.sanitizeChar) end function p.sanitizeTitletest2() return mw.ustring.gsub( "Ki vagy? (🌡️🌾⭐🗡️ VS 🪐 🪨 💣 🧿)", "(?:\\?|\\#)", p.sanitizeChar()) end function p.safetyTest() if string.len(frame.args[1]) < 500 then return frame.args[1] else return "" end end --[[ function array_iter(t) local i = 0 return function () i = i + 1 return t[i] end end --]] function p.listInline() --[[ This function is a godsend! https://www.mediawiki.org/wiki/Extension:Scribunto/Lua_reference_manual#mw.text.listToText --]] local spritedTable = {} for i,entry in ipairs(balls[tonumber(frame.args[1])]) do spritedTable[i] = "{{Sprite|named=1|linked=1|"..entry.."}}" end return mw.text.listToText( spritedTable , ", ", ", and " ) end function p.listNavbox() -- https://www.mediawiki.org/wiki/Extension:Scribunto/Lua_reference_manual#table.concat local spritedTable = {} for i,entry in ipairs(balls[tonumber(frame.args[1])]) do spritedTable[i] = "{{Sprite|named=1|linked=1|"..entry.."}}" end return table.concat( spritedTable , " • ") end function p.listCount() return table.maxn(balls[tonumber(frame.args[1])]) end -- https://www.mediawiki.org/wiki/Extension:Scribunto/Lua_reference_manual#table.maxn function p.tableTest() return balls[1][1] end function p.todaysBall() --[[ https://www.lua.org/pil/3.6.html The use of explicit indexing here is not strictly semantic; it's just to emphasize the rotation order. ]] local unixDay = math.floor(os.time()/86400) local ballTotalCount = 0 local ballCounts = {} for whichTable,subtable in ipairs(balls) do ballCounts[whichTable] = #subtable ballTotalCount = ballTotalCount + ballCounts[whichTable] end local cycleDayIndex, cycleStartingBall = unixDay % ballTotalCount, math.floor(unixDay/ballTotalCount) % ballTotalCount local cycleTodaysBall if ballTotalCount % 7 ~= 0 then cycleTodaysBall = (cycleStartingBall + cycleDayIndex*7) % ballTotalCount elseif ballTotalCount % 11 ~= 0 then cycleTodaysBall = (cycleStartingBall + cycleDayIndex*11) % ballTotalCount elseif ballTotalCount % 13 ~= 0 then cycleTodaysBall = (cycleStartingBall + cycleDayIndex*13) % ballTotalCount else cycleTodaysBall = (cycleStartingBall + cycleDayIndex*(ballTotalCount - 1)) % ballTotalCount end --[[ debug return cycleTodaysBall .. " " .. ballTotalCount .. " " .. os.time() .. " " .. math.floor(os.time()/86400) .. " " .. cycleDayIndex .. " " .. cycleStartingBall ]] for whichTable = 1, #balls do if ballCounts[whichTable] > cycleTodaysBall then return balls[whichTable][cycleTodaysBall + 1] else cycleTodaysBall = cycleTodaysBall - ballCounts[whichTable] end end --]] end return p; joabqpk48fq5aj8p0vizp0s8lmc86oe 2823759 2823758 2026-08-21T00:00:54Z Helpme2222 3106525 2823759 Scribunto text/plain -- My function for teaching grammar local p = {}; local frame = mw.getCurrentFrame() local grammatical_moods = { "Jelen ido", "Mult ido", "Felszolito mod", "Felteteles mod" } local balls = { grammatical_moods } function p.title() local grammatical_cases = { ablative = 1, inessive = { ANCOVA = "ANCOVA" } } local cases2 = "ba" local cases3 = "ba" -- if grammatical_cases.inessive[frame:getParent():getTitle()] then cases2 = "true" else cases2 = "false" end -- if "ANCOVA" == frame:getParent():getTitle() then cases3 = "true" else cases3 = "false" end local detected = false detected = detected or true return mw.title.getCurrentTitle() end function p.ifexist() return tonumber(frame:expandTemplate{ title = "User:Helpme2222/Sandbox", args = {frame.args[1]} }) end function p.performance() for i = 1,1000000000 do p.tableMake() end return end function p.performance1() local var = "" for i = 1,100000000 do if var[1] then end end return end function p.performance2() local var = "" for i = 1,100000000 do if type(var) == "table" then end end return end function p.tableMake() local loady = require("Module:Sandbox/22/") local var = { keyword = {loady.tableBake()}, kljuczslovo = {loady.tableBake()}, yaoshiwenzi = {loady.tableBake()}, llavepalabra = {loady.tableBake()}, } return var end function p.expand() return frame:expandTemplate{ title = "User:Helpme2222/Sandbox" } end function p.title3() return mw.title.getCurrentTitle().fullText end function p.title2() local grammatical_cases = { ablative = 1, inessive = { ANCOVA = "ANCOVA", ["Module:Sandbox/22"] = "Module:Sandbox/22" } } local concepts = { grammatical_cases, } local PAGENAME = tostring(mw.title.getCurrentTitle()) local detected = false local out = {} local debugger = {} for i, group in ipairs(concepts) do if group.inessive[PAGENAME] then table.insert(debugger,"Okay, managed TRUE on "..i..":"..group.ablative) detected = detected or true local formattedGroup = {} for memberKey, memberRendervalue in pairs(group.inessive) do table.insert(formattedGroup, "<li>" .. memberRendervalue .. "</li>") end table.insert(out, "<h3>" .. group.ablative .. "</h3><ul>" .. table.concat( formattedGroup ) .. "</ul>" ) table.insert(out, "this sucks ass") return "this sucks ass" else table.insert(debugger,"Managed FALSE on "..i..":"..group.ablative..". Comparator: "..PAGENAME..", ") end end return debugger --[[ if detected then return tostring(detected) .. table.concat(out) end return --]] end function p.sanitizeChar(capture) -- If the set of likely illegal characters to appear in title expands, a rewrite of this as a table is merited if capture == "?" then return "" elseif capture == "#" then return "No. " end end function p.sanitizeTitle() local title = frame.args[1] return mw.ustring.gsub( title, "(?:\\?|\\#)", p.sanitizeChar) end function p.sanitizeTitletest2() return mw.ustring.gsub( "Ki vagy? (🌡️🌾⭐🗡️ VS 🪐 🪨 💣 🧿)", "(?:\\?|\\#)", p.sanitizeChar()) end function p.safetyTest() if string.len(frame.args[1]) < 500 then return frame.args[1] else return "" end end --[[ function array_iter(t) local i = 0 return function () i = i + 1 return t[i] end end --]] function p.listInline() --[[ This function is a godsend! https://www.mediawiki.org/wiki/Extension:Scribunto/Lua_reference_manual#mw.text.listToText --]] local spritedTable = {} for i,entry in ipairs(balls[tonumber(frame.args[1])]) do spritedTable[i] = "{{Sprite|named=1|linked=1|"..entry.."}}" end return mw.text.listToText( spritedTable , ", ", ", and " ) end function p.listNavbox() -- https://www.mediawiki.org/wiki/Extension:Scribunto/Lua_reference_manual#table.concat local spritedTable = {} for i,entry in ipairs(balls[tonumber(frame.args[1])]) do spritedTable[i] = "{{Sprite|named=1|linked=1|"..entry.."}}" end return table.concat( spritedTable , " • ") end function p.listCount() return table.maxn(balls[tonumber(frame.args[1])]) end -- https://www.mediawiki.org/wiki/Extension:Scribunto/Lua_reference_manual#table.maxn function p.tableTest() return balls[1][1] end function p.todaysBall() --[[ https://www.lua.org/pil/3.6.html The use of explicit indexing here is not strictly semantic; it's just to emphasize the rotation order. ]] local unixDay = math.floor(os.time()/86400) local ballTotalCount = 0 local ballCounts = {} for whichTable,subtable in ipairs(balls) do ballCounts[whichTable] = #subtable ballTotalCount = ballTotalCount + ballCounts[whichTable] end local cycleDayIndex, cycleStartingBall = unixDay % ballTotalCount, math.floor(unixDay/ballTotalCount) % ballTotalCount local cycleTodaysBall if ballTotalCount % 7 ~= 0 then cycleTodaysBall = (cycleStartingBall + cycleDayIndex*7) % ballTotalCount elseif ballTotalCount % 11 ~= 0 then cycleTodaysBall = (cycleStartingBall + cycleDayIndex*11) % ballTotalCount elseif ballTotalCount % 13 ~= 0 then cycleTodaysBall = (cycleStartingBall + cycleDayIndex*13) % ballTotalCount else cycleTodaysBall = (cycleStartingBall + cycleDayIndex*(ballTotalCount - 1)) % ballTotalCount end --[[ debug return cycleTodaysBall .. " " .. ballTotalCount .. " " .. os.time() .. " " .. math.floor(os.time()/86400) .. " " .. cycleDayIndex .. " " .. cycleStartingBall ]] for whichTable = 1, #balls do if ballCounts[whichTable] > cycleTodaysBall then return balls[whichTable][cycleTodaysBall + 1] else cycleTodaysBall = cycleTodaysBall - ballCounts[whichTable] end end --]] end return p; kq9ab6bmljp458e46lzonn6qves6wqr 2823760 2823759 2026-08-21T00:01:50Z Helpme2222 3106525 2823760 Scribunto text/plain -- My function for teaching grammar local p = {}; local frame = mw.getCurrentFrame() local grammatical_moods = { "Jelen ido", "Mult ido", "Felszolito mod", "Felteteles mod" } local balls = { grammatical_moods } function p.title() local grammatical_cases = { ablative = 1, inessive = { ANCOVA = "ANCOVA" } } local cases2 = "ba" local cases3 = "ba" -- if grammatical_cases.inessive[frame:getParent():getTitle()] then cases2 = "true" else cases2 = "false" end -- if "ANCOVA" == frame:getParent():getTitle() then cases3 = "true" else cases3 = "false" end local detected = false detected = detected or true return mw.title.getCurrentTitle() end function p.ifexist() return tonumber(frame:expandTemplate{ title = "User:Helpme2222/Sandbox", args = {frame.args[1]} }) end function p.performance() for i = 1,100000000 do p.tableMake() end return end function p.performance1() local var = "" for i = 1,100000000 do if var[1] then end end return end function p.performance2() local var = "" for i = 1,100000000 do if type(var) == "table" then end end return end function p.tableMake() local loady = require("Module:Sandbox/22/") local var = { keyword = {loady.tableBake()}, kljuczslovo = {loady.tableBake()}, yaoshiwenzi = {loady.tableBake()}, llavepalabra = {loady.tableBake()}, } return var end function p.expand() return frame:expandTemplate{ title = "User:Helpme2222/Sandbox" } end function p.title3() return mw.title.getCurrentTitle().fullText end function p.title2() local grammatical_cases = { ablative = 1, inessive = { ANCOVA = "ANCOVA", ["Module:Sandbox/22"] = "Module:Sandbox/22" } } local concepts = { grammatical_cases, } local PAGENAME = tostring(mw.title.getCurrentTitle()) local detected = false local out = {} local debugger = {} for i, group in ipairs(concepts) do if group.inessive[PAGENAME] then table.insert(debugger,"Okay, managed TRUE on "..i..":"..group.ablative) detected = detected or true local formattedGroup = {} for memberKey, memberRendervalue in pairs(group.inessive) do table.insert(formattedGroup, "<li>" .. memberRendervalue .. "</li>") end table.insert(out, "<h3>" .. group.ablative .. "</h3><ul>" .. table.concat( formattedGroup ) .. "</ul>" ) table.insert(out, "this sucks ass") return "this sucks ass" else table.insert(debugger,"Managed FALSE on "..i..":"..group.ablative..". Comparator: "..PAGENAME..", ") end end return debugger --[[ if detected then return tostring(detected) .. table.concat(out) end return --]] end function p.sanitizeChar(capture) -- If the set of likely illegal characters to appear in title expands, a rewrite of this as a table is merited if capture == "?" then return "" elseif capture == "#" then return "No. " end end function p.sanitizeTitle() local title = frame.args[1] return mw.ustring.gsub( title, "(?:\\?|\\#)", p.sanitizeChar) end function p.sanitizeTitletest2() return mw.ustring.gsub( "Ki vagy? (🌡️🌾⭐🗡️ VS 🪐 🪨 💣 🧿)", "(?:\\?|\\#)", p.sanitizeChar()) end function p.safetyTest() if string.len(frame.args[1]) < 500 then return frame.args[1] else return "" end end --[[ function array_iter(t) local i = 0 return function () i = i + 1 return t[i] end end --]] function p.listInline() --[[ This function is a godsend! https://www.mediawiki.org/wiki/Extension:Scribunto/Lua_reference_manual#mw.text.listToText --]] local spritedTable = {} for i,entry in ipairs(balls[tonumber(frame.args[1])]) do spritedTable[i] = "{{Sprite|named=1|linked=1|"..entry.."}}" end return mw.text.listToText( spritedTable , ", ", ", and " ) end function p.listNavbox() -- https://www.mediawiki.org/wiki/Extension:Scribunto/Lua_reference_manual#table.concat local spritedTable = {} for i,entry in ipairs(balls[tonumber(frame.args[1])]) do spritedTable[i] = "{{Sprite|named=1|linked=1|"..entry.."}}" end return table.concat( spritedTable , " • ") end function p.listCount() return table.maxn(balls[tonumber(frame.args[1])]) end -- https://www.mediawiki.org/wiki/Extension:Scribunto/Lua_reference_manual#table.maxn function p.tableTest() return balls[1][1] end function p.todaysBall() --[[ https://www.lua.org/pil/3.6.html The use of explicit indexing here is not strictly semantic; it's just to emphasize the rotation order. ]] local unixDay = math.floor(os.time()/86400) local ballTotalCount = 0 local ballCounts = {} for whichTable,subtable in ipairs(balls) do ballCounts[whichTable] = #subtable ballTotalCount = ballTotalCount + ballCounts[whichTable] end local cycleDayIndex, cycleStartingBall = unixDay % ballTotalCount, math.floor(unixDay/ballTotalCount) % ballTotalCount local cycleTodaysBall if ballTotalCount % 7 ~= 0 then cycleTodaysBall = (cycleStartingBall + cycleDayIndex*7) % ballTotalCount elseif ballTotalCount % 11 ~= 0 then cycleTodaysBall = (cycleStartingBall + cycleDayIndex*11) % ballTotalCount elseif ballTotalCount % 13 ~= 0 then cycleTodaysBall = (cycleStartingBall + cycleDayIndex*13) % ballTotalCount else cycleTodaysBall = (cycleStartingBall + cycleDayIndex*(ballTotalCount - 1)) % ballTotalCount end --[[ debug return cycleTodaysBall .. " " .. ballTotalCount .. " " .. os.time() .. " " .. math.floor(os.time()/86400) .. " " .. cycleDayIndex .. " " .. cycleStartingBall ]] for whichTable = 1, #balls do if ballCounts[whichTable] > cycleTodaysBall then return balls[whichTable][cycleTodaysBall + 1] else cycleTodaysBall = cycleTodaysBall - ballCounts[whichTable] end end --]] end return p; 2xp23w0c41pzti2gpr51goix4tn662j 2823761 2823760 2026-08-21T00:02:19Z Helpme2222 3106525 2823761 Scribunto text/plain -- My function for teaching grammar local p = {}; local frame = mw.getCurrentFrame() local grammatical_moods = { "Jelen ido", "Mult ido", "Felszolito mod", "Felteteles mod" } local balls = { grammatical_moods } function p.title() local grammatical_cases = { ablative = 1, inessive = { ANCOVA = "ANCOVA" } } local cases2 = "ba" local cases3 = "ba" -- if grammatical_cases.inessive[frame:getParent():getTitle()] then cases2 = "true" else cases2 = "false" end -- if "ANCOVA" == frame:getParent():getTitle() then cases3 = "true" else cases3 = "false" end local detected = false detected = detected or true return mw.title.getCurrentTitle() end function p.ifexist() return tonumber(frame:expandTemplate{ title = "User:Helpme2222/Sandbox", args = {frame.args[1]} }) end function p.performance() for i = 1,10000000 do p.tableMake() end return end function p.performance1() local var = "" for i = 1,100000000 do if var[1] then end end return end function p.performance2() local var = "" for i = 1,100000000 do if type(var) == "table" then end end return end function p.tableMake() local loady = require("Module:Sandbox/22/") local var = { keyword = {loady.tableBake()}, kljuczslovo = {loady.tableBake()}, yaoshiwenzi = {loady.tableBake()}, llavepalabra = {loady.tableBake()}, } return var end function p.expand() return frame:expandTemplate{ title = "User:Helpme2222/Sandbox" } end function p.title3() return mw.title.getCurrentTitle().fullText end function p.title2() local grammatical_cases = { ablative = 1, inessive = { ANCOVA = "ANCOVA", ["Module:Sandbox/22"] = "Module:Sandbox/22" } } local concepts = { grammatical_cases, } local PAGENAME = tostring(mw.title.getCurrentTitle()) local detected = false local out = {} local debugger = {} for i, group in ipairs(concepts) do if group.inessive[PAGENAME] then table.insert(debugger,"Okay, managed TRUE on "..i..":"..group.ablative) detected = detected or true local formattedGroup = {} for memberKey, memberRendervalue in pairs(group.inessive) do table.insert(formattedGroup, "<li>" .. memberRendervalue .. "</li>") end table.insert(out, "<h3>" .. group.ablative .. "</h3><ul>" .. table.concat( formattedGroup ) .. "</ul>" ) table.insert(out, "this sucks ass") return "this sucks ass" else table.insert(debugger,"Managed FALSE on "..i..":"..group.ablative..". Comparator: "..PAGENAME..", ") end end return debugger --[[ if detected then return tostring(detected) .. table.concat(out) end return --]] end function p.sanitizeChar(capture) -- If the set of likely illegal characters to appear in title expands, a rewrite of this as a table is merited if capture == "?" then return "" elseif capture == "#" then return "No. " end end function p.sanitizeTitle() local title = frame.args[1] return mw.ustring.gsub( title, "(?:\\?|\\#)", p.sanitizeChar) end function p.sanitizeTitletest2() return mw.ustring.gsub( "Ki vagy? (🌡️🌾⭐🗡️ VS 🪐 🪨 💣 🧿)", "(?:\\?|\\#)", p.sanitizeChar()) end function p.safetyTest() if string.len(frame.args[1]) < 500 then return frame.args[1] else return "" end end --[[ function array_iter(t) local i = 0 return function () i = i + 1 return t[i] end end --]] function p.listInline() --[[ This function is a godsend! https://www.mediawiki.org/wiki/Extension:Scribunto/Lua_reference_manual#mw.text.listToText --]] local spritedTable = {} for i,entry in ipairs(balls[tonumber(frame.args[1])]) do spritedTable[i] = "{{Sprite|named=1|linked=1|"..entry.."}}" end return mw.text.listToText( spritedTable , ", ", ", and " ) end function p.listNavbox() -- https://www.mediawiki.org/wiki/Extension:Scribunto/Lua_reference_manual#table.concat local spritedTable = {} for i,entry in ipairs(balls[tonumber(frame.args[1])]) do spritedTable[i] = "{{Sprite|named=1|linked=1|"..entry.."}}" end return table.concat( spritedTable , " • ") end function p.listCount() return table.maxn(balls[tonumber(frame.args[1])]) end -- https://www.mediawiki.org/wiki/Extension:Scribunto/Lua_reference_manual#table.maxn function p.tableTest() return balls[1][1] end function p.todaysBall() --[[ https://www.lua.org/pil/3.6.html The use of explicit indexing here is not strictly semantic; it's just to emphasize the rotation order. ]] local unixDay = math.floor(os.time()/86400) local ballTotalCount = 0 local ballCounts = {} for whichTable,subtable in ipairs(balls) do ballCounts[whichTable] = #subtable ballTotalCount = ballTotalCount + ballCounts[whichTable] end local cycleDayIndex, cycleStartingBall = unixDay % ballTotalCount, math.floor(unixDay/ballTotalCount) % ballTotalCount local cycleTodaysBall if ballTotalCount % 7 ~= 0 then cycleTodaysBall = (cycleStartingBall + cycleDayIndex*7) % ballTotalCount elseif ballTotalCount % 11 ~= 0 then cycleTodaysBall = (cycleStartingBall + cycleDayIndex*11) % ballTotalCount elseif ballTotalCount % 13 ~= 0 then cycleTodaysBall = (cycleStartingBall + cycleDayIndex*13) % ballTotalCount else cycleTodaysBall = (cycleStartingBall + cycleDayIndex*(ballTotalCount - 1)) % ballTotalCount end --[[ debug return cycleTodaysBall .. " " .. ballTotalCount .. " " .. os.time() .. " " .. math.floor(os.time()/86400) .. " " .. cycleDayIndex .. " " .. cycleStartingBall ]] for whichTable = 1, #balls do if ballCounts[whichTable] > cycleTodaysBall then return balls[whichTable][cycleTodaysBall + 1] else cycleTodaysBall = cycleTodaysBall - ballCounts[whichTable] end end --]] end return p; ju5lva4l8aak5dm6kxx0esi6v0g665p 2823762 2823761 2026-08-21T00:02:44Z Helpme2222 3106525 2823762 Scribunto text/plain -- My function for teaching grammar local p = {}; local frame = mw.getCurrentFrame() local grammatical_moods = { "Jelen ido", "Mult ido", "Felszolito mod", "Felteteles mod" } local balls = { grammatical_moods } function p.title() local grammatical_cases = { ablative = 1, inessive = { ANCOVA = "ANCOVA" } } local cases2 = "ba" local cases3 = "ba" -- if grammatical_cases.inessive[frame:getParent():getTitle()] then cases2 = "true" else cases2 = "false" end -- if "ANCOVA" == frame:getParent():getTitle() then cases3 = "true" else cases3 = "false" end local detected = false detected = detected or true return mw.title.getCurrentTitle() end function p.ifexist() return tonumber(frame:expandTemplate{ title = "User:Helpme2222/Sandbox", args = {frame.args[1]} }) end function p.performance() for i = 1,1000000 do p.tableMake() end return end function p.performance1() local var = "" for i = 1,100000000 do if var[1] then end end return end function p.performance2() local var = "" for i = 1,100000000 do if type(var) == "table" then end end return end function p.tableMake() local loady = require("Module:Sandbox/22/") local var = { keyword = {loady.tableBake()}, kljuczslovo = {loady.tableBake()}, yaoshiwenzi = {loady.tableBake()}, llavepalabra = {loady.tableBake()}, } return var end function p.expand() return frame:expandTemplate{ title = "User:Helpme2222/Sandbox" } end function p.title3() return mw.title.getCurrentTitle().fullText end function p.title2() local grammatical_cases = { ablative = 1, inessive = { ANCOVA = "ANCOVA", ["Module:Sandbox/22"] = "Module:Sandbox/22" } } local concepts = { grammatical_cases, } local PAGENAME = tostring(mw.title.getCurrentTitle()) local detected = false local out = {} local debugger = {} for i, group in ipairs(concepts) do if group.inessive[PAGENAME] then table.insert(debugger,"Okay, managed TRUE on "..i..":"..group.ablative) detected = detected or true local formattedGroup = {} for memberKey, memberRendervalue in pairs(group.inessive) do table.insert(formattedGroup, "<li>" .. memberRendervalue .. "</li>") end table.insert(out, "<h3>" .. group.ablative .. "</h3><ul>" .. table.concat( formattedGroup ) .. "</ul>" ) table.insert(out, "this sucks ass") return "this sucks ass" else table.insert(debugger,"Managed FALSE on "..i..":"..group.ablative..". Comparator: "..PAGENAME..", ") end end return debugger --[[ if detected then return tostring(detected) .. table.concat(out) end return --]] end function p.sanitizeChar(capture) -- If the set of likely illegal characters to appear in title expands, a rewrite of this as a table is merited if capture == "?" then return "" elseif capture == "#" then return "No. " end end function p.sanitizeTitle() local title = frame.args[1] return mw.ustring.gsub( title, "(?:\\?|\\#)", p.sanitizeChar) end function p.sanitizeTitletest2() return mw.ustring.gsub( "Ki vagy? (🌡️🌾⭐🗡️ VS 🪐 🪨 💣 🧿)", "(?:\\?|\\#)", p.sanitizeChar()) end function p.safetyTest() if string.len(frame.args[1]) < 500 then return frame.args[1] else return "" end end --[[ function array_iter(t) local i = 0 return function () i = i + 1 return t[i] end end --]] function p.listInline() --[[ This function is a godsend! https://www.mediawiki.org/wiki/Extension:Scribunto/Lua_reference_manual#mw.text.listToText --]] local spritedTable = {} for i,entry in ipairs(balls[tonumber(frame.args[1])]) do spritedTable[i] = "{{Sprite|named=1|linked=1|"..entry.."}}" end return mw.text.listToText( spritedTable , ", ", ", and " ) end function p.listNavbox() -- https://www.mediawiki.org/wiki/Extension:Scribunto/Lua_reference_manual#table.concat local spritedTable = {} for i,entry in ipairs(balls[tonumber(frame.args[1])]) do spritedTable[i] = "{{Sprite|named=1|linked=1|"..entry.."}}" end return table.concat( spritedTable , " • ") end function p.listCount() return table.maxn(balls[tonumber(frame.args[1])]) end -- https://www.mediawiki.org/wiki/Extension:Scribunto/Lua_reference_manual#table.maxn function p.tableTest() return balls[1][1] end function p.todaysBall() --[[ https://www.lua.org/pil/3.6.html The use of explicit indexing here is not strictly semantic; it's just to emphasize the rotation order. ]] local unixDay = math.floor(os.time()/86400) local ballTotalCount = 0 local ballCounts = {} for whichTable,subtable in ipairs(balls) do ballCounts[whichTable] = #subtable ballTotalCount = ballTotalCount + ballCounts[whichTable] end local cycleDayIndex, cycleStartingBall = unixDay % ballTotalCount, math.floor(unixDay/ballTotalCount) % ballTotalCount local cycleTodaysBall if ballTotalCount % 7 ~= 0 then cycleTodaysBall = (cycleStartingBall + cycleDayIndex*7) % ballTotalCount elseif ballTotalCount % 11 ~= 0 then cycleTodaysBall = (cycleStartingBall + cycleDayIndex*11) % ballTotalCount elseif ballTotalCount % 13 ~= 0 then cycleTodaysBall = (cycleStartingBall + cycleDayIndex*13) % ballTotalCount else cycleTodaysBall = (cycleStartingBall + cycleDayIndex*(ballTotalCount - 1)) % ballTotalCount end --[[ debug return cycleTodaysBall .. " " .. ballTotalCount .. " " .. os.time() .. " " .. math.floor(os.time()/86400) .. " " .. cycleDayIndex .. " " .. cycleStartingBall ]] for whichTable = 1, #balls do if ballCounts[whichTable] > cycleTodaysBall then return balls[whichTable][cycleTodaysBall + 1] else cycleTodaysBall = cycleTodaysBall - ballCounts[whichTable] end end --]] end return p; po9slvyheawe7q82fan0rwd3q0qzt3y 2823763 2823762 2026-08-21T00:02:58Z Helpme2222 3106525 2823763 Scribunto text/plain -- My function for teaching grammar local p = {}; local frame = mw.getCurrentFrame() local grammatical_moods = { "Jelen ido", "Mult ido", "Felszolito mod", "Felteteles mod" } local balls = { grammatical_moods } function p.title() local grammatical_cases = { ablative = 1, inessive = { ANCOVA = "ANCOVA" } } local cases2 = "ba" local cases3 = "ba" -- if grammatical_cases.inessive[frame:getParent():getTitle()] then cases2 = "true" else cases2 = "false" end -- if "ANCOVA" == frame:getParent():getTitle() then cases3 = "true" else cases3 = "false" end local detected = false detected = detected or true return mw.title.getCurrentTitle() end function p.ifexist() return tonumber(frame:expandTemplate{ title = "User:Helpme2222/Sandbox", args = {frame.args[1]} }) end function p.performance() for i = 1,5000000 do p.tableMake() end return end function p.performance1() local var = "" for i = 1,100000000 do if var[1] then end end return end function p.performance2() local var = "" for i = 1,100000000 do if type(var) == "table" then end end return end function p.tableMake() local loady = require("Module:Sandbox/22/") local var = { keyword = {loady.tableBake()}, kljuczslovo = {loady.tableBake()}, yaoshiwenzi = {loady.tableBake()}, llavepalabra = {loady.tableBake()}, } return var end function p.expand() return frame:expandTemplate{ title = "User:Helpme2222/Sandbox" } end function p.title3() return mw.title.getCurrentTitle().fullText end function p.title2() local grammatical_cases = { ablative = 1, inessive = { ANCOVA = "ANCOVA", ["Module:Sandbox/22"] = "Module:Sandbox/22" } } local concepts = { grammatical_cases, } local PAGENAME = tostring(mw.title.getCurrentTitle()) local detected = false local out = {} local debugger = {} for i, group in ipairs(concepts) do if group.inessive[PAGENAME] then table.insert(debugger,"Okay, managed TRUE on "..i..":"..group.ablative) detected = detected or true local formattedGroup = {} for memberKey, memberRendervalue in pairs(group.inessive) do table.insert(formattedGroup, "<li>" .. memberRendervalue .. "</li>") end table.insert(out, "<h3>" .. group.ablative .. "</h3><ul>" .. table.concat( formattedGroup ) .. "</ul>" ) table.insert(out, "this sucks ass") return "this sucks ass" else table.insert(debugger,"Managed FALSE on "..i..":"..group.ablative..". Comparator: "..PAGENAME..", ") end end return debugger --[[ if detected then return tostring(detected) .. table.concat(out) end return --]] end function p.sanitizeChar(capture) -- If the set of likely illegal characters to appear in title expands, a rewrite of this as a table is merited if capture == "?" then return "" elseif capture == "#" then return "No. " end end function p.sanitizeTitle() local title = frame.args[1] return mw.ustring.gsub( title, "(?:\\?|\\#)", p.sanitizeChar) end function p.sanitizeTitletest2() return mw.ustring.gsub( "Ki vagy? (🌡️🌾⭐🗡️ VS 🪐 🪨 💣 🧿)", "(?:\\?|\\#)", p.sanitizeChar()) end function p.safetyTest() if string.len(frame.args[1]) < 500 then return frame.args[1] else return "" end end --[[ function array_iter(t) local i = 0 return function () i = i + 1 return t[i] end end --]] function p.listInline() --[[ This function is a godsend! https://www.mediawiki.org/wiki/Extension:Scribunto/Lua_reference_manual#mw.text.listToText --]] local spritedTable = {} for i,entry in ipairs(balls[tonumber(frame.args[1])]) do spritedTable[i] = "{{Sprite|named=1|linked=1|"..entry.."}}" end return mw.text.listToText( spritedTable , ", ", ", and " ) end function p.listNavbox() -- https://www.mediawiki.org/wiki/Extension:Scribunto/Lua_reference_manual#table.concat local spritedTable = {} for i,entry in ipairs(balls[tonumber(frame.args[1])]) do spritedTable[i] = "{{Sprite|named=1|linked=1|"..entry.."}}" end return table.concat( spritedTable , " • ") end function p.listCount() return table.maxn(balls[tonumber(frame.args[1])]) end -- https://www.mediawiki.org/wiki/Extension:Scribunto/Lua_reference_manual#table.maxn function p.tableTest() return balls[1][1] end function p.todaysBall() --[[ https://www.lua.org/pil/3.6.html The use of explicit indexing here is not strictly semantic; it's just to emphasize the rotation order. ]] local unixDay = math.floor(os.time()/86400) local ballTotalCount = 0 local ballCounts = {} for whichTable,subtable in ipairs(balls) do ballCounts[whichTable] = #subtable ballTotalCount = ballTotalCount + ballCounts[whichTable] end local cycleDayIndex, cycleStartingBall = unixDay % ballTotalCount, math.floor(unixDay/ballTotalCount) % ballTotalCount local cycleTodaysBall if ballTotalCount % 7 ~= 0 then cycleTodaysBall = (cycleStartingBall + cycleDayIndex*7) % ballTotalCount elseif ballTotalCount % 11 ~= 0 then cycleTodaysBall = (cycleStartingBall + cycleDayIndex*11) % ballTotalCount elseif ballTotalCount % 13 ~= 0 then cycleTodaysBall = (cycleStartingBall + cycleDayIndex*13) % ballTotalCount else cycleTodaysBall = (cycleStartingBall + cycleDayIndex*(ballTotalCount - 1)) % ballTotalCount end --[[ debug return cycleTodaysBall .. " " .. ballTotalCount .. " " .. os.time() .. " " .. math.floor(os.time()/86400) .. " " .. cycleDayIndex .. " " .. cycleStartingBall ]] for whichTable = 1, #balls do if ballCounts[whichTable] > cycleTodaysBall then return balls[whichTable][cycleTodaysBall + 1] else cycleTodaysBall = cycleTodaysBall - ballCounts[whichTable] end end --]] end return p; bh3fu4643g1r0o5pgkl77f0il8x7n71 2823765 2823763 2026-08-21T00:06:45Z Helpme2222 3106525 2823765 Scribunto text/plain -- My function for teaching grammar local p = {}; local frame = mw.getCurrentFrame() local grammatical_moods = { "Jelen ido", "Mult ido", "Felszolito mod", "Felteteles mod" } local balls = { grammatical_moods } function p.title() local grammatical_cases = { ablative = 1, inessive = { ANCOVA = "ANCOVA" } } local cases2 = "ba" local cases3 = "ba" -- if grammatical_cases.inessive[frame:getParent():getTitle()] then cases2 = "true" else cases2 = "false" end -- if "ANCOVA" == frame:getParent():getTitle() then cases3 = "true" else cases3 = "false" end local detected = false detected = detected or true return mw.title.getCurrentTitle() end function p.ifexist() return tonumber(frame:expandTemplate{ title = "User:Helpme2222/Sandbox", args = {frame.args[1]} }) end function p.performance() for i = 1,5000000 do p.tableMake() end return end function p.performance1() local var = "" for i = 1,100000000 do if var[1] then end end return end function p.performance2() local var = "" for i = 1,100000000 do if type(var) == "table" then end end return end p.counter = 0 function p.tableBake() p.counter = p.counter + 1 return p.counter end function p.tableMake() p.counter = 0 local var = { keyword = {p.tableBake()}, kljuczslovo = {p.tableBake()}, yaoshiwenzi = {p.tableBake()}, llavepalabra = {p.tableBake()}, } return var end function p.expand() return frame:expandTemplate{ title = "User:Helpme2222/Sandbox" } end function p.title3() return mw.title.getCurrentTitle().fullText end function p.title2() local grammatical_cases = { ablative = 1, inessive = { ANCOVA = "ANCOVA", ["Module:Sandbox/22"] = "Module:Sandbox/22" } } local concepts = { grammatical_cases, } local PAGENAME = tostring(mw.title.getCurrentTitle()) local detected = false local out = {} local debugger = {} for i, group in ipairs(concepts) do if group.inessive[PAGENAME] then table.insert(debugger,"Okay, managed TRUE on "..i..":"..group.ablative) detected = detected or true local formattedGroup = {} for memberKey, memberRendervalue in pairs(group.inessive) do table.insert(formattedGroup, "<li>" .. memberRendervalue .. "</li>") end table.insert(out, "<h3>" .. group.ablative .. "</h3><ul>" .. table.concat( formattedGroup ) .. "</ul>" ) table.insert(out, "this sucks ass") return "this sucks ass" else table.insert(debugger,"Managed FALSE on "..i..":"..group.ablative..". Comparator: "..PAGENAME..", ") end end return debugger --[[ if detected then return tostring(detected) .. table.concat(out) end return --]] end function p.sanitizeChar(capture) -- If the set of likely illegal characters to appear in title expands, a rewrite of this as a table is merited if capture == "?" then return "" elseif capture == "#" then return "No. " end end function p.sanitizeTitle() local title = frame.args[1] return mw.ustring.gsub( title, "(?:\\?|\\#)", p.sanitizeChar) end function p.sanitizeTitletest2() return mw.ustring.gsub( "Ki vagy? (🌡️🌾⭐🗡️ VS 🪐 🪨 💣 🧿)", "(?:\\?|\\#)", p.sanitizeChar()) end function p.safetyTest() if string.len(frame.args[1]) < 500 then return frame.args[1] else return "" end end --[[ function array_iter(t) local i = 0 return function () i = i + 1 return t[i] end end --]] function p.listInline() --[[ This function is a godsend! https://www.mediawiki.org/wiki/Extension:Scribunto/Lua_reference_manual#mw.text.listToText --]] local spritedTable = {} for i,entry in ipairs(balls[tonumber(frame.args[1])]) do spritedTable[i] = "{{Sprite|named=1|linked=1|"..entry.."}}" end return mw.text.listToText( spritedTable , ", ", ", and " ) end function p.listNavbox() -- https://www.mediawiki.org/wiki/Extension:Scribunto/Lua_reference_manual#table.concat local spritedTable = {} for i,entry in ipairs(balls[tonumber(frame.args[1])]) do spritedTable[i] = "{{Sprite|named=1|linked=1|"..entry.."}}" end return table.concat( spritedTable , " • ") end function p.listCount() return table.maxn(balls[tonumber(frame.args[1])]) end -- https://www.mediawiki.org/wiki/Extension:Scribunto/Lua_reference_manual#table.maxn function p.tableTest() return balls[1][1] end function p.todaysBall() --[[ https://www.lua.org/pil/3.6.html The use of explicit indexing here is not strictly semantic; it's just to emphasize the rotation order. ]] local unixDay = math.floor(os.time()/86400) local ballTotalCount = 0 local ballCounts = {} for whichTable,subtable in ipairs(balls) do ballCounts[whichTable] = #subtable ballTotalCount = ballTotalCount + ballCounts[whichTable] end local cycleDayIndex, cycleStartingBall = unixDay % ballTotalCount, math.floor(unixDay/ballTotalCount) % ballTotalCount local cycleTodaysBall if ballTotalCount % 7 ~= 0 then cycleTodaysBall = (cycleStartingBall + cycleDayIndex*7) % ballTotalCount elseif ballTotalCount % 11 ~= 0 then cycleTodaysBall = (cycleStartingBall + cycleDayIndex*11) % ballTotalCount elseif ballTotalCount % 13 ~= 0 then cycleTodaysBall = (cycleStartingBall + cycleDayIndex*13) % ballTotalCount else cycleTodaysBall = (cycleStartingBall + cycleDayIndex*(ballTotalCount - 1)) % ballTotalCount end --[[ debug return cycleTodaysBall .. " " .. ballTotalCount .. " " .. os.time() .. " " .. math.floor(os.time()/86400) .. " " .. cycleDayIndex .. " " .. cycleStartingBall ]] for whichTable = 1, #balls do if ballCounts[whichTable] > cycleTodaysBall then return balls[whichTable][cycleTodaysBall + 1] else cycleTodaysBall = cycleTodaysBall - ballCounts[whichTable] end end --]] end return p; f4s388m4m42kpitw346sp2k3nhjbx1y 0 331023 2823637 2823623 2026-08-20T12:07:00Z U3236349 3005692 2823637 wikitext text/x-wiki {{title|Sex differences in sexual arousal patterns:<br>How do patterns of sexual arousal differ between males and females? }} == Overview == {{RoundBoxTop|theme=4}} [[File:ChatGPT Image Aug 18, 2026, 10 10 45 PM.png|left|thumb|150px|'''Figure 1'''. Image depicting sexual arousal between a female and male]] "As John Gray once said "men are from mars and women are from venus." Think, Emma and Daniel have been dating for several months. They are attracted to each other, but their sexual desire emerge differently. Daniel is often aroused by Emma at the simple sight of her. Early in the relationship, Daniel was finding that it was taking longer for Emma to be sexually interested in him and thought that Emma was less attracted to him. Emma explains that she is attracted to him, but her arousal tends to build in response to how he treats her. {{RoundBoxBottom}}__TOC__''Explanation of the problem, issue, or topic: Briefly explain the problem, why it is important, and outline how psychological science can help.'' *Summarise what is sexual arousal and the purpose researchers believe it serves *Explain why studying sexual arousal patterns is important, then explain the issues that have arisen that warrant such understanding. *Explain the purpose this chapter will serve for readers - what the takeaway message is, and summarise my response to patterns of sexual arousal between men and women. Proposed start for overview: * Between 1938 to 1954, Alfred Kinsey produced two reports detailing how biological and social factors influence variations in human sexual desire and activity. The reports were designed to establish an empirical foundation to assist future clinicians, educators, and legal authorities concerning what humans actually experience during sexual activities, which was lacking before and during Kinsey's time. * Suggestions for why understanding sexual arousal in males and females is important: ** understand causes of real world problems: *** Sexual Dysfunction, High Risk Sexual Behaviour (BENSON, 2003). ** Means to explore basic questions about the nature of sexual arousal and how its different components are related to each other (BENSON, 2003). ** Develop more accurate and inclusive models of human motivation and behaviour. ** Informing and guiding therapies for various sexual disorders, answering theoretical and physiological questions about huamn sexual response patterns, providing diagnostic information regarding legally and clinically significant sexual attractions (e.g. attraction to minors and sexual disorders) (Katz et al., 2023). {{RoundBoxTop|theme=4}} '''Focus questions''' * What is sexual arousal? * Why do males and females need to be sexually aroused? * What factors influence sexual arousal in males and females? * Why is understanding sexual arousal important? {{RoundBoxBottom}} == Concept of sex == * Sex, in the context of human biology, generally refers to the fundamental categories of human species that are, in the broad sense, concerned with a combination of various biological traits that are unique to a subcategory of human species. * There are currently two recognised sexes in humans which are assigned at birth, males and females. * Females refer to humans which are biologically organised for the production and function of an ova, whereas males refer to humans organised for the production and function of sperm (Stévant et al., 2018; Ivan et al., 2022). [[File:Girl with a Pearl Earring.jpg|thumb|Figure 2. Painting of a Female - Some people have found that it radiates an intense and captivating intimacy.]] == Concept of sexual arousal == * Sexual arousal refers to the mental and physical response cultivated by subjective stimulation that prepares the body for reproductive behaviour and supports subjective feelings of desire (Calabrò et al., 2019, p. 1). *Sexual arousal is believed to serve as a motivational system for sexual behaviour which are likely to be shaped by learned associations, language, and social meanings rather than being determined solely by biological reproductive mechanisms (Roche & Barnes-Holmes, 2002). *Human adults can learn new sexual arousal cues by conditioning (T. Klucken ''et al.''Neural activations of the acquisition of conditioned sexual arousal: effects of contingency awareness and sex) - software and hardware develop through many years of personal experiences. == Significance of sexual arousal in humans == * * * == Sexual arousal in males == [[File:Tor-Arne Moen Natural selection.jpg|thumb|Figure 3. Male veiwing visual stimulus]] *In males, greater solitary desire predicted stronger genital sensations, whereas higher masturbation frequency was associated with lower reported genital sensations (Sánchez-Pérez et al., 2026). *Bisexual-identified men are not a uniform group. On average, bisexual men showed arousal to both male and female stimuli, supporting the existence of bisexual arousal but many tend to show stronger arousal to one sex than the other especially when they knowingly lean towards one sex than the other. *Bisexual men display significantly greater variation in arousal patterns than heterosexual or homosexual men (Slettevold et al., 2019). == Sexual arousal in females == [[File:Potrait painting.jpg|thumb|Figure 4. Shy female|250x250px]] *Sexual arousal in females serves as a coordinated psychophysiological response that prepares the body for sexual activity. Important component of human sexual functioning and reproductive processes (Lake Polan et al., 2003; Adebisi & Carlson, 2024). *More frequent masturbation was linked to stronger genital responses and higher subjective sexual arousal and the rewarding quality of orgasm was associated with stronger genital sensations (Sánchez-Pérez et al., 2026). *Heterosexual women showed greater genital arousal to images of erect penises than to images of aroused vulvas - demonstrates that sexual arousal is strongly influenced by both the gender of a sexual stimulus and visible signs of sexual readiness (Spape et al., 2014). *Sexual desire fluctuates substantially in both men and women. Men and women experience remarkably similar short term fluctuations and similarly influenced by emotional and relationship factors (Harris et al., 2023). == Value of understanding sexual arousal == * * * {{Robelbox|title=Test Yourself!|theme=12}}<div style="{{Robelbox/pad}}"> <quiz display=simple> {The purpose of quizzes is to provide an interactive learning feature: |type="()"} + True - False {Long and complex quiz questions are recommended: |type="()"} - True + False </quiz> {{Robelbox/close}} == Conclusion == * * * ==See also== * [[wikipedia:Sexual_arousal|Sexual arousal]] (Wikipedia). * [[Motivation and emotion/Book/2016/Sexual motivation and hormones|Sexual motivation and hormones: What role do hormones play in sexual motivation and sexual arousal]] (Book Chapter, 2016). ==References== Adebisi, O. Y., & Carlson, K. (2024). Female sexual interest and arousal disorder. In ''StatPearls''. StatPearls Publishing. Calabrò, R. S., Cacciola, A., Bruschetta, D., Milardi, D., Quattrini, F., Sciarrone, F., Rosa, G., Bramanti, P., & Anastasi, G. (2019). Neuroanatomy and function of human sexual behavior: A neglected or unknown issue? ''Brain and Behavior'', ''9''(12). <nowiki>https://doi.org/10.1002/brb3.1389</nowiki> Ivan, S., Daniela, O., & Jaroslava, B. D. (2022). Sex differences matter: Males and females are equal but not the same. ''Physiology & Behavior'', ''259''(Volume 259), 114038. <nowiki>https://doi.org/10.1016/j.physbeh.2022.114038</nowiki> Lake Polan, M., Desmond, J. E., Banner, L. L., Pryor, M. R., McCallum, S. W., Atlas, S. W., Glover, G. H., & Arnow, B. A. (2003). Female sexual arousal: A behavioral analysis. ''Fertility and Sterility'', ''80''(6), 1480–1487. <nowiki>https://doi.org/10.1016/s0015-0282(03)02210-6</nowiki> Roche, B., & Barnes-Holmes, D. (2002). Human sexual arousal: A modern behavioral approach. ''The Behavior Analyst Today'', ''3''(2), 145–154. <nowiki>https://doi.org/10.1037/h0099973</nowiki> Slettevold, E., Holmes, L., Gruia, D., Nyssen, C. P., Watts-Overall, T. M., & Rieger, G. (2019). Bisexual men with bisexual and monosexual genital arousal patterns. ''Biological Psychology'', ''148'', 107763. <nowiki>https://doi.org/10.1016/j.biopsycho.2019.107763</nowiki> Spape, J., Timmers, A. D., Yoon, S., Ponseti, J., & Chivers, M. L. (2014). Gender-specific genital and subjective sexual arousal to prepotent sexual features in heterosexual women and men. ''Biological Psychology'', ''102'', 1–9. <nowiki>https://doi.org/10.1016/j.biopsycho.2014.07.008</nowiki> Stévant, I., Papaioannou, M. D., & Nef, S. (2018). A brief history of sex determination. ''Molecular and Cellular Endocrinology'', ''468'', 3–10. <nowiki>https://doi.org/10.1016/j.mce.2018.04.004</nowiki> Sánchez-Pérez, G. M., Granados, R., Mangas, P., Cervilla, O., & Sierra, J. C. (2026). Validation of masturbation parameters: A laboratory study measuring psychophysiological and subjective sexual arousal. ''International Journal of Clinical and Health Psychology'', ''26''(1), 100662. <nowiki>https://doi.org/10.1016/j.ijchp.2025.100662</nowiki> ==External links== * [https://www.webmd.com/sex/features/sex-drive-how-do-men-women-compare Sex Drive: How do Men and Women Compare?] (Webmd.com). * [https://open.spotify.com/episode/41K95dG0MnHux15rtwywMl?si=A4zCgSxSS9KB10REgbA_dg Women's sexual health: desire, arousal, and orgasms, navigating pre-menopause, and enhancing satisfaction] (Spotify.com). * [https://open.spotify.com/episode/2plfCfD98Now1GMjadaKKq?si=XnkE8OvuSrSfJ-v-NQ9K-w Episode 16: What we get wrong about men's sexual desire] (Spotify.com). [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Sexual motivation]] [[Category:Motivation and emotion/Book/Gender]] 5hzzy98d34u17oo8l713tw9e43lt0ms 2823826 2823637 2026-08-21T04:43:49Z Jtneill 10242 {{fact}} 2823826 wikitext text/x-wiki {{title|Sex differences in sexual arousal patterns:<br>How do patterns of sexual arousal differ between males and females? }} == Overview == {{RoundBoxTop|theme=4}} [[File:ChatGPT Image Aug 18, 2026, 10 10 45 PM.png|left|thumb|150px|'''Figure 1'''. Image depicting sexual arousal between a female and male]] "As John Gray once said "men are from mars and women are from venus."{{fact}} Think, Emma and Daniel have been dating for several months. They are attracted to each other, but their sexual desire emerge differently. Daniel is often aroused by Emma at the simple sight of her. Early in the relationship, Daniel was finding that it was taking longer for Emma to be sexually interested in him and thought that Emma was less attracted to him. Emma explains that she is attracted to him, but her arousal tends to build in response to how he treats her. {{RoundBoxBottom}}__TOC__''Explanation of the problem, issue, or topic: Briefly explain the problem, why it is important, and outline how psychological science can help.'' *Summarise what is sexual arousal and the purpose researchers believe it serves *Explain why studying sexual arousal patterns is important, then explain the issues that have arisen that warrant such understanding. *Explain the purpose this chapter will serve for readers - what the takeaway message is, and summarise my response to patterns of sexual arousal between men and women. Proposed start for overview: * Between 1938 to 1954, Alfred Kinsey produced two reports detailing how biological and social factors influence variations in human sexual desire and activity. The reports were designed to establish an empirical foundation to assist future clinicians, educators, and legal authorities concerning what humans actually experience during sexual activities, which was lacking before and during Kinsey's time. * Suggestions for why understanding sexual arousal in males and females is important: ** understand causes of real world problems: *** Sexual Dysfunction, High Risk Sexual Behaviour (BENSON, 2003). ** Means to explore basic questions about the nature of sexual arousal and how its different components are related to each other (BENSON, 2003). ** Develop more accurate and inclusive models of human motivation and behaviour. ** Informing and guiding therapies for various sexual disorders, answering theoretical and physiological questions about huamn sexual response patterns, providing diagnostic information regarding legally and clinically significant sexual attractions (e.g. attraction to minors and sexual disorders) (Katz et al., 2023). {{RoundBoxTop|theme=4}} '''Focus questions''' * What is sexual arousal? * Why do males and females need to be sexually aroused? * What factors influence sexual arousal in males and females? * Why is understanding sexual arousal important? {{RoundBoxBottom}} == Concept of sex == * Sex, in the context of human biology, generally refers to the fundamental categories of human species that are, in the broad sense, concerned with a combination of various biological traits that are unique to a subcategory of human species. * There are currently two recognised sexes in humans which are assigned at birth, males and females. * Females refer to humans which are biologically organised for the production and function of an ova, whereas males refer to humans organised for the production and function of sperm (Stévant et al., 2018; Ivan et al., 2022). [[File:Girl with a Pearl Earring.jpg|thumb|Figure 2. Painting of a Female - Some people have found that it radiates an intense and captivating intimacy.]] == Concept of sexual arousal == * Sexual arousal refers to the mental and physical response cultivated by subjective stimulation that prepares the body for reproductive behaviour and supports subjective feelings of desire (Calabrò et al., 2019, p. 1). *Sexual arousal is believed to serve as a motivational system for sexual behaviour which are likely to be shaped by learned associations, language, and social meanings rather than being determined solely by biological reproductive mechanisms (Roche & Barnes-Holmes, 2002). *Human adults can learn new sexual arousal cues by conditioning (T. Klucken ''et al.''Neural activations of the acquisition of conditioned sexual arousal: effects of contingency awareness and sex) - software and hardware develop through many years of personal experiences. == Significance of sexual arousal in humans == * * * == Sexual arousal in males == [[File:Tor-Arne Moen Natural selection.jpg|thumb|Figure 3. Male veiwing visual stimulus]] *In males, greater solitary desire predicted stronger genital sensations, whereas higher masturbation frequency was associated with lower reported genital sensations (Sánchez-Pérez et al., 2026). *Bisexual-identified men are not a uniform group. On average, bisexual men showed arousal to both male and female stimuli, supporting the existence of bisexual arousal but many tend to show stronger arousal to one sex than the other especially when they knowingly lean towards one sex than the other. *Bisexual men display significantly greater variation in arousal patterns than heterosexual or homosexual men (Slettevold et al., 2019). == Sexual arousal in females == [[File:Potrait painting.jpg|thumb|Figure 4. Shy female|250x250px]] *Sexual arousal in females serves as a coordinated psychophysiological response that prepares the body for sexual activity. Important component of human sexual functioning and reproductive processes (Lake Polan et al., 2003; Adebisi & Carlson, 2024). *More frequent masturbation was linked to stronger genital responses and higher subjective sexual arousal and the rewarding quality of orgasm was associated with stronger genital sensations (Sánchez-Pérez et al., 2026). *Heterosexual women showed greater genital arousal to images of erect penises than to images of aroused vulvas - demonstrates that sexual arousal is strongly influenced by both the gender of a sexual stimulus and visible signs of sexual readiness (Spape et al., 2014). *Sexual desire fluctuates substantially in both men and women. Men and women experience remarkably similar short term fluctuations and similarly influenced by emotional and relationship factors (Harris et al., 2023). == Value of understanding sexual arousal == * * * {{Robelbox|title=Test Yourself!|theme=12}}<div style="{{Robelbox/pad}}"> <quiz display=simple> {The purpose of quizzes is to provide an interactive learning feature: |type="()"} + True - False {Long and complex quiz questions are recommended: |type="()"} - True + False </quiz> {{Robelbox/close}} == Conclusion == * * * ==See also== * [[wikipedia:Sexual_arousal|Sexual arousal]] (Wikipedia). * [[Motivation and emotion/Book/2016/Sexual motivation and hormones|Sexual motivation and hormones: What role do hormones play in sexual motivation and sexual arousal]] (Book Chapter, 2016). ==References== Adebisi, O. Y., & Carlson, K. (2024). Female sexual interest and arousal disorder. In ''StatPearls''. StatPearls Publishing. Calabrò, R. S., Cacciola, A., Bruschetta, D., Milardi, D., Quattrini, F., Sciarrone, F., Rosa, G., Bramanti, P., & Anastasi, G. (2019). Neuroanatomy and function of human sexual behavior: A neglected or unknown issue? ''Brain and Behavior'', ''9''(12). <nowiki>https://doi.org/10.1002/brb3.1389</nowiki> Ivan, S., Daniela, O., & Jaroslava, B. D. (2022). Sex differences matter: Males and females are equal but not the same. ''Physiology & Behavior'', ''259''(Volume 259), 114038. <nowiki>https://doi.org/10.1016/j.physbeh.2022.114038</nowiki> Lake Polan, M., Desmond, J. E., Banner, L. L., Pryor, M. R., McCallum, S. W., Atlas, S. W., Glover, G. H., & Arnow, B. A. (2003). Female sexual arousal: A behavioral analysis. ''Fertility and Sterility'', ''80''(6), 1480–1487. <nowiki>https://doi.org/10.1016/s0015-0282(03)02210-6</nowiki> Roche, B., & Barnes-Holmes, D. (2002). Human sexual arousal: A modern behavioral approach. ''The Behavior Analyst Today'', ''3''(2), 145–154. <nowiki>https://doi.org/10.1037/h0099973</nowiki> Slettevold, E., Holmes, L., Gruia, D., Nyssen, C. P., Watts-Overall, T. M., & Rieger, G. (2019). Bisexual men with bisexual and monosexual genital arousal patterns. ''Biological Psychology'', ''148'', 107763. <nowiki>https://doi.org/10.1016/j.biopsycho.2019.107763</nowiki> Spape, J., Timmers, A. D., Yoon, S., Ponseti, J., & Chivers, M. L. (2014). Gender-specific genital and subjective sexual arousal to prepotent sexual features in heterosexual women and men. ''Biological Psychology'', ''102'', 1–9. <nowiki>https://doi.org/10.1016/j.biopsycho.2014.07.008</nowiki> Stévant, I., Papaioannou, M. D., & Nef, S. (2018). A brief history of sex determination. ''Molecular and Cellular Endocrinology'', ''468'', 3–10. <nowiki>https://doi.org/10.1016/j.mce.2018.04.004</nowiki> Sánchez-Pérez, G. M., Granados, R., Mangas, P., Cervilla, O., & Sierra, J. C. (2026). Validation of masturbation parameters: A laboratory study measuring psychophysiological and subjective sexual arousal. ''International Journal of Clinical and Health Psychology'', ''26''(1), 100662. <nowiki>https://doi.org/10.1016/j.ijchp.2025.100662</nowiki> ==External links== * [https://www.webmd.com/sex/features/sex-drive-how-do-men-women-compare Sex Drive: How do Men and Women Compare?] (Webmd.com). * [https://open.spotify.com/episode/41K95dG0MnHux15rtwywMl?si=A4zCgSxSS9KB10REgbA_dg Women's sexual health: desire, arousal, and orgasms, navigating pre-menopause, and enhancing satisfaction] (Spotify.com). * [https://open.spotify.com/episode/2plfCfD98Now1GMjadaKKq?si=XnkE8OvuSrSfJ-v-NQ9K-w Episode 16: What we get wrong about men's sexual desire] (Spotify.com). [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Sexual motivation]] [[Category:Motivation and emotion/Book/Gender]] suoqfqpqbzn6cw8pl12a98m04ahg5r3 0 331034 2823750 2823334 2026-08-20T22:20:58Z U3222012 2968463 2823750 wikitext text/x-wiki {{title|Perfectionism and procrastination. What is the role of perfectionism in procrastination and what can be done about it?}} <div align=center>Edit the title and sub-title to match the wording (and casing) in the [[Motivation and emotion/Book/2025|2026 list of topics]].<br>[[Motivation and emotion/About/Staff|Seek approval]] for any changes.<br>Do not include your name (authorship is as per [[Special:History/{{PAGENAME}}|the page history]]).</div> __TOC__ ==Overview== {{RoundBoxTop|theme=3}} [[File:A picture is worth a thousand words.jpg|right|thumb|150px|'''Figure 1'''. Use a captioned image to illustrate the scenario]] ; Imagine this ... or Scenario ... or Case study or ... ?) Start with an engaging [[#Scenarios|scenario, example, or case study]] which illustrates the problem and engages reader interest. Present the scenario in a [[#Feature box|feature box]]. To change the box colour: # Edit source # Change "theme=3" to another number Include an image and cite it (e.g., see Figure 1). {{RoundBoxBottom}} The Overview section should provide: # '''Scenario''': A short, engaging case study or real-world example in a feature box, with an accompanying image (see above) # '''Explanation of the problem, issue, or topc''': Briefly explain the problem, why it is important, and outline how psychological science can help # '''Focus questions''': Unpack the sub-title into focus questions in a feature box Recommended length: 180 to 330 words. This template provides key headings, examples, and tips for each section. Gradually remove this generic information as the chapter develops. It is OK to retain some of the template material for the topic development, but it should all be removed for the final book chapter. Key resources: * [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 02]] explains about how to edit * [[Motivation and emotion/Assessment/Topic|Topic development guidelines]] * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] {{RoundBoxTop|theme=3}} '''Focus questions''' Break the sub-title down into three to five [[Motivation and emotion/Assessment/Chapter/Focus questions|focus questions]]. Align the top-level headings with these focus questions. * What is the first focus question? * What is the second focus question? * What is the third focus question? Ask [[w:Open-ended question|open-ended]] focus questions. For example: * Is there a relationship between weather and criminal behaviour? (closed-ended) * What is the relationship between weather and criminal behaviour? (open-ended) {{RoundBoxBottom}} ==Headings== Use this heading structure: * [[#Overview|Overview]] * 3 to 6 major headings tailored to the topic; can have sub-headings, but: ** avoid having only one sub-heading ** provide an introductory paragraph before breaking into sub-sections * [[#Conclusion|Conclusion]] * See also * References * External links ==Key points== For the topic development, for each heading and sub-heading: * Provide at least three bullet-points, including for the Overview and Conclusion * Include key citations ==Figures== [[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== Interactive learning features help to bring book chapters to life and can be embedded throughout the chapter. {{anchor|Scenarios}} ;Scenarios * Scenarios, case studies, or examples describe concepts in action * Can be real or fictional; if real, provide citations * Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Present using [[#Feature boxes|feature boxes]] {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted '''Table 1''' A Descriptive Caption Which Explains The Table Contents and its Relevance to the Text e.g., The 2 x 2 Johari Window Model Showing Knowing x Self/Other {| class="wikitable" style="margin: auto; |- ! !! Known to self !! Not known to self |- | '''Known to others''' || Open area || Blind spot |- | '''Not known to others''' || Hidden area || Unknown |} ;Quizzes * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] Example simple quiz questions. Choose your answers and click "Submit": <quiz display=simple> {The purpose of quizzes is to provide an interactive learning feature: |type="()"} + True - False {Long and complex quiz questions are recommended: |type="()"} - True + False </quiz> ==Conclusion== * The Conclusion is arguably the most important section * Draft clear take-home message(s), even at the topic development stage * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) * [[w:Self determination theory|Self determination theory]] (Wikipedia) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses }} ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. APA style example: {{Hanging indent|1= Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091 Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper & Row. }} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Perfectionism]] [[Category:Motivation and emotion/Book/Procrastination]] mcwe9wt3uia3jmdvc9da19lkvgz217r 2823824 2823750 2026-08-21T04:41:52Z Jtneill 10242 Adjust title formatting 2823824 wikitext text/x-wiki {{title|Perfectionism and procrastination:<br>What is the role of perfectionism in procrastination and what can be done about it?}} <div align=center>Edit the title and sub-title to match the wording (and casing) in the [[Motivation and emotion/Book/2025|2026 list of topics]].<br>[[Motivation and emotion/About/Staff|Seek approval]] for any changes.<br>Do not include your name (authorship is as per [[Special:History/{{PAGENAME}}|the page history]]).</div> __TOC__ ==Overview== {{RoundBoxTop|theme=3}} [[File:A picture is worth a thousand words.jpg|right|thumb|150px|'''Figure 1'''. Use a captioned image to illustrate the scenario]] ; Imagine this ... or Scenario ... or Case study or ... ?) Start with an engaging [[#Scenarios|scenario, example, or case study]] which illustrates the problem and engages reader interest. Present the scenario in a [[#Feature box|feature box]]. To change the box colour: # Edit source # Change "theme=3" to another number Include an image and cite it (e.g., see Figure 1). {{RoundBoxBottom}} The Overview section should provide: # '''Scenario''': A short, engaging case study or real-world example in a feature box, with an accompanying image (see above) # '''Explanation of the problem, issue, or topc''': Briefly explain the problem, why it is important, and outline how psychological science can help # '''Focus questions''': Unpack the sub-title into focus questions in a feature box Recommended length: 180 to 330 words. This template provides key headings, examples, and tips for each section. Gradually remove this generic information as the chapter develops. It is OK to retain some of the template material for the topic development, but it should all be removed for the final book chapter. Key resources: * [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 02]] explains about how to edit * [[Motivation and emotion/Assessment/Topic|Topic development guidelines]] * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] {{RoundBoxTop|theme=3}} '''Focus questions''' Break the sub-title down into three to five [[Motivation and emotion/Assessment/Chapter/Focus questions|focus questions]]. Align the top-level headings with these focus questions. * What is the first focus question? * What is the second focus question? * What is the third focus question? Ask [[w:Open-ended question|open-ended]] focus questions. For example: * Is there a relationship between weather and criminal behaviour? (closed-ended) * What is the relationship between weather and criminal behaviour? (open-ended) {{RoundBoxBottom}} ==Headings== Use this heading structure: * [[#Overview|Overview]] * 3 to 6 major headings tailored to the topic; can have sub-headings, but: ** avoid having only one sub-heading ** provide an introductory paragraph before breaking into sub-sections * [[#Conclusion|Conclusion]] * See also * References * External links ==Key points== For the topic development, for each heading and sub-heading: * Provide at least three bullet-points, including for the Overview and Conclusion * Include key citations ==Figures== [[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== Interactive learning features help to bring book chapters to life and can be embedded throughout the chapter. {{anchor|Scenarios}} ;Scenarios * Scenarios, case studies, or examples describe concepts in action * Can be real or fictional; if real, provide citations * Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Present using [[#Feature boxes|feature boxes]] {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted '''Table 1''' A Descriptive Caption Which Explains The Table Contents and its Relevance to the Text e.g., The 2 x 2 Johari Window Model Showing Knowing x Self/Other {| class="wikitable" style="margin: auto; |- ! !! Known to self !! Not known to self |- | '''Known to others''' || Open area || Blind spot |- | '''Not known to others''' || Hidden area || Unknown |} ;Quizzes * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] Example simple quiz questions. Choose your answers and click "Submit": <quiz display=simple> {The purpose of quizzes is to provide an interactive learning feature: |type="()"} + True - False {Long and complex quiz questions are recommended: |type="()"} - True + False </quiz> ==Conclusion== * The Conclusion is arguably the most important section * Draft clear take-home message(s), even at the topic development stage * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) * [[w:Self determination theory|Self determination theory]] (Wikipedia) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses }} ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. APA style example: {{Hanging indent|1= Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091 Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper & Row. }} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Perfectionism]] [[Category:Motivation and emotion/Book/Procrastination]] aektguccuyqku1kg4ci00k6vktyiroi 0 331046 2823638 2822244 2026-08-20T12:12:47Z U3253363 3106362 Added draft of overview. 2823638 wikitext text/x-wiki {{title|Self-concept and motivation:<br>How does self-concept relate to motivation?}} == Overview == {{RoundBoxTop|theme=3}} [[File:Sinclair Swimming.JPG|right|thumb|180px|'''Figure 1'''. Ash is a competitive swimmer and swims daily.]] Ash is a swimmer training for a national competition. Being a swimmer is the first thing Ash thinks of when she’s asked to describe herself and she’s eager to succeed in the upcoming competition. Ash wakes up at 4:00am every morning to swim four kilometres (Figure 1). Her friend Riley is always surprised by how Ash wakes up so early and swims so much. Why is Ash able to do this when many would find this a struggle?{{RoundBoxBottom}} Your self-concept is your understanding of who you are and how you feel about yourself. This includes a complex system of the attitudes, beliefs and judgements you hold about yourself. Self-concept guides you in answering the question “who am I?” (Wehrle & Fasbender, 2018). But its importance extends beyond answering that question. Self-concept influences how you think, feel and behave. Consider self-concept an internal compass which motivates and guides your choices, relationships and understanding of the world.   For Ash in our case study, being a swimmer and succeeding in the upcoming swimming competition are core to her self-concept. This guides and motivates her behaviour of swimming early every morning.   This chapter explores how our understanding of ourselves influences what we’re motivated to do and examines how what we repeatedly do subsequently shapes our self-concept. By understanding how and why we perceive ourselves the way we do, and the impacts of our self-concepts, we can better understand our behaviours, foster positive self-concept and embrace the motivational properties of self-concept.   {{RoundBoxTop|theme=3}} '''Focus questions''' *What is self-concept? *What are the key theories of self-concept? *How does self-concept influence motivation? *How does motivation influence self-concept? *How can our understanding of self-concept be used to improve motivation and wellbeing?{{RoundBoxBottom}} == Understanding self-concept == The self is central to humanhood and the scientific understanding of human behaviour. Thus, the question of “what makes me, me?” has been theorised about throughout history and is important to understand. This section details the core theories and properties of self-concept which will be referred to throughout the chapter.   Self-concept is a cognitive framework which is unique to, but encompasses, many of the popularly used “self-” constructs – [[self-esteem]] (perceived value of yourself), [[w:Self-efficacy|self-efficacy]] (perceived task capability), [[w:Self-image|self-image]] (description of yourself). See the linked pages for details on each of these separate constructs.   == Key points == For the topic development, for each heading and sub-heading: * Provide at least three bullet-points, including for the Overview and Conclusion * Include key citations == Figures == [[File:Thought_bubble.svg|right|thumb|157x157px|'''Figure 2'''. Example of an image with a descriptive caption.]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[c:|Wikimedia Commons]] * Images can be uploaded to [[c:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) == Learning features == Interactive learning features help to bring book chapters to life and can be embedded throughout the chapter. {{anchor|Scenarios}} ; Scenarios * Scenarios, case studies, or examples describe concepts in action * Can be real or fictional; if real, provide citations * Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Present using [[Motivation and emotion/Book/2026/Self-concept and motivation#Feature boxes|feature boxes]] {{anchor|Feature box}} ; Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[Motivation and emotion/Book/2026/Self-concept and motivation#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ; Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[wikipedia:Dreams|dreams]]) of dreams was provided by [[wikipedia:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ; Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted '''Table 1''' A Descriptive Caption Which Explains The Table Contents and its Relevance to the Text e.g., The 2 x 2 Johari Window Model Showing Knowing x Self/Other {| class="wikitable" style="margin: auto;" ! !Known to self !Not known to self |- |'''Known to others''' |Open area |Blind spot |- |'''Not known to others''' |Hidden area |Unknown |} ; Quizzes * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] Example simple quiz questions. Choose your answers and click "Submit":<quiz display="simple"> {The purpose of quizzes is to provide an interactive learning feature: |type="()"} + True - False {Long and complex quiz questions are recommended: |type="()"} - True + False </quiz> == Conclusion == * The Conclusion is arguably the most important section * Draft clear take-home message(s), even at the topic development stage * Together, the [[Motivation and emotion/Book/2026/Self-concept and motivation#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages?}} == See also == Provide [[Help:Contents/Links#Interwiki links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[wikipedia:|Wikipedia articles]]. Use [[wikipedia:Letter case#Sentence_casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) * [[wikipedia:Self determination theory|Self determination theory]] (Wikipedia) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses}} == References == This section lists the cited references in [[wikipedia:APA style|APA style]] (7th ed.) or [[wikipedia:Wikipedia:Citing sources|wiki style]]. APA style example: {{Hanging indent|Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091 Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper & Row.}}{{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted}} == External links == Provide [[Help:Contents/Links#External links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[wikipedia:Letter case#Sentence_casing|sentence casing]] and alphabetical order. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link}} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Self-concept]] [[Category:Motivation and emotion/Book/2026]] [[Category:Motivation and emotion/Book/Motivation]] tqy40be6cy4kmzdkbjqevfatdso7mn5 2823639 2823638 2026-08-20T12:17:38Z U3253363 3106362 Added drafted understanding self concept section. The drafted "significance for motivation" sentences in the table were rewritten for conciseness using Copilot AI. 2823639 wikitext text/x-wiki {{title|Self-concept and motivation:<br>How does self-concept relate to motivation?}} == Overview == {{RoundBoxTop|theme=3}} [[File:Sinclair Swimming.JPG|right|thumb|180px|'''Figure 1'''. Ash is a competitive swimmer and swims daily.]] Ash is a swimmer training for a national competition. Being a swimmer is the first thing Ash thinks of when she’s asked to describe herself and she’s eager to succeed in the upcoming competition. Ash wakes up at 4:00am every morning to swim four kilometres (Figure 1). Her friend Riley is always surprised by how Ash wakes up so early and swims so much. Why is Ash able to do this when many would find this a struggle?{{RoundBoxBottom}} Your self-concept is your understanding of who you are and how you feel about yourself. This includes a complex system of the attitudes, beliefs and judgements you hold about yourself. Self-concept guides you in answering the question “who am I?” (Wehrle & Fasbender, 2018). But its importance extends beyond answering that question. Self-concept influences how you think, feel and behave. Consider self-concept an internal compass which motivates and guides your choices, relationships and understanding of the world.   For Ash in our case study, being a swimmer and succeeding in the upcoming swimming competition are core to her self-concept. This guides and motivates her behaviour of swimming early every morning.   This chapter explores how our understanding of ourselves influences what we’re motivated to do and examines how what we repeatedly do subsequently shapes our self-concept. By understanding how and why we perceive ourselves the way we do, and the impacts of our self-concepts, we can better understand our behaviours, foster positive self-concept and embrace the motivational properties of self-concept.   {{RoundBoxTop|theme=3}} '''Focus questions''' *What is self-concept? *What are the key theories of self-concept? *How does self-concept influence motivation? *How does motivation influence self-concept? *How can our understanding of self-concept be used to improve motivation and wellbeing?{{RoundBoxBottom}} == Understanding self-concept == The self is central to humanhood and the scientific understanding of human behaviour. Thus, the question of “what makes me, me?” has been theorised about throughout history and is important to understand. This section details the core theories and properties of self-concept which will be referred to throughout the chapter.   Self-concept is a cognitive framework which is unique to, but encompasses, many of the popularly used “self-” constructs – [[self-esteem]] (perceived value of yourself), [[w:Self-efficacy|self-efficacy]] (perceived task capability), [[w:Self-image|self-image]] (description of yourself). See the linked pages for details on each of these separate constructs. ==== William James ==== James (1892) proposed the self consists of two parts: “I”, the subjective thinker and “knower”, and “me” the material, social and “known” self. This philosophical framework laid the basis for the development of further empirical theories of self-concept and catapulted psychological identity research.   ==== The looking-glass self ==== Cooley (1902) framed the individual as a social being, theorising that self-concept is a reflection of the responses and evaluations of individuals within one’s environment. Self-concept is developed through the imagined judgement of others, and individuals become the people others say they are (Siljanovska & Stojcevska, 2018). ==== Rogers’ self-theory ==== Rogers (1959), a humanist psychologist, proposed self-concept is a dynamic, organised system which consists of three parts: the real self (how you see yourself), ideal self (who you would like to be), and self-worth (how much you value yourself). He proposed that individuals behave in accordance with their self-concept, a stepping stone toward the contemporary understanding of how self-beliefs influence motivation (Ismail & Tekke, 2015; Yousefi & Kiani, 2014).   ==== The multidimensional self-concept model ==== Shavelson et al. (1992) were critical of the lack of theoretical and methodological rigor supporting studies of self-concept. They built upon previous theories, suggesting self-concept is the perception of oneself shaped by experience and evaluations, but proposed self-concept is organised, multifaceted and hierarchical (Marsh & Shavelson, 2010). An individual’s self-concept is comprised of academic, social, emotional and physical dimensions which each divide into further subsets of increasing specificity and are closer related to actual behaviour (see Figure 2 - '''''TBC'''''). This original model was later refined by developing and analysing the Self Description Questionnaire and produced a model which captures the correlations between each aspect of self-concept (see Figure 2; Marsh & Shavelson, 1985). This hierarchical model predicts behaviour and feelings more accurately than previous general theories (cite studies). ==== Properties of self-concept   ==== Although these theories each approach self-concept differently, several common properties emerge across them. Self-concept appears to be a multifaceted, hierarchical, socially developed, and dynamic system of self-knowledge (Figure __). These properties are particularly important as they assist us in understanding the motivational effects of self-concept.   {| class="wikitable" |+Figure __. Summary table of properties and their significance for motivation |'''Property''' |'''Theory''' |'''Significance for motivation''' |- |Multifaceted |James, Rogers, Multidimensional model |Different aspects of the self motivate different behaviours |- |Hierarchical   |Multidimensional model |General and specific domains influence each other and different behaviours |- |Socially developed |The looking glass self |Social feedback influences which behaviours are pursued   |- |Dynamic |Rogers, Multidimensional model |Self-concept changes with experience |- |Evaluative |Rogers |Perceived self-worth affects responses to success/failure |- |Descriptive   |Rogers, Multidimensional model |Identity beliefs influence goals and expectations |} == Key points == For the topic development, for each heading and sub-heading: * Provide at least three bullet-points, including for the Overview and Conclusion * Include key citations == Figures == [[File:Thought_bubble.svg|right|thumb|157x157px|'''Figure 2'''. Example of an image with a descriptive caption.]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[c:|Wikimedia Commons]] * Images can be uploaded to [[c:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) == Learning features == Interactive learning features help to bring book chapters to life and can be embedded throughout the chapter. {{anchor|Scenarios}} ; Scenarios * Scenarios, case studies, or examples describe concepts in action * Can be real or fictional; if real, provide citations * Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Present using [[Motivation and emotion/Book/2026/Self-concept and motivation#Feature boxes|feature boxes]] {{anchor|Feature box}} ; Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[Motivation and emotion/Book/2026/Self-concept and motivation#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ; Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[wikipedia:Dreams|dreams]]) of dreams was provided by [[wikipedia:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ; Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted '''Table 1''' A Descriptive Caption Which Explains The Table Contents and its Relevance to the Text e.g., The 2 x 2 Johari Window Model Showing Knowing x Self/Other {| class="wikitable" style="margin: auto;" ! !Known to self !Not known to self |- |'''Known to others''' |Open area |Blind spot |- |'''Not known to others''' |Hidden area |Unknown |} ; Quizzes * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] Example simple quiz questions. Choose your answers and click "Submit":<quiz display="simple"> {The purpose of quizzes is to provide an interactive learning feature: |type="()"} + True - False {Long and complex quiz questions are recommended: |type="()"} - True + False </quiz> == Conclusion == * The Conclusion is arguably the most important section * Draft clear take-home message(s), even at the topic development stage * Together, the [[Motivation and emotion/Book/2026/Self-concept and motivation#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages?}} == See also == Provide [[Help:Contents/Links#Interwiki links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[wikipedia:|Wikipedia articles]]. Use [[wikipedia:Letter case#Sentence_casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) * [[wikipedia:Self determination theory|Self determination theory]] (Wikipedia) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses}} == References == This section lists the cited references in [[wikipedia:APA style|APA style]] (7th ed.) or [[wikipedia:Wikipedia:Citing sources|wiki style]]. APA style example: {{Hanging indent|Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091 Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper & Row.}}{{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted}} == External links == Provide [[Help:Contents/Links#External links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[wikipedia:Letter case#Sentence_casing|sentence casing]] and alphabetical order. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link}} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Self-concept]] [[Category:Motivation and emotion/Book/2026]] [[Category:Motivation and emotion/Book/Motivation]] fqk1wpy3lwus12ighuvqv35w4o6x53w 2823640 2823639 2026-08-20T12:20:28Z U3253363 3106362 Fiddling with table formatting. 2823640 wikitext text/x-wiki {{title|Self-concept and motivation:<br>How does self-concept relate to motivation?}} == Overview == {{RoundBoxTop|theme=3}} [[File:Sinclair Swimming.JPG|right|thumb|180px|'''Figure 1'''. Ash is a competitive swimmer and swims daily.]] Ash is a swimmer training for a national competition. Being a swimmer is the first thing Ash thinks of when she’s asked to describe herself and she’s eager to succeed in the upcoming competition. Ash wakes up at 4:00am every morning to swim four kilometres (Figure 1). Her friend Riley is always surprised by how Ash wakes up so early and swims so much. Why is Ash able to do this when many would find this a struggle?{{RoundBoxBottom}} Your self-concept is your understanding of who you are and how you feel about yourself. This includes a complex system of the attitudes, beliefs and judgements you hold about yourself. Self-concept guides you in answering the question “who am I?” (Wehrle & Fasbender, 2018). But its importance extends beyond answering that question. Self-concept influences how you think, feel and behave. Consider self-concept an internal compass which motivates and guides your choices, relationships and understanding of the world.   For Ash in our case study, being a swimmer and succeeding in the upcoming swimming competition are core to her self-concept. This guides and motivates her behaviour of swimming early every morning.   This chapter explores how our understanding of ourselves influences what we’re motivated to do and examines how what we repeatedly do subsequently shapes our self-concept. By understanding how and why we perceive ourselves the way we do, and the impacts of our self-concepts, we can better understand our behaviours, foster positive self-concept and embrace the motivational properties of self-concept.   {{RoundBoxTop|theme=3}} '''Focus questions''' *What is self-concept? *What are the key theories of self-concept? *How does self-concept influence motivation? *How does motivation influence self-concept? *How can our understanding of self-concept be used to improve motivation and wellbeing?{{RoundBoxBottom}} == Understanding self-concept == The self is central to humanhood and the scientific understanding of human behaviour. Thus, the question of “what makes me, me?” has been theorised about throughout history and is important to understand. This section details the core theories and properties of self-concept which will be referred to throughout the chapter.   Self-concept is a cognitive framework which is unique to, but encompasses, many of the popularly used “self-” constructs – [[self-esteem]] (perceived value of yourself), [[w:Self-efficacy|self-efficacy]] (perceived task capability), [[w:Self-image|self-image]] (description of yourself). See the linked pages for details on each of these separate constructs. ==== William James ==== James (1892) proposed the self consists of two parts: “I”, the subjective thinker and “knower”, and “me” the material, social and “known” self. This philosophical framework laid the basis for the development of further empirical theories of self-concept and catapulted psychological identity research.   ==== The looking-glass self ==== Cooley (1902) framed the individual as a social being, theorising that self-concept is a reflection of the responses and evaluations of individuals within one’s environment. Self-concept is developed through the imagined judgement of others, and individuals become the people others say they are (Siljanovska & Stojcevska, 2018). ==== Rogers’ self-theory ==== Rogers (1959), a humanist psychologist, proposed self-concept is a dynamic, organised system which consists of three parts: the real self (how you see yourself), ideal self (who you would like to be), and self-worth (how much you value yourself). He proposed that individuals behave in accordance with their self-concept, a stepping stone toward the contemporary understanding of how self-beliefs influence motivation (Ismail & Tekke, 2015; Yousefi & Kiani, 2014).   ==== The multidimensional self-concept model ==== Shavelson et al. (1992) were critical of the lack of theoretical and methodological rigor supporting studies of self-concept. They built upon previous theories, suggesting self-concept is the perception of oneself shaped by experience and evaluations, but proposed self-concept is organised, multifaceted and hierarchical (Marsh & Shavelson, 2010). An individual’s self-concept is comprised of academic, social, emotional and physical dimensions which each divide into further subsets of increasing specificity and are closer related to actual behaviour (see Figure 2 - '''''TBC'''''). This original model was later refined by developing and analysing the Self Description Questionnaire and produced a model which captures the correlations between each aspect of self-concept (see Figure 2; Marsh & Shavelson, 1985). This hierarchical model predicts behaviour and feelings more accurately than previous general theories (cite studies). ==== Properties of self-concept   ==== Although these theories each approach self-concept differently, several common properties emerge across them. Self-concept appears to be a multifaceted, hierarchical, socially developed, and dynamic system of self-knowledge (Figure __). These properties are particularly important as they assist us in understanding the motivational effects of self-concept.   {| class="wikitable" |+'''Figure __.''' Summary table of properties and their significance for motivation |'''Property''' |'''Theory''' |'''Significance for motivation''' |- |Multifaceted |James, Rogers, Multidimensional model |Different aspects of the self motivate different behaviours |- |Hierarchical   |Multidimensional model |General and specific domains influence each other and different behaviours |- |Socially developed |The looking glass self |Social feedback influences which behaviours are pursued   |- |Dynamic |Rogers, Multidimensional model |Self-concept changes with experience |- |Evaluative |Rogers |Perceived self-worth affects responses to success/failure |- |Descriptive   |Rogers, Multidimensional model |Identity beliefs influence goals and expectations |} == Key points == For the topic development, for each heading and sub-heading: * Provide at least three bullet-points, including for the Overview and Conclusion * Include key citations == Figures == [[File:Thought_bubble.svg|right|thumb|157x157px|'''Figure 2'''. Example of an image with a descriptive caption.]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[c:|Wikimedia Commons]] * Images can be uploaded to [[c:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) == Learning features == Interactive learning features help to bring book chapters to life and can be embedded throughout the chapter. {{anchor|Scenarios}} ; Scenarios * Scenarios, case studies, or examples describe concepts in action * Can be real or fictional; if real, provide citations * Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Present using [[Motivation and emotion/Book/2026/Self-concept and motivation#Feature boxes|feature boxes]] {{anchor|Feature box}} ; Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[Motivation and emotion/Book/2026/Self-concept and motivation#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ; Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[wikipedia:Dreams|dreams]]) of dreams was provided by [[wikipedia:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ; Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted '''Table 1''' A Descriptive Caption Which Explains The Table Contents and its Relevance to the Text e.g., The 2 x 2 Johari Window Model Showing Knowing x Self/Other {| class="wikitable" style="margin: auto;" ! !Known to self !Not known to self |- |'''Known to others''' |Open area |Blind spot |- |'''Not known to others''' |Hidden area |Unknown |} ; Quizzes * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] Example simple quiz questions. Choose your answers and click "Submit":<quiz display="simple"> {The purpose of quizzes is to provide an interactive learning feature: |type="()"} + True - False {Long and complex quiz questions are recommended: |type="()"} - True + False </quiz> == Conclusion == * The Conclusion is arguably the most important section * Draft clear take-home message(s), even at the topic development stage * Together, the [[Motivation and emotion/Book/2026/Self-concept and motivation#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages?}} == See also == Provide [[Help:Contents/Links#Interwiki links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[wikipedia:|Wikipedia articles]]. Use [[wikipedia:Letter case#Sentence_casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) * [[wikipedia:Self determination theory|Self determination theory]] (Wikipedia) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses}} == References == This section lists the cited references in [[wikipedia:APA style|APA style]] (7th ed.) or [[wikipedia:Wikipedia:Citing sources|wiki style]]. APA style example: {{Hanging indent|Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091 Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper & Row.}}{{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted}} == External links == Provide [[Help:Contents/Links#External links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[wikipedia:Letter case#Sentence_casing|sentence casing]] and alphabetical order. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link}} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Self-concept]] [[Category:Motivation and emotion/Book/2026]] [[Category:Motivation and emotion/Book/Motivation]] kyhkrtc4plvpuhxtuxoq4g8429x6uq9 0 331049 2823864 2822938 2026-08-21T11:17:19Z U3263365 3104938 Added subtitle 2823864 wikitext text/x-wiki {{title|Adolescent risk-taking and reward-system development<br>How does reward circuit maturation influence adolescent sensation-seeking and impulsive behaviours?}} <div align=center>Edit above to match the wording (and [[w:Stylistic or specialised usage|casing]]) in the [[Motivation and emotion/Book/2026|2026 list of topics]].<br>[[Motivation and emotion/About/Staff|Seek approval]] for any changes.<br>Do not include your name (authorship is as per the [[Special:History/{{PAGENAME}}|page's history]]).</div> __TOC__ ==Overview== {{RoundBoxTop|theme=3}} [[File:A picture is worth a thousand words.jpg|right|thumb|150px|'''Figure 1'''. Use a captioned image to illustrate the scenario]] ; Imagine this ... or Scenario ... or Case study or ... ?) Start with an engaging [[#Scenarios|scenario, example, or case study]] which illustrates the problem and engages reader interest. Present the scenario in a [[#Feature box|feature box]]. To change the box colour: # Edit source # Change "theme=3" to another number Include an image and cite it (e.g., see Figure 1). {{RoundBoxBottom}} The Overview section should provide: # '''Scenario''': A short, engaging case study or real-world example in a feature box, with an accompanying image (see above) # '''Explanation of the problem, issue, or topc''': Briefly explain the problem, why it is important, and outline how psychological science can help # '''Focus questions''': Unpack the sub-title into focus questions in a feature box Recommended length: 180 to 330 words. This template provides key headings, examples, and tips for each section. Gradually remove this generic information as the chapter develops. It is OK to retain some template material for the topic development, but it should all be removed from the book chapter. Key resources: * [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] explains how to edit * [[Motivation and emotion/Assessment/Topic|Topic development guidelines]] * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] {{RoundBoxTop|theme=3}} '''Focus questions''' Break the sub-title down into three to five [[Motivation and emotion/Assessment/Chapter/Focus questions|focus questions]]. Align the top-level headings with these focus questions. * What is the first focus question? * What is the second focus question? * What is the third focus question? Ask [[w:Open-ended question|open-ended]] questions. For example: {{cross}} Is there a relationship between weather and criminal behaviour? (closed-ended)<br>{{tick}} What is the relationship between weather and criminal behaviour? (open-ended) {{RoundBoxBottom}} ==Headings== Use this heading structure: * [[#Overview|Overview]] * 3 to 6 major headings tailored to the topic; can have sub-headings: ** avoid sections with only one sub-heading (use 0 or 2+ sub-headings) ** provide an introductory paragraph before breaking into sub-sections * [[#Conclusion|Conclusion]] * [[#See also|See also]] * [[#References|References]] * [[#External links|External links]] ==Key points== * For the topic development, provide at least three bullet-points for each heading and sub-heading, including the Overview and Conclusion * Include key citations ==Figures== [[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]] * For the book chapter, use several figures to illustrate concepts, add interest, and to serve as examples * For the topic development, use at least one figure (even if not ideal) to show that you know how to embed, caption, and cite a figure * Figures can show any kind of media such as photos, diagrams, graphs, video, audio, and so on * Embed figures throughout the chapter, starting with the scenario in the Overview section * Provide descriptive figure captions (use '''Figure #''' and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== Learning features help to bring book chapters to life and can be embedded throughout the chapter. Here are some options: {{anchor|Scenarios}} ;Scenarios * Scenarios, case studies, or examples that illustrate concepts in action * Present using [[#Feature boxes|feature boxes]]; can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Can be real or fictional; if real, provide citation(s) {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted '''Table 1''' A Descriptive Caption Explains The Table Contents and its Relevance to the Text e.g., The 2 x 2 Johari Window Model Showing the Relationship Between Known/Unknown and Self/Other {| class="wikitable" style="margin: auto; |- ! !! Known to self !! Not known to self |- | '''Known to others''' || Open area || Blind spot |- | '''Not known to others''' || Hidden area || Unknown |} ;Quizzes * One or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as the take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] Example simple quiz questions. Choose your answers and click "Submit": <quiz display=simple> {The purpose of quizzes is to provide an interactive learning feature: |type="()"} + True - False {Long and complex quiz questions are recommended: |type="()"} - True + False </quiz> ==Conclusion== * Arguably the most important section * Provide at least three bullet-points for this section even at the topic development stage, based on preliminary thinking * For the book chapter, develop clear take-home message(s) that address the focus questions based on psychological theory and research * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing this problem * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== [[Help:Contents/Links#Interwiki_links|Internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) * [[w:Self determination theory|Self determination theory]] (Wikipedia) {{tip|Suggestions for this section: * Link to the most relevant internal resources about the topic * Include the source in parentheses }} ==References== Provide the references for all citations in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. Alternatively, you can use wiki style (as used on Wikipedia), as long as the information is complete and the formatting is consistent. APA style example: {{Hanging indent|1= Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091 Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper & Row. }} {{tip|Suggestions for this section: * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) ** Hanging indent: Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: *** Use "Edit source" *** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== [[Help:Contents/Links#External_links|External links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Link to the most relevant external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] b56m1xuem3b1e5kymmvilwypwv38ccw 2 331094 2823754 2823333 2026-08-20T23:21:48Z U3275909 3106769 2823754 wikitext text/x-wiki == About me == Hello! My name is '''Georgia Russell,''' and I am a third-year student at the [https://www.canberra.edu.au/future-students/study-at-uc?utm_source=google&utm_medium=search&utm_campaign=Always+On+Domestic+Search+2026&utm_term=broad+match&utm_content=undergrad&ef_id=CjwKCAjwqJXUBhBNEiwA8BgG7s38ZFwUdkDDrBRtqOENmM_QdB3O6RJP15KuNxQNvXoB15MYk-wAhxoCopgQAvD_BwE:G:s&s_kwcid=AL!10441!3!793584539699!b!!g!!uc%20degrees!20950774508!158167391013&gad_source=1&gad_campaignid=20950774508&gbraid=0AAAAADQmSqtSqxRjhI7_V9DA-TxXE_SRD&gclid=CjwKCAjwqJXUBhBNEiwA8BgG7s38ZFwUdkDDrBRtqOENmM_QdB3O6RJP15KuNxQNvXoB15MYk-wAhxoCopgQAvD_BwE University of Canberra] studying a double degree in Psychology and Health Science Human Movement and taking the class [[Motivation and emotion/Assessment/Chapter|Motivation and Emotion]]. I am particularly interested in the relationship between psychological wellbeing, physical performance, and sport. My origin long-term goal was to become a [[wikipedia:Sport_psychology|sport psychologist]] and support athletes with their mental health, motivation, confidence, and performance. However, I have been looking further into joining defence by becoming a performance psychologist for individuals in the airforce to help cope with anxiety, stress and pressure to succeed. [[File:With Coach Nikitan.jpg|thumb|'''Figure 1 .''' Sport psychology is an essential to channel physiological performance and mental performance ]] == Book chapter I’m working on == I am currently developing a book chapter titled [[Motivation and emotion/Book/2026/Mindsets and stigma|Mindsets and Stigma]] for the ''Motivation and Emotion'' book chapter project. The chapter explores how different mindsets influence stigma, including the way people perceive, judge, and respond to individuals experiencing mental health difficulties. It also examines how psychological research may help reduce stigma and encourage more understanding and supportive attitudes. == Social contributions == I am interested in contributing to the wellbeing of others through psychology, health promotion, and community involvement. While playing with the Bungendore Mudchooks Rugby Union team, throughout my season I have organised and held sessions with other players, coaches and management about mindfulness before important games and how to prepare the mind before the game as well as the strength of the body. This new system was valued and appreciated amongst coaches and players and has been entered as a training exercise and requirement within both the male and female teams. Through my studies, I hope to develop the knowledge and practical skills needed to support people from diverse backgrounds. I am particularly passionate about mental health awareness, reducing stigma, and helping create environments where people feel comfortable seeking support. == Online profiles == You can also find me through the following profiles: * University of Canberra * LinkedIn: Add your LinkedIn profile link here * Wikiversity contributions: <nowiki>[[Special:Contributions/YourUsername|View my contributions]]</nowiki> t2ux5l0ludpghvsmzstz251bz1hzgal 0 331098 2823752 2823634 2026-08-20T22:52:01Z U3284040 3106549 2823752 wikitext text/x-wiki {{title|Social connection and emotion regulation<br>How do social relationships help regulate people's emotions?}} __TOC__ ==Overview== {{RoundBoxTop|theme=3}} [[File:A picture is worth a thousand words.jpg|right|thumb|150px|'''Figure 1'''. Use a captioned image to illustrate the scenario]] ; Imagine this ... or Scenario ... or Case study or ... ?) Start with an engaging [[#Scenarios|scenario, example, or case study]] which illustrates the problem and engages reader interest. Present the scenario in a [[#Feature box|feature box]]. To change the box colour: # Edit source # Change "theme=3" to another number Include an image and cite it (e.g., see Figure 1). {{RoundBoxBottom}} The Overview section should provide: # '''Scenario''': A short, engaging case study or real-world example in a feature box, with an accompanying image (see above) # '''Explanation of the problem, issue, or topc''': Briefly explain the problem, why it is important, and outline how psychological science can help # '''Focus questions''': Unpack the sub-title into focus questions in a feature box Recommended length: 180 to 330 words. This template provides key headings, examples, and tips for each section. Gradually remove this generic information as the chapter develops. It is OK to retain some of the template material for the topic development, but it should all be removed for the final book chapter. Key resources: * [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 02]] explains about how to edit * [[Motivation and emotion/Assessment/Topic|Topic development guidelines]] * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] {{RoundBoxTop|theme=3}} '''Focus questions''' Break the sub-title down into three to five [[Motivation and emotion/Assessment/Chapter/Focus questions|focus questions]]. Align the top-level headings with these focus questions. * What is the first focus question? * What is the second focus question? * What is the third focus question? Ask [[w:Open-ended question|open-ended]] focus questions. For example: * Is there a relationship between weather and criminal behaviour? (closed-ended) * What is the relationship between weather and criminal behaviour? (open-ended) {{RoundBoxBottom}} ==What is Emotional Regulation?== * Key point 1 * Key Point 2 * Key Point 3 ==Benefits of Social Connection== * Key point 1 - subheading for co-regulation * Key Point 2 * Key Point 3 ==Loneliness and Poor Social Connection (Rename Title)== * Key point 1 - Loneliness * Key Point 2 - Social Anxiety * Key Point 3 ==Info For Assignment== '''Headings''' Use this heading structure: * [[#Overview|Overview]] * 3 to 6 major headings tailored to the topic; can have sub-headings, but: ** avoid having only one sub-heading ** provide an introductory paragraph before breaking into sub-sections * [[#Conclusion|Conclusion]] * See also * References * External links '''Key points''' For the topic development, for each heading and sub-heading: * Provide at least three bullet-points, including for the Overview and Conclusion * Include key citations '''Figures''' [[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) '''Learning features''' Interactive learning features help to bring book chapters to life and can be embedded throughout the chapter. {{anchor|Scenarios}} ;Scenarios * Scenarios, case studies, or examples describe concepts in action * Can be real or fictional; if real, provide citations * Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Present using [[#Feature boxes|feature boxes]] {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted '''Table 1''' A Descriptive Caption Which Explains The Table Contents and its Relevance to the Text e.g., The 2 x 2 Johari Window Model Showing Knowing x Self/Other {| class="wikitable" style="margin: auto; |- ! !! Known to self !! Not known to self |- | '''Known to others''' || Open area || Blind spot |- | '''Not known to others''' || Hidden area || Unknown |} ;Quizzes * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] Example simple quiz questions. Choose your answers and click "Submit": <quiz display=simple> {The purpose of quizzes is to provide an interactive learning feature: |type="()"} + True - False {Long and complex quiz questions are recommended: |type="()"} - True + False </quiz> ==Conclusion== * The Conclusion is arguably the most important section * Draft clear take-home message(s), even at the topic development stage * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== * [[Motivation and emotion/Book/2019/Social support and emotion]] - Use for inspiration * [[Motivation and emotion/Book/2025/Social media and emotion regulation]] - Use for inspiration Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) * [[w:Self determination theory|Self determination theory]] (Wikipedia) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses }} ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. APA style example: {{Hanging indent|1= Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091 Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper & Row. }} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Emotional self-regulation]] [[Category:Motivation and emotion/Book/Social connection]] 0wnudnl7clxqa3wqn801bwe82cw5pqg 2823827 2823752 2026-08-21T04:44:54Z Jtneill 10242 Replace colon to separate title and subtitle 2823827 wikitext text/x-wiki {{title|Social connection and emotion regulation:<br>How do social relationships help regulate people's emotions?}} __TOC__ ==Overview== {{RoundBoxTop|theme=3}} [[File:A picture is worth a thousand words.jpg|right|thumb|150px|'''Figure 1'''. Use a captioned image to illustrate the scenario]] ; Imagine this ... or Scenario ... or Case study or ... ?) Start with an engaging [[#Scenarios|scenario, example, or case study]] which illustrates the problem and engages reader interest. Present the scenario in a [[#Feature box|feature box]]. To change the box colour: # Edit source # Change "theme=3" to another number Include an image and cite it (e.g., see Figure 1). {{RoundBoxBottom}} The Overview section should provide: # '''Scenario''': A short, engaging case study or real-world example in a feature box, with an accompanying image (see above) # '''Explanation of the problem, issue, or topc''': Briefly explain the problem, why it is important, and outline how psychological science can help # '''Focus questions''': Unpack the sub-title into focus questions in a feature box Recommended length: 180 to 330 words. This template provides key headings, examples, and tips for each section. Gradually remove this generic information as the chapter develops. It is OK to retain some of the template material for the topic development, but it should all be removed for the final book chapter. Key resources: * [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 02]] explains about how to edit * [[Motivation and emotion/Assessment/Topic|Topic development guidelines]] * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] {{RoundBoxTop|theme=3}} '''Focus questions''' Break the sub-title down into three to five [[Motivation and emotion/Assessment/Chapter/Focus questions|focus questions]]. Align the top-level headings with these focus questions. * What is the first focus question? * What is the second focus question? * What is the third focus question? Ask [[w:Open-ended question|open-ended]] focus questions. For example: * Is there a relationship between weather and criminal behaviour? (closed-ended) * What is the relationship between weather and criminal behaviour? (open-ended) {{RoundBoxBottom}} ==What is Emotional Regulation?== * Key point 1 * Key Point 2 * Key Point 3 ==Benefits of Social Connection== * Key point 1 - subheading for co-regulation * Key Point 2 * Key Point 3 ==Loneliness and Poor Social Connection (Rename Title)== * Key point 1 - Loneliness * Key Point 2 - Social Anxiety * Key Point 3 ==Info For Assignment== '''Headings''' Use this heading structure: * [[#Overview|Overview]] * 3 to 6 major headings tailored to the topic; can have sub-headings, but: ** avoid having only one sub-heading ** provide an introductory paragraph before breaking into sub-sections * [[#Conclusion|Conclusion]] * See also * References * External links '''Key points''' For the topic development, for each heading and sub-heading: * Provide at least three bullet-points, including for the Overview and Conclusion * Include key citations '''Figures''' [[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) '''Learning features''' Interactive learning features help to bring book chapters to life and can be embedded throughout the chapter. {{anchor|Scenarios}} ;Scenarios * Scenarios, case studies, or examples describe concepts in action * Can be real or fictional; if real, provide citations * Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Present using [[#Feature boxes|feature boxes]] {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted '''Table 1''' A Descriptive Caption Which Explains The Table Contents and its Relevance to the Text e.g., The 2 x 2 Johari Window Model Showing Knowing x Self/Other {| class="wikitable" style="margin: auto; |- ! !! Known to self !! Not known to self |- | '''Known to others''' || Open area || Blind spot |- | '''Not known to others''' || Hidden area || Unknown |} ;Quizzes * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] Example simple quiz questions. Choose your answers and click "Submit": <quiz display=simple> {The purpose of quizzes is to provide an interactive learning feature: |type="()"} + True - False {Long and complex quiz questions are recommended: |type="()"} - True + False </quiz> ==Conclusion== * The Conclusion is arguably the most important section * Draft clear take-home message(s), even at the topic development stage * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== * [[Motivation and emotion/Book/2019/Social support and emotion]] - Use for inspiration * [[Motivation and emotion/Book/2025/Social media and emotion regulation]] - Use for inspiration Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) * [[w:Self determination theory|Self determination theory]] (Wikipedia) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses }} ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. APA style example: {{Hanging indent|1= Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091 Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper & Row. }} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Emotional self-regulation]] [[Category:Motivation and emotion/Book/Social connection]] sdx6maf2za4w4c8h4p7o76yri3otsas 0 331099 2823771 2823453 2026-08-21T01:03:11Z U3285438 3103750 /* See also */ added internal wiki links to book chapter and Wikipedia link. 2823771 wikitext text/x-wiki {{title|Emotion dysregulation:<br>What is emotion dysregulation, what are its consequences, and how can it be managed?}} __TOC__ ==Overview== {{RoundBoxTop|theme=2}} [[File:Microsoft Fluent UI – ic fluent desktop cursor 20 regular.svg|Microsoft_Fluent_UI_–_ic_fluent_desktop_cursor_20_regular|150px|right|thumb|'''Figure 1.''' Repeatedly clicking the laptop trackpad to elicit a response.]] '''Scenario: Disproportionate anger response''' You are trying to upload an assignment for your statistics class last minute and the submissions portal freezes exactly as you press “submit”. You watch the cursor’s loading icon spin again and again, likely because the portal is overwhelmed by other last minute submissions. Though you still have 15 minutes before the deadline, you find yourself continuing to aggressively spam click the laptop trackpad and become consumed by a feeling of frustration (see Figure 1). You can feel your heart rate increase, your jaw tighten and leg shake beneath the desk. Then the trackpad becomes stuck and will not click anymore. You shove your laptop aside and question why nothing ever goes your way. Later, you wonder why you did not just wait a few minutes for the submissions portal to respond. {{RoundBoxBottom}} The Overview section should provide: # '''Scenario''': A short, engaging case study or real-world example in a feature box, with an accompanying image (see above) # '''Explanation of the problem, issue, or topic''': Briefly explain the problem, why it is important, and outline how psychological science can help # '''Focus questions''': Unpack the sub-title into focus questions in a feature box Recommended length: 180 to 330 words. This template provides key headings, examples, and tips for each section. Gradually remove this generic information as the chapter develops. It is OK to retain some of the template material for the topic development, but it should all be removed for the final book chapter. Key resources: * [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 02]] explains about how to edit * [[Motivation and emotion/Assessment/Topic|Topic development guidelines]] * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] {{RoundBoxTop|theme=2}}'''Focus questions''' 1. How can emotion dysregulation be defined? 2. How does emotion dysregulation impact daily functioning? 3. What is the associated between emotion dysregulation and psychological disorders? 4. What strategies can help manage emotion dysregulation? 5. How does emotion dysregulation present across contexts?{{RoundBoxBottom}} ==Headings== Use this heading structure: * [[#Overview|Overview]] * 3 to 6 major headings tailored to the topic; can have sub-headings, but: ** avoid having only one sub-heading ** provide an introductory paragraph before breaking into sub-sections * [[#Conclusion|Conclusion]] * See also * References * External links ==Key points== For the topic development, for each heading and sub-heading: * Provide at least three bullet-points, including for the Overview and Conclusion * Include key citations ==Figures== [[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== Interactive learning features help to bring book chapters to life and can be embedded throughout the chapter. {{anchor|Scenarios}} ;Scenarios * Scenarios, case studies, or examples describe concepts in action * Can be real or fictional; if real, provide citations * Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Present using [[#Feature boxes|feature boxes]] {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted '''Table 1''' A Descriptive Caption Which Explains The Table Contents and its Relevance to the Text e.g., The 2 x 2 Johari Window Model Showing Knowing x Self/Other {| class="wikitable" style="margin: auto; |- ! !! Known to self !! Not known to self |- | '''Known to others''' || Open area || Blind spot |- | '''Not known to others''' || Hidden area || Unknown |} ;Quizzes * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] Example simple quiz questions. Choose your answers and click "Submit": <quiz display=simple> {The purpose of quizzes is to provide an interactive learning feature: |type="()"} + True - False {Long and complex quiz questions are recommended: |type="()"} - True + False </quiz> ==Conclusion== * The Conclusion is arguably the most important section * Draft clear take-home message(s), even at the topic development stage * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== * [[Motivation and emotion/Book/2025/Cognitive strategies and emotion regulation|Cognitive strategies and emotion regulation]] (Book chapter, 2025) * [[Motivation and emotion/Book/2025/Dialectical behaviour therapy and emotion regulation|Dialectical behaviour therapy and emotion regulation]] (Book chapter, 2025) * [[w:Emotional_self-regulation|Emotional self-regulation]] (Wikipedia) * [[Motivation and emotion/Book/2025/Social media and emotional dysregulation|Social media and emotional dysregulation]] (Book chapter, 2025) ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. APA style example: {{Hanging indent|1= Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091 Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper & Row. }} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== * [https://www.ted.com/talks/ted_ed_how_to_manage_your_emotions How to manage your emotions] (TED-Ed) [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Emotional self-regulation]] j0y8esv8xdqgqwcvo86rlduskh86fxk 2823785 2823771 2026-08-21T01:47:46Z U3285438 3103750 /* Overview */ drafting headings and some subheadings. 2823785 wikitext text/x-wiki {{title|Emotion dysregulation:<br>What is emotion dysregulation, what are its consequences, and how can it be managed?}} __TOC__ ==Overview== {{RoundBoxTop|theme=2}} [[File:Microsoft Fluent UI – ic fluent desktop cursor 20 regular.svg|Microsoft_Fluent_UI_–_ic_fluent_desktop_cursor_20_regular|150px|right|thumb|'''Figure 1.''' Repeatedly clicking the laptop trackpad to elicit a response.]] '''Scenario: Disproportionate anger response''' You are trying to upload an assignment for your statistics class last minute and the submissions portal freezes exactly as you press “submit”. You watch the cursor’s loading icon spin again and again, likely because the portal is overwhelmed by other last minute submissions. Though you still have 15 minutes before the deadline, you find yourself continuing to aggressively spam click the laptop trackpad and become consumed by a feeling of frustration (see Figure 1). You can feel your heart rate increase, your jaw tighten and leg shake beneath the desk. Then the trackpad becomes stuck and will not click anymore. You shove your laptop aside and question why nothing ever goes your way. Later, you wonder why you did not just wait a few minutes for the submissions portal to respond. {{RoundBoxBottom}} The Overview section should provide: # '''Scenario''': A short, engaging case study or real-world example in a feature box, with an accompanying image (see above) # '''Explanation of the problem, issue, or topic''': Briefly explain the problem, why it is important, and outline how psychological science can help # '''Focus questions''': Unpack the sub-title into focus questions in a feature box Recommended length: 180 to 330 words. This template provides key headings, examples, and tips for each section. Gradually remove this generic information as the chapter develops. It is OK to retain some of the template material for the topic development, but it should all be removed for the final book chapter. Key resources: * [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 02]] explains about how to edit * [[Motivation and emotion/Assessment/Topic|Topic development guidelines]] * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] {{RoundBoxTop|theme=2}}'''Focus questions''' 1. How can emotion dysregulation be defined? 2. How can psychological theories help explain experiences of emotion dysregulation? 3. How does emotion dysregulation impact daily functioning? 4. What is the associated between emotion dysregulation and psychological disorders? 5. What strategies can help manage emotion dysregulation? {{RoundBoxBottom}} ==Defining emotion dysregulation == * (Initial paragraph) === Core features of emotion dysregulation === * === Emotion dysregulation in adults vs. children === * ==Psychological models to help explain emotion dysregulation == * ==Impact of emotion dysregulation on our day-to-day lives== * ==Association between psychological disorders and emotion dysregulation== * == Strategies to manage emotion dysregulation == * ==Conclusion== * The Conclusion is arguably the most important section * Draft clear take-home message(s), even at the topic development stage * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== * [[Motivation and emotion/Book/2025/Cognitive strategies and emotion regulation|Cognitive strategies and emotion regulation]] (Book chapter, 2025) * [[Motivation and emotion/Book/2025/Dialectical behaviour therapy and emotion regulation|Dialectical behaviour therapy and emotion regulation]] (Book chapter, 2025) * [[w:Emotional_self-regulation|Emotional self-regulation]] (Wikipedia) * [[Motivation and emotion/Book/2025/Social media and emotional dysregulation|Social media and emotional dysregulation]] (Book chapter, 2025) ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. APA style example: {{Hanging indent|1= Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091 Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper & Row. }} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== * [https://www.ted.com/talks/ted_ed_how_to_manage_your_emotions How to manage your emotions] (TED-Ed) [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Emotional self-regulation]] e2ybj9s23e3b82mfmjzw76nw48vqpu3 2823790 2823785 2026-08-21T01:58:47Z U3285438 3103750 /* Overview */ change figure 1 to be more engaging. 2823790 wikitext text/x-wiki {{title|Emotion dysregulation:<br>What is emotion dysregulation, what are its consequences, and how can it be managed?}} __TOC__ ==Overview== {{RoundBoxTop|theme=2}} [[File:Burnout At Work - Occupational Burnout.jpg|Burnout_At_Work_-_Occupational_Burnout|150px|right|thumb|'''Figure 1.''' Frustrated after repeatedly clicking trackpad to elicit a response.]] '''Scenario: Disproportionate anger response''' You are trying to upload an assignment for your statistics class last minute and the submissions portal freezes exactly as you press “submit”. You watch the cursor’s loading icon spin again and again, likely because the portal is overwhelmed by other last minute submissions. Though you still have 15 minutes before the deadline, you find yourself continuing to aggressively spam click the laptop trackpad and become consumed by a feeling of frustration (see Figure 1). You can feel your heart rate increase, your jaw tighten and leg shake beneath the desk. Then the trackpad becomes stuck and will not click anymore. You shove your laptop aside and question why nothing ever goes your way. Later, you wonder why you did not just wait a few minutes for the submissions portal to respond. {{RoundBoxBottom}} The Overview section should provide: # '''Scenario''': A short, engaging case study or real-world example in a feature box, with an accompanying image (see above) # '''Explanation of the problem, issue, or topic''': Briefly explain the problem, why it is important, and outline how psychological science can help # '''Focus questions''': Unpack the sub-title into focus questions in a feature box Recommended length: 180 to 330 words. This template provides key headings, examples, and tips for each section. Gradually remove this generic information as the chapter develops. It is OK to retain some of the template material for the topic development, but it should all be removed for the final book chapter. Key resources: * [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 02]] explains about how to edit * [[Motivation and emotion/Assessment/Topic|Topic development guidelines]] * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] {{RoundBoxTop|theme=2}}'''Focus questions''' 1. How can emotion dysregulation be defined? 2. How can psychological theories help explain experiences of emotion dysregulation? 3. How does emotion dysregulation impact daily functioning? 4. What is the associated between emotion dysregulation and psychological disorders? 5. What strategies can help manage emotion dysregulation? {{RoundBoxBottom}} ==Defining emotion dysregulation == * (Initial paragraph) === Core features of emotion dysregulation === * === Emotion dysregulation in adults vs. children === * ==Psychological models to help explain emotion dysregulation == * ==Impact of emotion dysregulation on our day-to-day lives== * ==Association between psychological disorders and emotion dysregulation== * == Strategies to manage emotion dysregulation == * ==Conclusion== * The Conclusion is arguably the most important section * Draft clear take-home message(s), even at the topic development stage * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== * [[Motivation and emotion/Book/2025/Cognitive strategies and emotion regulation|Cognitive strategies and emotion regulation]] (Book chapter, 2025) * [[Motivation and emotion/Book/2025/Dialectical behaviour therapy and emotion regulation|Dialectical behaviour therapy and emotion regulation]] (Book chapter, 2025) * [[w:Emotional_self-regulation|Emotional self-regulation]] (Wikipedia) * [[Motivation and emotion/Book/2025/Social media and emotional dysregulation|Social media and emotional dysregulation]] (Book chapter, 2025) ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. APA style example: {{Hanging indent|1= Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091 Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper & Row. }} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== * [https://www.ted.com/talks/ted_ed_how_to_manage_your_emotions How to manage your emotions] (TED-Ed) [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Emotional self-regulation]] 3s35tzr5oqbbu2jkp9gznpj96b3yb9n 0 331100 2823786 2823625 2026-08-21T01:51:58Z U3239236 3106753 /* Focus Questions */ 2823786 wikitext text/x-wiki {{title|Emotional intelligence }}'''How does emotional intelligence affect emotional wellbeing?'''<div align=center>Edit the title and sub-title to match the wording (and casing) in the [[Motivation and emotion/Book/2025|2026 list of topics]].<br>[[Motivation and emotion/About/Staff|Seek approval]] for any changes.<br>Do not include your name (authorship is as per [[Special:History/{{PAGENAME}}|the page history]]).</div> __TOC__ ==Overview== {{RoundBoxTop|theme=3}}Imagine Sophie, a university student who has several assessments due while also dealing with conflict with a close friend. After receiving a disappointing mark, Sophie initially feels frustrated, embarrassed, and overwhelmed. Rather than immediately reacting, she recognises that disappointment and stress are influencing how she is thinking about the situation. She takes some time to regulate her emotions, considers why the result affected her so strongly, and later talks calmly with her friend about the conflict. Another student experiencing the same circumstances might struggle to identify what they are feeling, become increasingly overwhelmed, or react impulsively. Why might people respond so differently to similar emotional situations? One possible explanation involves emotional intelligence (EI) the ability to perceive, understand, use, and regulate emotion. Emotional intelligence may influence how people interpret and respond to emotional experiences and, consequently, their emotional wellbeing. Emotional wellbeing involves more than simply experiencing positive emotions or avoiding negative ones. It concerns how people experience and manage emotions and their broader capacity to function psychologically. Understanding the relationship between emotional intelligence and emotional wellbeing is important because difficult emotions are unavoidable. Psychological research can help explain whether emotionally intelligent abilities support wellbeing, which components of emotional intelligence may be particularly important, and the psychological processes that could explain this relationship. {{RoundBoxBottom}} The Overview section should provide: # '''Scenario''': A short, engaging case study or real-world example in a feature box, with an accompanying image (see above) # '''Explanation of the problem, issue, or topc''': Briefly explain the problem, why it is important, and outline how psychological science can help # '''Focus questions''': Unpack the sub-title into focus questions in a feature box Recommended length: 180 to 330 words. This template provides key headings, examples, and tips for each section. Gradually remove this generic information as the chapter develops. It is OK to retain some of the template material for the topic development, but it should all be removed for the final book chapter. Key resources: * [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 02]] explains about how to edit * [[Motivation and emotion/Assessment/Topic|Topic development guidelines]] * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] === Emotional intelligence and emotional wellbeing === Emotional intelligence may play an important role in how people recognise, understand, and regulate their emotions. These emotional abilities may influence how people cope with difficult experiences, maintain positive emotions, and support their overall emotional wellbeing. However, emotional intelligence is a complex construct, and different emotional abilities may contribute to wellbeing in different ways. * '''What are emotional intelligence and emotional wellbeing?''' (Define emotional intelligence and emotional wellbeing. Explain that emotional intelligence generally involves recognising, understanding, using, and managing emotions. Explain emotional wellbeing and clarify that wellbeing does not simply mean always experiencing positive emotions. Introduce the idea that there are different models of emotional intelligence.) '''Research needed:''' A foundational source defining emotional intelligence, such as '''Mayer and Salovey''', plus a reliable source defining emotional/subjective wellbeing. * '''What is the relationship between emotional intelligence and emotional wellbeing?''' (Discuss research showing whether higher emotional intelligence is associated with greater emotional or psychological wellbeing. Consider outcomes such as positive affect, life satisfaction, happiness, stress, and negative emotional experiences. Be careful to distinguish an association from evidence that emotional intelligence directly causes better wellbeing.) '''Research needed:''' Meta-analyses or empirical studies examining the association between emotional intelligence and wellbeing. * '''How does emotional intelligence influence emotional wellbeing?''' (Discuss the psychological processes that may explain the relationship. Emotional intelligence may help people recognise what they are feeling, understand why they are experiencing an emotion, regulate difficult emotions, cope with stress, and manage interpersonal situations. These processes may help explain why emotional intelligence is associated with wellbeing.) '''Research needed:''' Research connecting emotional intelligence with emotion regulation, coping, stress management, and social functioning, as well as research linking these processes with wellbeing. * '''Which components of emotional intelligence are particularly important for emotional wellbeing?''' (Discuss whether different components of emotional intelligence contribute differently to wellbeing. Consider emotion perception, using emotion, emotion understanding, and emotion management/regulation. Emotion regulation may be particularly relevant, but this needs to be evaluated using research rather than assumed.) '''Research needed:''' Studies comparing different dimensions or branches of emotional intelligence and their relationships with wellbeing, particularly emotion regulation/management. * '''How can emotional intelligence be developed to support emotional wellbeing?''' ''(Discuss whether emotional intelligence can be improved through training or psychological interventions. Consider strategies aimed at emotional awareness, understanding emotions, emotion regulation, and interpersonal skills. Examine whether improving these abilities actually leads to improvements in wellbeing and acknowledge limitations in the evidence.)'' '''Research needed:''' Intervention studies and preferably systematic reviews or meta-analyses of emotional intelligence training and its effects on emotional or psychological wellbeing. == Focus Questions == * What are emotional intelligence and emotional wellbeing? * What is the relationship between emotional intelligence and emotional wellbeing? * How does emotional intelligence influence emotional wellbeing? * How can emotional intelligence be developed to support emotional wellbeing? * Which components of emotional intelligence are particularly important for emotional wellbeing? * How can emotional intelligence be developed to support emotional wellbeing? == What are emotional intelligence and emotional wellbeing? == Before examining their relationship, it is important to establish what psychologists mean by emotional intelligence and emotional wellbeing. Both are multidimensional concepts, and different theoretical approaches influence how they are measured and understood. == Defining emotional intelligence == * Introduce emotional intelligence. * Explain that EI concerns the processing and management of emotional information. * Explain that EI is not simply "being emotional" or "being a nice person". * Introduce major conceptualisations of EI. * Explain why differences in definitions matter when examining research. === Ability model of emotional intelligence === Introduce Mayer and Salovey's ability model. Explain the four branches: # Perceiving emotions # Using emotions to facilitate thought # Understanding emotions # Managing emotions Explain briefly how each ability could theoretically contribute to wellbeing. '''Figure 1. The four-branch model of emotional intelligence''' Create a simple diagram showing: Perceiving emotions → Using emotions → Understanding emotions → Managing emotions == Trait emotional intelligence == * Explain trait EI. * Distinguish trait EI from ability EI. * Explain that trait EI concerns people's perceptions of their emotional abilities and tendencies. * Briefly introduce why trait EI is relevant to emotional wellbeing. == Defining emotional wellbeing == * Define emotional wellbeing. * Explain that wellbeing is not simply the absence of mental illness. * Discuss positive and negative affect. * Discuss emotional functioning and life satisfaction where relevant. * Explain that experiencing negative emotions does not automatically indicate poor emotional wellbeing. === Emotional wellbeing versus always feeling positive === A useful distinction should be established here: Emotionally healthy people can still experience sadness, anger, anxiety, disappointment, and stress. Healthy emotional functioning may instead involve recognising emotions, understanding their causes, regulating them appropriately, and recovering from difficult experiences. == Key points == For the topic development, for each heading and sub-heading: * Provide at least three bullet-points, including for the Overview and Conclusion * Include key citations ==Figures== [[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== Interactive learning features help to bring book chapters to life and can be embedded throughout the chapter. {{anchor|Scenarios}} ;Scenarios * Scenarios, case studies, or examples describe concepts in action * Can be real or fictional; if real, provide citations * Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Present using [[#Feature boxes|feature boxes]] {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted '''Table 1''' A Descriptive Caption Which Explains The Table Contents and its Relevance to the Text e.g., The 2 x 2 Johari Window Model Showing Knowing x Self/Other {| class="wikitable" style="margin: auto; |- ! !! Known to self !! Not known to self |- | '''Known to others''' || Open area || Blind spot |- | '''Not known to others''' || Hidden area || Unknown |} ;Quizzes * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] Example simple quiz questions. Choose your answers and click "Submit": <quiz display=simple> {The purpose of quizzes is to provide an interactive learning feature: |type="()"} + True - False {Long and complex quiz questions are recommended: |type="()"} - True + False </quiz> ==Conclusion== * The Conclusion is arguably the most important section * Draft clear take-home message(s), even at the topic development stage * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) * [[w:Self determination theory|Self determination theory]] (Wikipedia) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses }} ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. APA style example: {{Hanging indent|1= Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091 Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper & Row. }} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Emotional intelligence]] [[Category:Motivation and emotion/Book/Well-being]] gthvt18cici1f0j7tbf166f1z2pga27 2823803 2823786 2026-08-21T04:04:56Z U3239236 3106753 2823803 wikitext text/x-wiki {{title|Emotional intelligence }} '''How does emotional intelligence affect emotional wellbeing?'''<div align=center>Edit the title and sub-title to match the wording (and casing) in the [[Motivation and emotion/Book/2025|2026 list of topics]].<br>[[Motivation and emotion/About/Staff|Seek approval]] for any changes.<br>Do not include your name (authorship is as per [[Special:History/{{PAGENAME}}|the page history]]).</div> __TOC__ ==Overview== {{RoundBoxTop|theme=3}}Imagine Sophie, a university student who has several assessments due while also dealing with conflict with a close friend. After receiving a disappointing mark, Sophie initially feels frustrated, embarrassed, and overwhelmed. Rather than immediately reacting, she recognises that disappointment and stress are influencing how she is thinking about the situation. She takes some time to regulate her emotions, considers why the result affected her so strongly, and later talks calmly with her friend about the conflict. Another student experiencing the same circumstances might struggle to identify what they are feeling, become increasingly overwhelmed, or react impulsively. Why might people respond so differently to similar emotional situations? One possible explanation involves emotional intelligence (EI) the ability to perceive, understand, use, and regulate emotion. Emotional intelligence may influence how people interpret and respond to emotional experiences and, consequently, their emotional wellbeing. Emotional wellbeing involves more than simply experiencing positive emotions or avoiding negative ones. It concerns how people experience and manage emotions and their broader capacity to function psychologically. Understanding the relationship between emotional intelligence and emotional wellbeing is important because difficult emotions are unavoidable. Psychological research can help explain whether emotionally intelligent abilities support wellbeing, which components of emotional intelligence may be particularly important, and the psychological processes that could explain this relationship. {{RoundBoxBottom}} The Overview section should provide: # '''Scenario''': A short, engaging case study or real-world example in a feature box, with an accompanying image (see above) # '''Explanation of the problem, issue, or topc''': Briefly explain the problem, why it is important, and outline how psychological science can help # '''Focus questions''': Unpack the sub-title into focus questions in a feature box Recommended length: 180 to 330 words. This template provides key headings, examples, and tips for each section. Gradually remove this generic information as the chapter develops. It is OK to retain some of the template material for the topic development, but it should all be removed for the final book chapter. Key resources: * [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 02]] explains about how to edit * [[Motivation and emotion/Assessment/Topic|Topic development guidelines]] * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] === Emotional intelligence and emotional wellbeing === Emotional intelligence may play an important role in how people recognise, understand, and regulate their emotions. These emotional abilities may influence how people cope with difficult experiences, maintain positive emotions, and support their overall emotional wellbeing. However, emotional intelligence is a complex construct, and different emotional abilities may contribute to wellbeing in different ways. * '''What are emotional intelligence and emotional wellbeing?''' (Define emotional intelligence and emotional wellbeing. Explain that emotional intelligence generally involves recognising, understanding, using, and managing emotions. Explain emotional wellbeing and clarify that wellbeing does not simply mean always experiencing positive emotions. Introduce the idea that there are different models of emotional intelligence.) '''Research needed:''' A foundational source defining emotional intelligence, such as '''Mayer and Salovey''', plus a reliable source defining emotional/subjective wellbeing. * '''What is the relationship between emotional intelligence and emotional wellbeing?''' (Discuss research showing whether higher emotional intelligence is associated with greater emotional or psychological wellbeing. Consider outcomes such as positive affect, life satisfaction, happiness, stress, and negative emotional experiences. Be careful to distinguish an association from evidence that emotional intelligence directly causes better wellbeing.) '''Research needed:''' Meta-analyses or empirical studies examining the association between emotional intelligence and wellbeing. * '''How does emotional intelligence influence emotional wellbeing?''' (Discuss the psychological processes that may explain the relationship. Emotional intelligence may help people recognise what they are feeling, understand why they are experiencing an emotion, regulate difficult emotions, cope with stress, and manage interpersonal situations. These processes may help explain why emotional intelligence is associated with wellbeing.) '''Research needed:''' Research connecting emotional intelligence with emotion regulation, coping, stress management, and social functioning, as well as research linking these processes with wellbeing. * '''Which components of emotional intelligence are particularly important for emotional wellbeing?''' (Discuss whether different components of emotional intelligence contribute differently to wellbeing. Consider emotion perception, using emotion, emotion understanding, and emotion management/regulation. Emotion regulation may be particularly relevant, but this needs to be evaluated using research rather than assumed.) '''Research needed:''' Studies comparing different dimensions or branches of emotional intelligence and their relationships with wellbeing, particularly emotion regulation/management. * '''How can emotional intelligence be developed to support emotional wellbeing?''' ''(Discuss whether emotional intelligence can be improved through training or psychological interventions. Consider strategies aimed at emotional awareness, understanding emotions, emotion regulation, and interpersonal skills. Examine whether improving these abilities actually leads to improvements in wellbeing and acknowledge limitations in the evidence.)'' '''Research needed:''' Intervention studies and preferably systematic reviews or meta-analyses of emotional intelligence training and its effects on emotional or psychological wellbeing. == Focus Questions == * What are emotional intelligence and emotional wellbeing? * What is the relationship between emotional intelligence and emotional wellbeing? * How does emotional intelligence influence emotional wellbeing? * How can emotional intelligence be developed to support emotional wellbeing? * Which components of emotional intelligence are particularly important for emotional wellbeing? * How can emotional intelligence be developed to support emotional wellbeing? == What are emotional intelligence and emotional wellbeing? == Before examining their relationship, it is important to establish what psychologists mean by emotional intelligence and emotional wellbeing. Both are multidimensional concepts, and different theoretical approaches influence how they are measured and understood. == Defining emotional intelligence == * Introduce emotional intelligence. * Explain that EI concerns the processing and management of emotional information. * Explain that EI is not simply "being emotional" or "being a nice person". * Introduce major conceptualisations of EI. * Explain why differences in definitions matter when examining research. === Ability model of emotional intelligence === Introduce Mayer and Salovey's ability model. Explain the four branches: # Perceiving emotions # Using emotions to facilitate thought # Understanding emotions # Managing emotions Explain briefly how each ability could theoretically contribute to wellbeing. '''Figure 1. The four-branch model of emotional intelligence''' Create a simple diagram showing: Perceiving emotions → Using emotions → Understanding emotions → Managing emotions == Trait emotional intelligence == * Explain trait EI. * Distinguish trait EI from ability EI. * Explain that trait EI concerns people's perceptions of their emotional abilities and tendencies. * Briefly introduce why trait EI is relevant to emotional wellbeing. == Defining emotional wellbeing == * Define emotional wellbeing. * Explain that wellbeing is not simply the absence of mental illness. * Discuss positive and negative affect. * Discuss emotional functioning and life satisfaction where relevant. * Explain that experiencing negative emotions does not automatically indicate poor emotional wellbeing. === Emotional wellbeing versus always feeling positive === A useful distinction should be established here: Emotionally healthy people can still experience sadness, anger, anxiety, disappointment, and stress. Healthy emotional functioning may instead involve recognising emotions, understanding their causes, regulating them appropriately, and recovering from difficult experiences. == Key points == For the topic development, for each heading and sub-heading: * Provide at least three bullet-points, including for the Overview and Conclusion * Include key citations ==Figures== [[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== Interactive learning features help to bring book chapters to life and can be embedded throughout the chapter. {{anchor|Scenarios}} ;Scenarios * Scenarios, case studies, or examples describe concepts in action * Can be real or fictional; if real, provide citations * Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Present using [[#Feature boxes|feature boxes]] {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted '''Table 1''' A Descriptive Caption Which Explains The Table Contents and its Relevance to the Text e.g., The 2 x 2 Johari Window Model Showing Knowing x Self/Other {| class="wikitable" style="margin: auto; |- ! !! Known to self !! Not known to self |- | '''Known to others''' || Open area || Blind spot |- | '''Not known to others''' || Hidden area || Unknown |} ;Quizzes * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] Example simple quiz questions. Choose your answers and click "Submit": <quiz display=simple> {The purpose of quizzes is to provide an interactive learning feature: |type="()"} + True - False {Long and complex quiz questions are recommended: |type="()"} - True + False </quiz> ==Conclusion== * The Conclusion is arguably the most important section * Draft clear take-home message(s), even at the topic development stage * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) * [[w:Self determination theory|Self determination theory]] (Wikipedia) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses }} ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. APA style example: {{Hanging indent|1= Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091 Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper & Row. }} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Emotional intelligence]] [[Category:Motivation and emotion/Book/Well-being]] lpd82krytzq51gh7m5w6z8jr42ksfjb 2823805 2823803 2026-08-21T04:10:58Z U3239236 3106753 2823805 wikitext text/x-wiki {{title|Emotional intelligence }} '''How does emotional intelligence affect emotional wellbeing?'''<div align=center>Edit the title and sub-title to match the wording (and casing) in the [[Motivation and emotion/Book/2025|2026 list of topics]].<br>[[Motivation and emotion/About/Staff|Seek approval]] for any changes.<br>Do not include your name (authorship is as per [[Special:History/{{PAGENAME}}|the page history]]).</div> __TOC__ ==Overview== {{RoundBoxTop|theme=3}}Imagine Sophie, a university student who has several assessments due while also dealing with conflict with a close friend. After receiving a disappointing mark, Sophie initially feels frustrated, embarrassed, and overwhelmed. Rather than immediately reacting, she recognises that disappointment and stress are influencing how she is thinking about the situation. She takes some time to regulate her emotions, considers why the result affected her so strongly, and later talks calmly with her friend about the conflict. Another student experiencing the same circumstances might struggle to identify what they are feeling, become increasingly overwhelmed, or react impulsively. Why might people respond so differently to similar emotional situations? One possible explanation involves emotional intelligence (EI) the ability to perceive, understand, use, and regulate emotion. Emotional intelligence may influence how people interpret and respond to emotional experiences and, consequently, their emotional wellbeing. Emotional wellbeing involves more than simply experiencing positive emotions or avoiding negative ones. It concerns how people experience and manage emotions and their broader capacity to function psychologically. Understanding the relationship between emotional intelligence and emotional wellbeing is important because difficult emotions are unavoidable. Psychological research can help explain whether emotionally intelligent abilities support wellbeing, which components of emotional intelligence may be particularly important, and the psychological processes that could explain this relationship. {{RoundBoxBottom}} The Overview section should provide: # '''Scenario''': A short, engaging case study or real-world example in a feature box, with an accompanying image (see above) # '''Explanation of the problem, issue, or topc''': Briefly explain the problem, why it is important, and outline how psychological science can help # '''Focus questions''': Unpack the sub-title into focus questions in a feature box Recommended length: 180 to 330 words. This template provides key headings, examples, and tips for each section. Gradually remove this generic information as the chapter develops. It is OK to retain some of the template material for the topic development, but it should all be removed for the final book chapter. Key resources: * [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 02]] explains about how to edit * [[Motivation and emotion/Assessment/Topic|Topic development guidelines]] * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] === Emotional intelligence and emotional wellbeing === [[File:Model of EI.png|thumb|Figure 1. ''Mayor and Salovey's Emotional Intelligence model'' ]] Emotional intelligence may play an important role in how people recognise, understand, and regulate their emotions. These emotional abilities may influence how people cope with difficult experiences, maintain positive emotions, and support their overall emotional wellbeing. However, emotional intelligence is a complex construct, and different emotional abilities may contribute to wellbeing in different ways. * '''What are emotional intelligence and emotional wellbeing?''' (Define emotional intelligence and emotional wellbeing. Explain that emotional intelligence generally involves recognising, understanding, using, and managing emotions. Explain emotional wellbeing and clarify that wellbeing does not simply mean always experiencing positive emotions. Introduce the idea that there are different models of emotional intelligence.) '''Research needed:''' A foundational source defining emotional intelligence, such as '''Mayer and Salovey''', plus a reliable source defining emotional/subjective wellbeing. * '''What is the relationship between emotional intelligence and emotional wellbeing?''' (Discuss research showing whether higher emotional intelligence is associated with greater emotional or psychological wellbeing. Consider outcomes such as positive affect, life satisfaction, happiness, stress, and negative emotional experiences. Be careful to distinguish an association from evidence that emotional intelligence directly causes better wellbeing.) '''Research needed:''' Meta-analyses or empirical studies examining the association between emotional intelligence and wellbeing. * '''How does emotional intelligence influence emotional wellbeing?''' (Discuss the psychological processes that may explain the relationship. Emotional intelligence may help people recognise what they are feeling, understand why they are experiencing an emotion, regulate difficult emotions, cope with stress, and manage interpersonal situations. These processes may help explain why emotional intelligence is associated with wellbeing.) '''Research needed:''' Research connecting emotional intelligence with emotion regulation, coping, stress management, and social functioning, as well as research linking these processes with wellbeing. * '''Which components of emotional intelligence are particularly important for emotional wellbeing?''' (Discuss whether different components of emotional intelligence contribute differently to wellbeing. Consider emotion perception, using emotion, emotion understanding, and emotion management/regulation. Emotion regulation may be particularly relevant, but this needs to be evaluated using research rather than assumed.) '''Research needed:''' Studies comparing different dimensions or branches of emotional intelligence and their relationships with wellbeing, particularly emotion regulation/management. * '''How can emotional intelligence be developed to support emotional wellbeing?''' (Discuss whether emotional intelligence can be improved through training or psychological interventions. Consider strategies aimed at emotional awareness, understanding emotions, emotion regulation, and interpersonal skills. Examine whether improving these abilities actually leads to improvements in wellbeing and acknowledge limitations in the evidence.) '''Research needed:''' Intervention studies and preferably systematic reviews or meta-analyses of emotional intelligence training and its effects on emotional or psychological wellbeing. == Focus Questions == * What are emotional intelligence and emotional wellbeing? * What is the relationship between emotional intelligence and emotional wellbeing? * How does emotional intelligence influence emotional wellbeing? * How can emotional intelligence be developed to support emotional wellbeing? * Which components of emotional intelligence are particularly important for emotional wellbeing? * How can emotional intelligence be developed to support emotional wellbeing? == What are emotional intelligence and emotional wellbeing? == Before examining their relationship, it is important to establish what psychologists mean by emotional intelligence and emotional wellbeing. Both are multidimensional concepts, and different theoretical approaches influence how they are measured and understood. == Defining emotional intelligence == * Introduce emotional intelligence. * Explain that EI concerns the processing and management of emotional information. * Explain that EI is not simply "being emotional" or "being a nice person". * Introduce major conceptualisations of EI. * Explain why differences in definitions matter when examining research. === Ability model of emotional intelligence === Introduce Mayer and Salovey's ability model. Explain the four branches: # Perceiving emotions # Using emotions to facilitate thought # Understanding emotions # Managing emotions Explain briefly how each ability could theoretically contribute to wellbeing. '''Figure 1. The four-branch model of emotional intelligence''' Create a simple diagram showing: Perceiving emotions → Using emotions → Understanding emotions → Managing emotions == Trait emotional intelligence == * Explain trait EI. * Distinguish trait EI from ability EI. * Explain that trait EI concerns people's perceptions of their emotional abilities and tendencies. * Briefly introduce why trait EI is relevant to emotional wellbeing. == Defining emotional wellbeing == * Define emotional wellbeing. * Explain that wellbeing is not simply the absence of mental illness. * Discuss positive and negative affect. * Discuss emotional functioning and life satisfaction where relevant. * Explain that experiencing negative emotions does not automatically indicate poor emotional wellbeing. === Emotional wellbeing versus always feeling positive === A useful distinction should be established here: Emotionally healthy people can still experience sadness, anger, anxiety, disappointment, and stress. Healthy emotional functioning may instead involve recognising emotions, understanding their causes, regulating them appropriately, and recovering from difficult experiences. == Key points == For the topic development, for each heading and sub-heading: * Provide at least three bullet-points, including for the Overview and Conclusion * Include key citations ==Figures== [[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== Interactive learning features help to bring book chapters to life and can be embedded throughout the chapter. {{anchor|Scenarios}} ;Scenarios * Scenarios, case studies, or examples describe concepts in action * Can be real or fictional; if real, provide citations * Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Present using [[#Feature boxes|feature boxes]] {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted '''Table 1''' A Descriptive Caption Which Explains The Table Contents and its Relevance to the Text e.g., The 2 x 2 Johari Window Model Showing Knowing x Self/Other {| class="wikitable" style="margin: auto; |- ! !! Known to self !! Not known to self |- | '''Known to others''' || Open area || Blind spot |- | '''Not known to others''' || Hidden area || Unknown |} ;Quizzes * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] Example simple quiz questions. Choose your answers and click "Submit": <quiz display=simple> {The purpose of quizzes is to provide an interactive learning feature: |type="()"} + True - False {Long and complex quiz questions are recommended: |type="()"} - True + False </quiz> ==Conclusion== * The Conclusion is arguably the most important section * Draft clear take-home message(s), even at the topic development stage * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) * [[w:Self determination theory|Self determination theory]] (Wikipedia) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses }} ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. APA style example: {{Hanging indent|1= Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091 Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper & Row. }} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Emotional intelligence]] [[Category:Motivation and emotion/Book/Well-being]] qo8j1p1sakat4tnnyfhbmlm69jjt28d 2823806 2823805 2026-08-21T04:13:26Z U3239236 3106753 2823806 wikitext text/x-wiki = . Emotional Intelligence = {{title| How does Emotional Intelligence affect Emotional Wellbeing? }}<div align="center"></div> __TOC__ ==Overview== {{RoundBoxTop|theme=3}}Imagine Sophie, a university student who has several assessments due while also dealing with conflict with a close friend. After receiving a disappointing mark, Sophie initially feels frustrated, embarrassed, and overwhelmed. Rather than immediately reacting, she recognises that disappointment and stress are influencing how she is thinking about the situation. She takes some time to regulate her emotions, considers why the result affected her so strongly, and later talks calmly with her friend about the conflict. Another student experiencing the same circumstances might struggle to identify what they are feeling, become increasingly overwhelmed, or react impulsively. Why might people respond so differently to similar emotional situations? One possible explanation involves emotional intelligence (EI) the ability to perceive, understand, use, and regulate emotion. Emotional intelligence may influence how people interpret and respond to emotional experiences and, consequently, their emotional wellbeing. Emotional wellbeing involves more than simply experiencing positive emotions or avoiding negative ones. It concerns how people experience and manage emotions and their broader capacity to function psychologically. Understanding the relationship between emotional intelligence and emotional wellbeing is important because difficult emotions are unavoidable. Psychological research can help explain whether emotionally intelligent abilities support wellbeing, which components of emotional intelligence may be particularly important, and the psychological processes that could explain this relationship. {{RoundBoxBottom}} The Overview section should provide: # '''Scenario''': A short, engaging case study or real-world example in a feature box, with an accompanying image (see above) # '''Explanation of the problem, issue, or topc''': Briefly explain the problem, why it is important, and outline how psychological science can help # '''Focus questions''': Unpack the sub-title into focus questions in a feature box Recommended length: 180 to 330 words. This template provides key headings, examples, and tips for each section. Gradually remove this generic information as the chapter develops. It is OK to retain some of the template material for the topic development, but it should all be removed for the final book chapter. Key resources: * [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 02]] explains about how to edit * [[Motivation and emotion/Assessment/Topic|Topic development guidelines]] * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] === Emotional intelligence and emotional wellbeing === [[File:Model of EI.png|thumb|Figure 1. ''Mayor and Salovey's Emotional Intelligence model'' ]] Emotional intelligence may play an important role in how people recognise, understand, and regulate their emotions. These emotional abilities may influence how people cope with difficult experiences, maintain positive emotions, and support their overall emotional wellbeing. However, emotional intelligence is a complex construct, and different emotional abilities may contribute to wellbeing in different ways. * '''What are emotional intelligence and emotional wellbeing?''' (Define emotional intelligence and emotional wellbeing. Explain that emotional intelligence generally involves recognising, understanding, using, and managing emotions. Explain emotional wellbeing and clarify that wellbeing does not simply mean always experiencing positive emotions. Introduce the idea that there are different models of emotional intelligence.) '''Research needed:''' A foundational source defining emotional intelligence, such as '''Mayer and Salovey''', plus a reliable source defining emotional/subjective wellbeing. * '''What is the relationship between emotional intelligence and emotional wellbeing?''' (Discuss research showing whether higher emotional intelligence is associated with greater emotional or psychological wellbeing. Consider outcomes such as positive affect, life satisfaction, happiness, stress, and negative emotional experiences. Be careful to distinguish an association from evidence that emotional intelligence directly causes better wellbeing.) '''Research needed:''' Meta-analyses or empirical studies examining the association between emotional intelligence and wellbeing. * '''How does emotional intelligence influence emotional wellbeing?''' (Discuss the psychological processes that may explain the relationship. Emotional intelligence may help people recognise what they are feeling, understand why they are experiencing an emotion, regulate difficult emotions, cope with stress, and manage interpersonal situations. These processes may help explain why emotional intelligence is associated with wellbeing.) '''Research needed:''' Research connecting emotional intelligence with emotion regulation, coping, stress management, and social functioning, as well as research linking these processes with wellbeing. * '''Which components of emotional intelligence are particularly important for emotional wellbeing?''' (Discuss whether different components of emotional intelligence contribute differently to wellbeing. Consider emotion perception, using emotion, emotion understanding, and emotion management/regulation. Emotion regulation may be particularly relevant, but this needs to be evaluated using research rather than assumed.) '''Research needed:''' Studies comparing different dimensions or branches of emotional intelligence and their relationships with wellbeing, particularly emotion regulation/management. * '''How can emotional intelligence be developed to support emotional wellbeing?''' (Discuss whether emotional intelligence can be improved through training or psychological interventions. Consider strategies aimed at emotional awareness, understanding emotions, emotion regulation, and interpersonal skills. Examine whether improving these abilities actually leads to improvements in wellbeing and acknowledge limitations in the evidence.) '''Research needed:''' Intervention studies and preferably systematic reviews or meta-analyses of emotional intelligence training and its effects on emotional or psychological wellbeing. == Focus Questions == * What are emotional intelligence and emotional wellbeing? * What is the relationship between emotional intelligence and emotional wellbeing? * How does emotional intelligence influence emotional wellbeing? * How can emotional intelligence be developed to support emotional wellbeing? * Which components of emotional intelligence are particularly important for emotional wellbeing? * How can emotional intelligence be developed to support emotional wellbeing? == What are emotional intelligence and emotional wellbeing? == Before examining their relationship, it is important to establish what psychologists mean by emotional intelligence and emotional wellbeing. Both are multidimensional concepts, and different theoretical approaches influence how they are measured and understood. == Defining emotional intelligence == * Introduce emotional intelligence. * Explain that EI concerns the processing and management of emotional information. * Explain that EI is not simply "being emotional" or "being a nice person". * Introduce major conceptualisations of EI. * Explain why differences in definitions matter when examining research. === Ability model of emotional intelligence === Introduce Mayer and Salovey's ability model. Explain the four branches: # Perceiving emotions # Using emotions to facilitate thought # Understanding emotions # Managing emotions Explain briefly how each ability could theoretically contribute to wellbeing. '''Figure 1. The four-branch model of emotional intelligence''' Create a simple diagram showing: Perceiving emotions → Using emotions → Understanding emotions → Managing emotions == Trait emotional intelligence == * Explain trait EI. * Distinguish trait EI from ability EI. * Explain that trait EI concerns people's perceptions of their emotional abilities and tendencies. * Briefly introduce why trait EI is relevant to emotional wellbeing. == Defining emotional wellbeing == * Define emotional wellbeing. * Explain that wellbeing is not simply the absence of mental illness. * Discuss positive and negative affect. * Discuss emotional functioning and life satisfaction where relevant. * Explain that experiencing negative emotions does not automatically indicate poor emotional wellbeing. === Emotional wellbeing versus always feeling positive === A useful distinction should be established here: Emotionally healthy people can still experience sadness, anger, anxiety, disappointment, and stress. Healthy emotional functioning may instead involve recognising emotions, understanding their causes, regulating them appropriately, and recovering from difficult experiences. == Key points == For the topic development, for each heading and sub-heading: * Provide at least three bullet-points, including for the Overview and Conclusion * Include key citations ==Figures== [[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== Interactive learning features help to bring book chapters to life and can be embedded throughout the chapter. {{anchor|Scenarios}} ;Scenarios * Scenarios, case studies, or examples describe concepts in action * Can be real or fictional; if real, provide citations * Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Present using [[#Feature boxes|feature boxes]] {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted '''Table 1''' A Descriptive Caption Which Explains The Table Contents and its Relevance to the Text e.g., The 2 x 2 Johari Window Model Showing Knowing x Self/Other {| class="wikitable" style="margin: auto; |- ! !! Known to self !! Not known to self |- | '''Known to others''' || Open area || Blind spot |- | '''Not known to others''' || Hidden area || Unknown |} ;Quizzes * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] Example simple quiz questions. Choose your answers and click "Submit": <quiz display=simple> {The purpose of quizzes is to provide an interactive learning feature: |type="()"} + True - False {Long and complex quiz questions are recommended: |type="()"} - True + False </quiz> ==Conclusion== * The Conclusion is arguably the most important section * Draft clear take-home message(s), even at the topic development stage * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) * [[w:Self determination theory|Self determination theory]] (Wikipedia) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses }} ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. APA style example: {{Hanging indent|1= Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091 Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper & Row. }} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Emotional intelligence]] [[Category:Motivation and emotion/Book/Well-being]] 5y91qhkit4sbunwcep8p1s3w6chi72u 2823808 2823806 2026-08-21T04:14:00Z U3239236 3106753 /* . Emotional Intelligence 2823808 wikitext text/x-wiki = Emotional Intelligence = {{title| How does Emotional Intelligence affect Emotional Wellbeing? }}<div align="center"></div> __TOC__ ==Overview== {{RoundBoxTop|theme=3}}Imagine Sophie, a university student who has several assessments due while also dealing with conflict with a close friend. After receiving a disappointing mark, Sophie initially feels frustrated, embarrassed, and overwhelmed. Rather than immediately reacting, she recognises that disappointment and stress are influencing how she is thinking about the situation. She takes some time to regulate her emotions, considers why the result affected her so strongly, and later talks calmly with her friend about the conflict. Another student experiencing the same circumstances might struggle to identify what they are feeling, become increasingly overwhelmed, or react impulsively. Why might people respond so differently to similar emotional situations? One possible explanation involves emotional intelligence (EI) the ability to perceive, understand, use, and regulate emotion. Emotional intelligence may influence how people interpret and respond to emotional experiences and, consequently, their emotional wellbeing. Emotional wellbeing involves more than simply experiencing positive emotions or avoiding negative ones. It concerns how people experience and manage emotions and their broader capacity to function psychologically. Understanding the relationship between emotional intelligence and emotional wellbeing is important because difficult emotions are unavoidable. Psychological research can help explain whether emotionally intelligent abilities support wellbeing, which components of emotional intelligence may be particularly important, and the psychological processes that could explain this relationship. {{RoundBoxBottom}} The Overview section should provide: # '''Scenario''': A short, engaging case study or real-world example in a feature box, with an accompanying image (see above) # '''Explanation of the problem, issue, or topc''': Briefly explain the problem, why it is important, and outline how psychological science can help # '''Focus questions''': Unpack the sub-title into focus questions in a feature box Recommended length: 180 to 330 words. This template provides key headings, examples, and tips for each section. Gradually remove this generic information as the chapter develops. It is OK to retain some of the template material for the topic development, but it should all be removed for the final book chapter. Key resources: * [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 02]] explains about how to edit * [[Motivation and emotion/Assessment/Topic|Topic development guidelines]] * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] === Emotional intelligence and emotional wellbeing === [[File:Model of EI.png|thumb|Figure 1. ''Mayor and Salovey's Emotional Intelligence model'' ]] Emotional intelligence may play an important role in how people recognise, understand, and regulate their emotions. These emotional abilities may influence how people cope with difficult experiences, maintain positive emotions, and support their overall emotional wellbeing. However, emotional intelligence is a complex construct, and different emotional abilities may contribute to wellbeing in different ways. * '''What are emotional intelligence and emotional wellbeing?''' (Define emotional intelligence and emotional wellbeing. Explain that emotional intelligence generally involves recognising, understanding, using, and managing emotions. Explain emotional wellbeing and clarify that wellbeing does not simply mean always experiencing positive emotions. Introduce the idea that there are different models of emotional intelligence.) '''Research needed:''' A foundational source defining emotional intelligence, such as '''Mayer and Salovey''', plus a reliable source defining emotional/subjective wellbeing. * '''What is the relationship between emotional intelligence and emotional wellbeing?''' (Discuss research showing whether higher emotional intelligence is associated with greater emotional or psychological wellbeing. Consider outcomes such as positive affect, life satisfaction, happiness, stress, and negative emotional experiences. Be careful to distinguish an association from evidence that emotional intelligence directly causes better wellbeing.) '''Research needed:''' Meta-analyses or empirical studies examining the association between emotional intelligence and wellbeing. * '''How does emotional intelligence influence emotional wellbeing?''' (Discuss the psychological processes that may explain the relationship. Emotional intelligence may help people recognise what they are feeling, understand why they are experiencing an emotion, regulate difficult emotions, cope with stress, and manage interpersonal situations. These processes may help explain why emotional intelligence is associated with wellbeing.) '''Research needed:''' Research connecting emotional intelligence with emotion regulation, coping, stress management, and social functioning, as well as research linking these processes with wellbeing. * '''Which components of emotional intelligence are particularly important for emotional wellbeing?''' (Discuss whether different components of emotional intelligence contribute differently to wellbeing. Consider emotion perception, using emotion, emotion understanding, and emotion management/regulation. Emotion regulation may be particularly relevant, but this needs to be evaluated using research rather than assumed.) '''Research needed:''' Studies comparing different dimensions or branches of emotional intelligence and their relationships with wellbeing, particularly emotion regulation/management. * '''How can emotional intelligence be developed to support emotional wellbeing?''' (Discuss whether emotional intelligence can be improved through training or psychological interventions. Consider strategies aimed at emotional awareness, understanding emotions, emotion regulation, and interpersonal skills. Examine whether improving these abilities actually leads to improvements in wellbeing and acknowledge limitations in the evidence.) '''Research needed:''' Intervention studies and preferably systematic reviews or meta-analyses of emotional intelligence training and its effects on emotional or psychological wellbeing. == Focus Questions == * What are emotional intelligence and emotional wellbeing? * What is the relationship between emotional intelligence and emotional wellbeing? * How does emotional intelligence influence emotional wellbeing? * How can emotional intelligence be developed to support emotional wellbeing? * Which components of emotional intelligence are particularly important for emotional wellbeing? * How can emotional intelligence be developed to support emotional wellbeing? == What are emotional intelligence and emotional wellbeing? == Before examining their relationship, it is important to establish what psychologists mean by emotional intelligence and emotional wellbeing. Both are multidimensional concepts, and different theoretical approaches influence how they are measured and understood. == Defining emotional intelligence == * Introduce emotional intelligence. * Explain that EI concerns the processing and management of emotional information. * Explain that EI is not simply "being emotional" or "being a nice person". * Introduce major conceptualisations of EI. * Explain why differences in definitions matter when examining research. === Ability model of emotional intelligence === Introduce Mayer and Salovey's ability model. Explain the four branches: # Perceiving emotions # Using emotions to facilitate thought # Understanding emotions # Managing emotions Explain briefly how each ability could theoretically contribute to wellbeing. '''Figure 1. The four-branch model of emotional intelligence''' Create a simple diagram showing: Perceiving emotions → Using emotions → Understanding emotions → Managing emotions == Trait emotional intelligence == * Explain trait EI. * Distinguish trait EI from ability EI. * Explain that trait EI concerns people's perceptions of their emotional abilities and tendencies. * Briefly introduce why trait EI is relevant to emotional wellbeing. == Defining emotional wellbeing == * Define emotional wellbeing. * Explain that wellbeing is not simply the absence of mental illness. * Discuss positive and negative affect. * Discuss emotional functioning and life satisfaction where relevant. * Explain that experiencing negative emotions does not automatically indicate poor emotional wellbeing. === Emotional wellbeing versus always feeling positive === A useful distinction should be established here: Emotionally healthy people can still experience sadness, anger, anxiety, disappointment, and stress. Healthy emotional functioning may instead involve recognising emotions, understanding their causes, regulating them appropriately, and recovering from difficult experiences. == Key points == For the topic development, for each heading and sub-heading: * Provide at least three bullet-points, including for the Overview and Conclusion * Include key citations ==Figures== [[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== Interactive learning features help to bring book chapters to life and can be embedded throughout the chapter. {{anchor|Scenarios}} ;Scenarios * Scenarios, case studies, or examples describe concepts in action * Can be real or fictional; if real, provide citations * Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Present using [[#Feature boxes|feature boxes]] {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted '''Table 1''' A Descriptive Caption Which Explains The Table Contents and its Relevance to the Text e.g., The 2 x 2 Johari Window Model Showing Knowing x Self/Other {| class="wikitable" style="margin: auto; |- ! !! Known to self !! Not known to self |- | '''Known to others''' || Open area || Blind spot |- | '''Not known to others''' || Hidden area || Unknown |} ;Quizzes * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] Example simple quiz questions. Choose your answers and click "Submit": <quiz display=simple> {The purpose of quizzes is to provide an interactive learning feature: |type="()"} + True - False {Long and complex quiz questions are recommended: |type="()"} - True + False </quiz> ==Conclusion== * The Conclusion is arguably the most important section * Draft clear take-home message(s), even at the topic development stage * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) * [[w:Self determination theory|Self determination theory]] (Wikipedia) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses }} ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. APA style example: {{Hanging indent|1= Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091 Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper & Row. }} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Emotional intelligence]] [[Category:Motivation and emotion/Book/Well-being]] 33rkv8956vjpv591cg9y7d6s192hb2j 2823809 2823808 2026-08-21T04:14:45Z U3239236 3106753 2823809 wikitext text/x-wiki = Emotional Intelligence = {{title| How does Emotional Intelligence affect Emotional Wellbeing? }}<div align="center"></div> __TOC__ ==Overview== {{RoundBoxTop|theme=3}}Imagine Sophie, a university student who has several assessments due while also dealing with conflict with a close friend. After receiving a disappointing mark, Sophie initially feels frustrated, embarrassed, and overwhelmed. Rather than immediately reacting, she recognises that disappointment and stress are influencing how she is thinking about the situation. She takes some time to regulate her emotions, considers why the result affected her so strongly, and later talks calmly with her friend about the conflict. Another student experiencing the same circumstances might struggle to identify what they are feeling, become increasingly overwhelmed, or react impulsively. Why might people respond so differently to similar emotional situations? One possible explanation involves emotional intelligence (EI) the ability to perceive, understand, use, and regulate emotion. Emotional intelligence may influence how people interpret and respond to emotional experiences and, consequently, their emotional wellbeing. Emotional wellbeing involves more than simply experiencing positive emotions or avoiding negative ones. It concerns how people experience and manage emotions and their broader capacity to function psychologically. Understanding the relationship between emotional intelligence and emotional wellbeing is important because difficult emotions are unavoidable. Psychological research can help explain whether emotionally intelligent abilities support wellbeing, which components of emotional intelligence may be particularly important, and the psychological processes that could explain this relationship. {{RoundBoxBottom}} The Overview section should provide: # '''Scenario''': A short, engaging case study or real-world example in a feature box, with an accompanying image (see above) # '''Explanation of the problem, issue, or topc''': Briefly explain the problem, why it is important, and outline how psychological science can help # '''Focus questions''': Unpack the sub-title into focus questions in a feature box Recommended length: 180 to 330 words. This template provides key headings, examples, and tips for each section. Gradually remove this generic information as the chapter develops. It is OK to retain some of the template material for the topic development, but it should all be removed for the final book chapter. Key resources: * [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 02]] explains about how to edit * [[Motivation and emotion/Assessment/Topic|Topic development guidelines]] * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] === Emotional intelligence and emotional wellbeing === [[File:Model of EI.png|thumb|Figure 1. ''Mayor and Salovey's Emotional Intelligence model'' ]] Emotional intelligence may play an important role in how people recognise, understand, and regulate their emotions. These emotional abilities may influence how people cope with difficult experiences, maintain positive emotions, and support their overall emotional wellbeing. However, emotional intelligence is a complex construct, and different emotional abilities may contribute to wellbeing in different ways. * '''What are emotional intelligence and emotional wellbeing?''' (Define emotional intelligence and emotional wellbeing. Explain that emotional intelligence generally involves recognising, understanding, using, and managing emotions. Explain emotional wellbeing and clarify that wellbeing does not simply mean always experiencing positive emotions. Introduce the idea that there are different models of emotional intelligence.) '''Research needed:''' A foundational source defining emotional intelligence, such as Mayer and Salovey, plus a reliable source defining emotional/subjective wellbeing. * '''What is the relationship between emotional intelligence and emotional wellbeing?''' (Discuss research showing whether higher emotional intelligence is associated with greater emotional or psychological wellbeing. Consider outcomes such as positive affect, life satisfaction, happiness, stress, and negative emotional experiences. Be careful to distinguish an association from evidence that emotional intelligence directly causes better wellbeing.) '''Research needed:''' Meta-analyses or empirical studies examining the association between emotional intelligence and wellbeing. * '''How does emotional intelligence influence emotional wellbeing?''' (Discuss the psychological processes that may explain the relationship. Emotional intelligence may help people recognise what they are feeling, understand why they are experiencing an emotion, regulate difficult emotions, cope with stress, and manage interpersonal situations. These processes may help explain why emotional intelligence is associated with wellbeing.) '''Research needed:''' Research connecting emotional intelligence with emotion regulation, coping, stress management, and social functioning, as well as research linking these processes with wellbeing. * '''Which components of emotional intelligence are particularly important for emotional wellbeing?''' (Discuss whether different components of emotional intelligence contribute differently to wellbeing. Consider emotion perception, using emotion, emotion understanding, and emotion management/regulation. Emotion regulation may be particularly relevant, but this needs to be evaluated using research rather than assumed.) '''Research needed:''' Studies comparing different dimensions or branches of emotional intelligence and their relationships with wellbeing, particularly emotion regulation/management. * '''How can emotional intelligence be developed to support emotional wellbeing?''' (Discuss whether emotional intelligence can be improved through training or psychological interventions. Consider strategies aimed at emotional awareness, understanding emotions, emotion regulation, and interpersonal skills. Examine whether improving these abilities actually leads to improvements in wellbeing and acknowledge limitations in the evidence.) '''Research needed:''' Intervention studies and preferably systematic reviews or meta-analyses of emotional intelligence training and its effects on emotional or psychological wellbeing. == Focus Questions == * What are emotional intelligence and emotional wellbeing? * What is the relationship between emotional intelligence and emotional wellbeing? * How does emotional intelligence influence emotional wellbeing? * How can emotional intelligence be developed to support emotional wellbeing? * Which components of emotional intelligence are particularly important for emotional wellbeing? * How can emotional intelligence be developed to support emotional wellbeing? == What are emotional intelligence and emotional wellbeing? == Before examining their relationship, it is important to establish what psychologists mean by emotional intelligence and emotional wellbeing. Both are multidimensional concepts, and different theoretical approaches influence how they are measured and understood. == Defining emotional intelligence == * Introduce emotional intelligence. * Explain that EI concerns the processing and management of emotional information. * Explain that EI is not simply "being emotional" or "being a nice person". * Introduce major conceptualisations of EI. * Explain why differences in definitions matter when examining research. === Ability model of emotional intelligence === Introduce Mayer and Salovey's ability model. Explain the four branches: # Perceiving emotions # Using emotions to facilitate thought # Understanding emotions # Managing emotions Explain briefly how each ability could theoretically contribute to wellbeing. '''Figure 1. The four-branch model of emotional intelligence''' Create a simple diagram showing: Perceiving emotions → Using emotions → Understanding emotions → Managing emotions == Trait emotional intelligence == * Explain trait EI. * Distinguish trait EI from ability EI. * Explain that trait EI concerns people's perceptions of their emotional abilities and tendencies. * Briefly introduce why trait EI is relevant to emotional wellbeing. == Defining emotional wellbeing == * Define emotional wellbeing. * Explain that wellbeing is not simply the absence of mental illness. * Discuss positive and negative affect. * Discuss emotional functioning and life satisfaction where relevant. * Explain that experiencing negative emotions does not automatically indicate poor emotional wellbeing. === Emotional wellbeing versus always feeling positive === A useful distinction should be established here: Emotionally healthy people can still experience sadness, anger, anxiety, disappointment, and stress. Healthy emotional functioning may instead involve recognising emotions, understanding their causes, regulating them appropriately, and recovering from difficult experiences. == Key points == For the topic development, for each heading and sub-heading: * Provide at least three bullet-points, including for the Overview and Conclusion * Include key citations ==Figures== [[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== Interactive learning features help to bring book chapters to life and can be embedded throughout the chapter. {{anchor|Scenarios}} ;Scenarios * Scenarios, case studies, or examples describe concepts in action * Can be real or fictional; if real, provide citations * Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Present using [[#Feature boxes|feature boxes]] {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted '''Table 1''' A Descriptive Caption Which Explains The Table Contents and its Relevance to the Text e.g., The 2 x 2 Johari Window Model Showing Knowing x Self/Other {| class="wikitable" style="margin: auto; |- ! !! Known to self !! Not known to self |- | '''Known to others''' || Open area || Blind spot |- | '''Not known to others''' || Hidden area || Unknown |} ;Quizzes * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] Example simple quiz questions. Choose your answers and click "Submit": <quiz display=simple> {The purpose of quizzes is to provide an interactive learning feature: |type="()"} + True - False {Long and complex quiz questions are recommended: |type="()"} - True + False </quiz> ==Conclusion== * The Conclusion is arguably the most important section * Draft clear take-home message(s), even at the topic development stage * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) * [[w:Self determination theory|Self determination theory]] (Wikipedia) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses }} ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. APA style example: {{Hanging indent|1= Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091 Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper & Row. }} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Emotional intelligence]] [[Category:Motivation and emotion/Book/Well-being]] az2m1d7f7k7exh6vsfk2zrwctenkoi5 2823815 2823809 2026-08-21T04:31:13Z Jtneill 10242 Adjust title layout 2823815 wikitext text/x-wiki {{title|Emotional Intelligence:<br>How does Emotional Intelligence affect Emotional Wellbeing?}} __TOC__ ==Overview== {{RoundBoxTop|theme=3}}Imagine Sophie, a university student who has several assessments due while also dealing with conflict with a close friend. After receiving a disappointing mark, Sophie initially feels frustrated, embarrassed, and overwhelmed. Rather than immediately reacting, she recognises that disappointment and stress are influencing how she is thinking about the situation. She takes some time to regulate her emotions, considers why the result affected her so strongly, and later talks calmly with her friend about the conflict. Another student experiencing the same circumstances might struggle to identify what they are feeling, become increasingly overwhelmed, or react impulsively. Why might people respond so differently to similar emotional situations? One possible explanation involves emotional intelligence (EI) the ability to perceive, understand, use, and regulate emotion. Emotional intelligence may influence how people interpret and respond to emotional experiences and, consequently, their emotional wellbeing. Emotional wellbeing involves more than simply experiencing positive emotions or avoiding negative ones. It concerns how people experience and manage emotions and their broader capacity to function psychologically. Understanding the relationship between emotional intelligence and emotional wellbeing is important because difficult emotions are unavoidable. Psychological research can help explain whether emotionally intelligent abilities support wellbeing, which components of emotional intelligence may be particularly important, and the psychological processes that could explain this relationship. {{RoundBoxBottom}} The Overview section should provide: # '''Scenario''': A short, engaging case study or real-world example in a feature box, with an accompanying image (see above) # '''Explanation of the problem, issue, or topc''': Briefly explain the problem, why it is important, and outline how psychological science can help # '''Focus questions''': Unpack the sub-title into focus questions in a feature box Recommended length: 180 to 330 words. This template provides key headings, examples, and tips for each section. Gradually remove this generic information as the chapter develops. It is OK to retain some of the template material for the topic development, but it should all be removed for the final book chapter. Key resources: * [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 02]] explains about how to edit * [[Motivation and emotion/Assessment/Topic|Topic development guidelines]] * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] === Emotional intelligence and emotional wellbeing === [[File:Model of EI.png|thumb|Figure 1. ''Mayor and Salovey's Emotional Intelligence model'' ]] Emotional intelligence may play an important role in how people recognise, understand, and regulate their emotions. These emotional abilities may influence how people cope with difficult experiences, maintain positive emotions, and support their overall emotional wellbeing. However, emotional intelligence is a complex construct, and different emotional abilities may contribute to wellbeing in different ways. * '''What are emotional intelligence and emotional wellbeing?''' (Define emotional intelligence and emotional wellbeing. Explain that emotional intelligence generally involves recognising, understanding, using, and managing emotions. Explain emotional wellbeing and clarify that wellbeing does not simply mean always experiencing positive emotions. Introduce the idea that there are different models of emotional intelligence.) '''Research needed:''' A foundational source defining emotional intelligence, such as Mayer and Salovey, plus a reliable source defining emotional/subjective wellbeing. * '''What is the relationship between emotional intelligence and emotional wellbeing?''' (Discuss research showing whether higher emotional intelligence is associated with greater emotional or psychological wellbeing. Consider outcomes such as positive affect, life satisfaction, happiness, stress, and negative emotional experiences. Be careful to distinguish an association from evidence that emotional intelligence directly causes better wellbeing.) '''Research needed:''' Meta-analyses or empirical studies examining the association between emotional intelligence and wellbeing. * '''How does emotional intelligence influence emotional wellbeing?''' (Discuss the psychological processes that may explain the relationship. Emotional intelligence may help people recognise what they are feeling, understand why they are experiencing an emotion, regulate difficult emotions, cope with stress, and manage interpersonal situations. These processes may help explain why emotional intelligence is associated with wellbeing.) '''Research needed:''' Research connecting emotional intelligence with emotion regulation, coping, stress management, and social functioning, as well as research linking these processes with wellbeing. * '''Which components of emotional intelligence are particularly important for emotional wellbeing?''' (Discuss whether different components of emotional intelligence contribute differently to wellbeing. Consider emotion perception, using emotion, emotion understanding, and emotion management/regulation. Emotion regulation may be particularly relevant, but this needs to be evaluated using research rather than assumed.) '''Research needed:''' Studies comparing different dimensions or branches of emotional intelligence and their relationships with wellbeing, particularly emotion regulation/management. * '''How can emotional intelligence be developed to support emotional wellbeing?''' (Discuss whether emotional intelligence can be improved through training or psychological interventions. Consider strategies aimed at emotional awareness, understanding emotions, emotion regulation, and interpersonal skills. Examine whether improving these abilities actually leads to improvements in wellbeing and acknowledge limitations in the evidence.) '''Research needed:''' Intervention studies and preferably systematic reviews or meta-analyses of emotional intelligence training and its effects on emotional or psychological wellbeing. == Focus Questions == * What are emotional intelligence and emotional wellbeing? * What is the relationship between emotional intelligence and emotional wellbeing? * How does emotional intelligence influence emotional wellbeing? * How can emotional intelligence be developed to support emotional wellbeing? * Which components of emotional intelligence are particularly important for emotional wellbeing? * How can emotional intelligence be developed to support emotional wellbeing? == What are emotional intelligence and emotional wellbeing? == Before examining their relationship, it is important to establish what psychologists mean by emotional intelligence and emotional wellbeing. Both are multidimensional concepts, and different theoretical approaches influence how they are measured and understood. == Defining emotional intelligence == * Introduce emotional intelligence. * Explain that EI concerns the processing and management of emotional information. * Explain that EI is not simply "being emotional" or "being a nice person". * Introduce major conceptualisations of EI. * Explain why differences in definitions matter when examining research. === Ability model of emotional intelligence === Introduce Mayer and Salovey's ability model. Explain the four branches: # Perceiving emotions # Using emotions to facilitate thought # Understanding emotions # Managing emotions Explain briefly how each ability could theoretically contribute to wellbeing. '''Figure 1. The four-branch model of emotional intelligence''' Create a simple diagram showing: Perceiving emotions → Using emotions → Understanding emotions → Managing emotions == Trait emotional intelligence == * Explain trait EI. * Distinguish trait EI from ability EI. * Explain that trait EI concerns people's perceptions of their emotional abilities and tendencies. * Briefly introduce why trait EI is relevant to emotional wellbeing. == Defining emotional wellbeing == * Define emotional wellbeing. * Explain that wellbeing is not simply the absence of mental illness. * Discuss positive and negative affect. * Discuss emotional functioning and life satisfaction where relevant. * Explain that experiencing negative emotions does not automatically indicate poor emotional wellbeing. === Emotional wellbeing versus always feeling positive === A useful distinction should be established here: Emotionally healthy people can still experience sadness, anger, anxiety, disappointment, and stress. Healthy emotional functioning may instead involve recognising emotions, understanding their causes, regulating them appropriately, and recovering from difficult experiences. == Key points == For the topic development, for each heading and sub-heading: * Provide at least three bullet-points, including for the Overview and Conclusion * Include key citations ==Figures== [[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== Interactive learning features help to bring book chapters to life and can be embedded throughout the chapter. {{anchor|Scenarios}} ;Scenarios * Scenarios, case studies, or examples describe concepts in action * Can be real or fictional; if real, provide citations * Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Present using [[#Feature boxes|feature boxes]] {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted '''Table 1''' A Descriptive Caption Which Explains The Table Contents and its Relevance to the Text e.g., The 2 x 2 Johari Window Model Showing Knowing x Self/Other {| class="wikitable" style="margin: auto; |- ! !! Known to self !! Not known to self |- | '''Known to others''' || Open area || Blind spot |- | '''Not known to others''' || Hidden area || Unknown |} ;Quizzes * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] Example simple quiz questions. Choose your answers and click "Submit": <quiz display=simple> {The purpose of quizzes is to provide an interactive learning feature: |type="()"} + True - False {Long and complex quiz questions are recommended: |type="()"} - True + False </quiz> ==Conclusion== * The Conclusion is arguably the most important section * Draft clear take-home message(s), even at the topic development stage * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) * [[w:Self determination theory|Self determination theory]] (Wikipedia) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses }} ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. APA style example: {{Hanging indent|1= Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091 Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper & Row. }} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Emotional intelligence]] [[Category:Motivation and emotion/Book/Well-being]] mkrznjtep3s08f8aeglnf7sh5z2vzcn 0 331103 2823768 2823384 2026-08-21T00:53:31Z U3247927 3005952 2823768 wikitext text/x-wiki {{title|Romantic entertainment and love beliefs:<br>How do romantic entertainment influence beliefs and expectations about love and romantic relationships?}} <div align=center>Edit the title and sub-title to match the wording (and casing) in the [[Motivation and emotion/Book/2025|2026 list of topics]].<br>[[Motivation and emotion/About/Staff|Seek approval]] for any changes.<br>Do not include your name (authorship is as per [[Special:History/{{PAGENAME}}|the page history]]).</div> __TOC__ ==Overview== [[File:ChatGPT Image of couple watching romantic media together.png|right|375x375px]]'''Figure 1'''. A couple watching a romantic comedy, illustrating exposure to romantic entertainment. The Overview section should provide: # '''Scenario''': A short, engaging case study or real-world example in a feature box, with an accompanying image (see above) # '''Explanation of the problem, issue, or topc''': Briefly explain the problem, why it is important, and outline how psychological science can help # '''Focus questions''': Unpack the sub-title into focus questions in a feature box Recommended length: 180 to 330 words. This template provides key headings, examples, and tips for each section. Gradually remove this generic information as the chapter develops. It is OK to retain some of the template material for the topic development, but it should all be removed for the final book chapter. Key resources: * [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 02]] explains about how to edit * [[Motivation and emotion/Assessment/Topic|Topic development guidelines]] * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] {{RoundBoxTop|theme=3}} '''Focus questions''' Break the sub-title down into three to five [[Motivation and emotion/Assessment/Chapter/Focus questions|focus questions]]. Align the top-level headings with these focus questions. * What is the first focus question? * What is the second focus question? * What is the third focus question? Ask [[w:Open-ended question|open-ended]] focus questions. For example: * Is there a relationship between weather and criminal behaviour? (closed-ended) * What is the relationship between weather and criminal behaviour? (open-ended) {{RoundBoxBottom}} ==Headings== Use this heading structure: * [[#Overview|Overview]] * 3 to 6 major headings tailored to the topic; can have sub-headings, but: ** avoid having only one sub-heading ** provide an introductory paragraph before breaking into sub-sections * [[#Conclusion|Conclusion]] * See also * References * External links ==Key points== For the topic development, for each heading and sub-heading: * Provide at least three bullet-points, including for the Overview and Conclusion * Include key citations ==Figures== [[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== Interactive learning features help to bring book chapters to life and can be embedded throughout the chapter. {{anchor|Scenarios}} ;Scenarios * Scenarios, case studies, or examples describe concepts in action * Can be real or fictional; if real, provide citations * Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Present using [[#Feature boxes|feature boxes]] {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted '''Table 1''' A Descriptive Caption Which Explains The Table Contents and its Relevance to the Text e.g., The 2 x 2 Johari Window Model Showing Knowing x Self/Other {| class="wikitable" style="margin: auto; |- ! !! Known to self !! Not known to self |- | '''Known to others''' || Open area || Blind spot |- | '''Not known to others''' || Hidden area || Unknown |} ;Quizzes * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] Example simple quiz questions. Choose your answers and click "Submit": <quiz display=simple> {The purpose of quizzes is to provide an interactive learning feature: |type="()"} + True - False {Long and complex quiz questions are recommended: |type="()"} - True + False </quiz> ==Conclusion== * The Conclusion is arguably the most important section * Draft clear take-home message(s), even at the topic development stage * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) * [[w:Self determination theory|Self determination theory]] (Wikipedia) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses }} ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. APA style example: {{Hanging indent|1= Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091 Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper & Row. }} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Love]] dz7h8hzb2gm4c99y31eldvbk3ovr54i 2823770 2823768 2026-08-21T00:57:35Z U3247927 3005952 changed location of image 2823770 wikitext text/x-wiki {{title|Romantic entertainment and love beliefs:<br>How do romantic entertainment influence beliefs and expectations about love and romantic relationships?}} <div align=center>Edit the title and sub-title to match the wording (and casing) in the [[Motivation and emotion/Book/2025|2026 list of topics]].<br>[[Motivation and emotion/About/Staff|Seek approval]] for any changes.<br>Do not include your name (authorship is as per [[Special:History/{{PAGENAME}}|the page history]]).</div> __TOC__ ==Overview== '''Figure 1'''. A couple watching a romantic comedy, illustrating exposure to romantic entertainment. The Overview section should provide: # '''Scenario''': A short, engaging case study or real-world example in a feature box, with an accompanying image (see above) # # '''Explanation of the problem, issue, or topc''': Briefly explain the problem, why it is important, and outline how psychological science can help # '''Focus questions''': Unpack the sub-title into focus questions in a feature box Recommended length: 180 to 330 words. This template provides key headings, examples, and tips for each section. Gradually remove this generic information as the chapter develops. It is OK to retain some of the template material for the topic development, but it should all be removed for the final book chapter. Key resources: * [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 02]] explains about how to edit * [[Motivation and emotion/Assessment/Topic|Topic development guidelines]] * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] {{RoundBoxTop|theme=3}} '''Focus questions''' Break the sub-title down into three to five [[Motivation and emotion/Assessment/Chapter/Focus questions|focus questions]]. Align the top-level headings with these focus questions. * What is the first focus question? * What is the second focus question? * What is the third focus question? Ask [[w:Open-ended question|open-ended]] focus questions. For example: * Is there a relationship between weather and criminal behaviour? (closed-ended) * What is the relationship between weather and criminal behaviour? (open-ended) {{RoundBoxBottom}} ==Headings== Use this heading structure: * [[#Overview|Overview]] * 3 to 6 major headings tailored to the topic; can have sub-headings, but: ** avoid having only one sub-heading ** provide an introductory paragraph before breaking into sub-sections * [[#Conclusion|Conclusion]] * See also * References * External links ==Key points== For the topic development, for each heading and sub-heading: * Provide at least three bullet-points, including for the Overview and Conclusion * Include key citations ==Figures== [[File:ChatGPT Image of couple watching romantic media together.png|thumb|140x140px|'''Figure 1.''' A couple watching a romantic comedy, illustrating exposure to romantic entertainment. ]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== Interactive learning features help to bring book chapters to life and can be embedded throughout the chapter. {{anchor|Scenarios}} ;Scenarios * Scenarios, case studies, or examples describe concepts in action * Can be real or fictional; if real, provide citations * Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Present using [[#Feature boxes|feature boxes]] {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted '''Table 1''' A Descriptive Caption Which Explains The Table Contents and its Relevance to the Text e.g., The 2 x 2 Johari Window Model Showing Knowing x Self/Other {| class="wikitable" style="margin: auto; |- ! !! Known to self !! Not known to self |- | '''Known to others''' || Open area || Blind spot |- | '''Not known to others''' || Hidden area || Unknown |} ;Quizzes * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] Example simple quiz questions. Choose your answers and click "Submit": <quiz display=simple> {The purpose of quizzes is to provide an interactive learning feature: |type="()"} + True - False {Long and complex quiz questions are recommended: |type="()"} - True + False </quiz> ==Conclusion== * The Conclusion is arguably the most important section * Draft clear take-home message(s), even at the topic development stage * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) * [[w:Self determination theory|Self determination theory]] (Wikipedia) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses }} ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. APA style example: {{Hanging indent|1= Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091 Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper & Row. }} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Love]] nyzji93ahxx1kxh4ak7ummeocrfw8q3 2823773 2823770 2026-08-21T01:12:17Z U3247927 3005952 edited title 2823773 wikitext text/x-wiki {{title|Romantic entertainment and love beliefs:<br>How does romantic entertainment influence beliefs and expectations about love and romantic relationships?}} <div align=center>Edit the title and sub-title to match the wording (and casing) in the [[Motivation and emotion/Book/2025|2026 list of topics]].<br>[[Motivation and emotion/About/Staff|Seek approval]] for any changes.<br>Do not include your name (authorship is as per [[Special:History/{{PAGENAME}}|the page history]]).</div> __TOC__ Overview '''Figure 1'''. A couple watching a romantic comedy, illustrating exposure to romantic entertainment. The Overview section should provide: # '''Scenario''': A short, engaging case study or real-world example in a feature box, with an accompanying image (see above) # # '''Explanation of the problem, issue, or topc''': Briefly explain the problem, why it is important, and outline how psychological science can help # '''Focus questions''': Unpack the sub-title into focus questions in a feature box Recommended length: 180 to 330 words. This template provides key headings, examples, and tips for each section. Gradually remove this generic information as the chapter develops. It is OK to retain some of the template material for the topic development, but it should all be removed for the final book chapter. Key resources: * [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 02]] explains about how to edit * [[Motivation and emotion/Assessment/Topic|Topic development guidelines]] * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] {{RoundBoxTop|theme=3}} '''Focus questions''' Break the sub-title down into three to five [[Motivation and emotion/Assessment/Chapter/Focus questions|focus questions]]. Align the top-level headings with these focus questions. * What is the first focus question? * What is the second focus question? * What is the third focus question? Ask [[w:Open-ended question|open-ended]] focus questions. For example: * Is there a relationship between weather and criminal behaviour? (closed-ended) * What is the relationship between weather and criminal behaviour? (open-ended) {{RoundBoxBottom}} ==Headings== Use this heading structure: * [[#Overview|Overview]] * 3 to 6 major headings tailored to the topic; can have sub-headings, but: ** avoid having only one sub-heading ** provide an introductory paragraph before breaking into sub-sections * [[#Conclusion|Conclusion]] * See also * References * External links ==Key points== For the topic development, for each heading and sub-heading: * Provide at least three bullet-points, including for the Overview and Conclusion * Include key citations ==Figures== [[File:ChatGPT Image of couple watching romantic media together.png|thumb|140x140px|'''Figure 1.''' A couple watching a romantic comedy, illustrating exposure to romantic entertainment. ]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== Interactive learning features help to bring book chapters to life and can be embedded throughout the chapter. {{anchor|Scenarios}} ;Scenarios * Scenarios, case studies, or examples describe concepts in action * Can be real or fictional; if real, provide citations * Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Present using [[#Feature boxes|feature boxes]] {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted '''Table 1''' A Descriptive Caption Which Explains The Table Contents and its Relevance to the Text e.g., The 2 x 2 Johari Window Model Showing Knowing x Self/Other {| class="wikitable" style="margin: auto; |- ! !! Known to self !! Not known to self |- | '''Known to others''' || Open area || Blind spot |- | '''Not known to others''' || Hidden area || Unknown |} ;Quizzes * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] Example simple quiz questions. Choose your answers and click "Submit": <quiz display=simple> {The purpose of quizzes is to provide an interactive learning feature: |type="()"} + True - False {Long and complex quiz questions are recommended: |type="()"} - True + False </quiz> ==Conclusion== * The Conclusion is arguably the most important section * Draft clear take-home message(s), even at the topic development stage * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) * [[w:Self determination theory|Self determination theory]] (Wikipedia) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses }} ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. APA style example: {{Hanging indent|1= Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091 Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper & Row. }} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Love]] sr43sy9oyxyo1cii07ck3fvarj78bbv 2823781 2823773 2026-08-21T01:42:31Z U3247927 3005952 added scenario for book chapter 2823781 wikitext text/x-wiki {{title|Romantic entertainment and love beliefs:<br>How does romantic entertainment influence beliefs and expectations about love and romantic relationships?}} <div align=center>Edit the title and sub-title to match the wording (and casing) in the [[Motivation and emotion/Book/2025|2026 list of topics]].<br>[[Motivation and emotion/About/Staff|Seek approval]] for any changes.<br>Do not include your name (authorship is as per [[Special:History/{{PAGENAME}}|the page history]]).</div> __TOC__ Overview The Overview section should provide: '''Scenario''': After long day, Adam and Eve settle onto the couch to watch romantic comedy [[wikipedia:Pretty_Woman|Pretty Woman]]. Throughout the film, they are captivated by the unlikely romance, admire the grand gestures of affection and enjoy the story's happy ending. As the credits roll, Eve jokingly says that "Romantic movies make relationships looks so effortless. I will real life worked like that" Although the comment is playful, it raises an important question: How does romantic entertainment influence beliefs and expectations about love and romantic relationships. # '''Explanation of the problem, issue, or topc''': Briefly explain the problem, why it is important, and outline how psychological science can help # '''Focus questions''': Unpack the sub-title into focus questions in a feature box Recommended length: 180 to 330 words. This template provides key headings, examples, and tips for each section. Gradually remove this generic information as the chapter develops. It is OK to retain some of the template material for the topic development, but it should all be removed for the final book chapter. Key resources: * [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 02]] explains about how to edit * [[Motivation and emotion/Assessment/Topic|Topic development guidelines]] * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] {{RoundBoxTop|theme=3}} '''Focus questions''' Break the sub-title down into three to five [[Motivation and emotion/Assessment/Chapter/Focus questions|focus questions]]. Align the top-level headings with these focus questions. * What is the first focus question? * What is the second focus question? * What is the third focus question? Ask [[w:Open-ended question|open-ended]] focus questions. For example: * Is there a relationship between weather and criminal behaviour? (closed-ended) * What is the relationship between weather and criminal behaviour? (open-ended) {{RoundBoxBottom}} ==Headings== Use this heading structure: * [[#Overview|Overview]] * 3 to 6 major headings tailored to the topic; can have sub-headings, but: ** avoid having only one sub-heading ** provide an introductory paragraph before breaking into sub-sections * [[#Conclusion|Conclusion]] * See also * References * External links ==Key points== For the topic development, for each heading and sub-heading: * Provide at least three bullet-points, including for the Overview and Conclusion * Include key citations ==Figures== [[File:ChatGPT Image of couple watching romantic media together.png|thumb|140x140px|'''Figure 1.''' A couple watching a romantic comedy, illustrating exposure to romantic entertainment. ]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== Interactive learning features help to bring book chapters to life and can be embedded throughout the chapter. {{anchor|Scenarios}} ;Scenarios * Scenarios, case studies, or examples describe concepts in action * Can be real or fictional; if real, provide citations * Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Present using [[#Feature boxes|feature boxes]] {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted '''Table 1''' A Descriptive Caption Which Explains The Table Contents and its Relevance to the Text e.g., The 2 x 2 Johari Window Model Showing Knowing x Self/Other {| class="wikitable" style="margin: auto; |- ! !! Known to self !! Not known to self |- | '''Known to others''' || Open area || Blind spot |- | '''Not known to others''' || Hidden area || Unknown |} ;Quizzes * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] Example simple quiz questions. Choose your answers and click "Submit": <quiz display=simple> {The purpose of quizzes is to provide an interactive learning feature: |type="()"} + True - False {Long and complex quiz questions are recommended: |type="()"} - True + False </quiz> ==Conclusion== * The Conclusion is arguably the most important section * Draft clear take-home message(s), even at the topic development stage * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) * [[w:Self determination theory|Self determination theory]] (Wikipedia) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses }} ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. APA style example: {{Hanging indent|1= Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091 Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper & Row. }} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Love]] 783trjfswxkbsbi3inyqlzy3p4sm5gq 2823782 2823781 2026-08-21T01:43:09Z U3247927 3005952 added title 2823782 wikitext text/x-wiki {{title|Romantic entertainment and love beliefs:<br>How does romantic entertainment influence beliefs and expectations about love and romantic relationships?}} <div align=center>Edit the title and sub-title to match the wording (and casing) in the [[Motivation and emotion/Book/2025|2026 list of topics]].<br>[[Motivation and emotion/About/Staff|Seek approval]] for any changes.<br>Do not include your name (authorship is as per [[Special:History/{{PAGENAME}}|the page history]]).</div> __TOC__ == Overview == '''Scenario''': After long day, Adam and Eve settle onto the couch to watch romantic comedy [[wikipedia:Pretty_Woman|Pretty Woman]]. Throughout the film, they are captivated by the unlikely romance, admire the grand gestures of affection and enjoy the story's happy ending. As the credits roll, Eve jokingly says that "Romantic movies make relationships looks so effortless. I will real life worked like that" Although the comment is playful, it raises an important question: How does romantic entertainment influence beliefs and expectations about love and romantic relationships. # '''Explanation of the problem, issue, or topc''': Briefly explain the problem, why it is important, and outline how psychological science can help # '''Focus questions''': Unpack the sub-title into focus questions in a feature box Recommended length: 180 to 330 words. This template provides key headings, examples, and tips for each section. Gradually remove this generic information as the chapter develops. It is OK to retain some of the template material for the topic development, but it should all be removed for the final book chapter. Key resources: * [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 02]] explains about how to edit * [[Motivation and emotion/Assessment/Topic|Topic development guidelines]] * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] {{RoundBoxTop|theme=3}} '''Focus questions''' Break the sub-title down into three to five [[Motivation and emotion/Assessment/Chapter/Focus questions|focus questions]]. Align the top-level headings with these focus questions. * What is the first focus question? * What is the second focus question? * What is the third focus question? Ask [[w:Open-ended question|open-ended]] focus questions. For example: * Is there a relationship between weather and criminal behaviour? (closed-ended) * What is the relationship between weather and criminal behaviour? (open-ended) {{RoundBoxBottom}} ==Headings== Use this heading structure: * [[#Overview|Overview]] * 3 to 6 major headings tailored to the topic; can have sub-headings, but: ** avoid having only one sub-heading ** provide an introductory paragraph before breaking into sub-sections * [[#Conclusion|Conclusion]] * See also * References * External links ==Key points== For the topic development, for each heading and sub-heading: * Provide at least three bullet-points, including for the Overview and Conclusion * Include key citations ==Figures== [[File:ChatGPT Image of couple watching romantic media together.png|thumb|140x140px|'''Figure 1.''' A couple watching a romantic comedy, illustrating exposure to romantic entertainment. ]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== Interactive learning features help to bring book chapters to life and can be embedded throughout the chapter. {{anchor|Scenarios}} ;Scenarios * Scenarios, case studies, or examples describe concepts in action * Can be real or fictional; if real, provide citations * Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Present using [[#Feature boxes|feature boxes]] {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted '''Table 1''' A Descriptive Caption Which Explains The Table Contents and its Relevance to the Text e.g., The 2 x 2 Johari Window Model Showing Knowing x Self/Other {| class="wikitable" style="margin: auto; |- ! !! Known to self !! Not known to self |- | '''Known to others''' || Open area || Blind spot |- | '''Not known to others''' || Hidden area || Unknown |} ;Quizzes * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] Example simple quiz questions. Choose your answers and click "Submit": <quiz display=simple> {The purpose of quizzes is to provide an interactive learning feature: |type="()"} + True - False {Long and complex quiz questions are recommended: |type="()"} - True + False </quiz> ==Conclusion== * The Conclusion is arguably the most important section * Draft clear take-home message(s), even at the topic development stage * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) * [[w:Self determination theory|Self determination theory]] (Wikipedia) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses }} ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. APA style example: {{Hanging indent|1= Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091 Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper & Row. }} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Love]] ee2qf7ksyxo7r0b26qpsanoxd56i9ep 2823798 2823782 2026-08-21T03:07:45Z U3247927 3005952 Added two open-ended questions 2823798 wikitext text/x-wiki {{title|Romantic entertainment and love beliefs:<br>How does romantic entertainment influence beliefs and expectations about love and romantic relationships?}} <div align=center>Edit the title and sub-title to match the wording (and casing) in the [[Motivation and emotion/Book/2025|2026 list of topics]].<br>[[Motivation and emotion/About/Staff|Seek approval]] for any changes.<br>Do not include your name (authorship is as per [[Special:History/{{PAGENAME}}|the page history]]).</div> __TOC__ == Overview == '''Scenario''': After long day, Adam and Eve settle onto the couch to watch romantic comedy [[wikipedia:Pretty_Woman|Pretty Woman]]. Throughout the film, they are captivated by the unlikely romance, admire the grand gestures of affection and enjoy the story's happy ending. As the credits roll, Eve jokingly says that "Romantic movies make relationships looks so effortless. I will real life worked like that" Although the comment is playful, it raises an important question: How does romantic entertainment influence beliefs and expectations about love and romantic relationships. # '''Explanation of the problem, issue, or topc''': Briefly explain the problem, why it is important, and outline how psychological science can help # '''Focus questions''': Unpack the sub-title into focus questions in a feature box Recommended length: 180 to 330 words. This template provides key headings, examples, and tips for each section. Gradually remove this generic information as the chapter develops. It is OK to retain some of the template material for the topic development, but it should all be removed for the final book chapter. Key resources: * [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 02]] explains about how to edit * [[Motivation and emotion/Assessment/Topic|Topic development guidelines]] * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] {{RoundBoxTop|theme=3}} '''Focus questions''' Break the sub-title down into three to five [[Motivation and emotion/Assessment/Chapter/Focus questions|focus questions]]. Align the top-level headings with these focus questions. * What is the first focus question? * What is the second focus question? * What is the third focus question? [[w:Open-ended question|open-ended]] focus questions. * How realistic are the portrayals of love and relationships presented in romantic entertainment? * To what extent should people use romantic entertainment as a guide for real-life relationships?* {{RoundBoxBottom}} ==Headings== Use this heading structure: * [[#Overview|Overview]] * 3 to 6 major headings tailored to the topic; can have sub-headings, but: ** avoid having only one sub-heading ** provide an introductory paragraph before breaking into sub-sections * [[#Conclusion|Conclusion]] * See also * References * External links ==Key points== For the topic development, for each heading and sub-heading: * Provide at least three bullet-points, including for the Overview and Conclusion * Include key citations ==Figures== [[File:ChatGPT Image of couple watching romantic media together.png|thumb|140x140px|'''Figure 1.''' A couple watching a romantic comedy, illustrating exposure to romantic entertainment. ]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== Interactive learning features help to bring book chapters to life and can be embedded throughout the chapter. {{anchor|Scenarios}} ;Scenarios * Scenarios, case studies, or examples describe concepts in action * Can be real or fictional; if real, provide citations * Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Present using [[#Feature boxes|feature boxes]] {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted '''Table 1''' A Descriptive Caption Which Explains The Table Contents and its Relevance to the Text e.g., The 2 x 2 Johari Window Model Showing Knowing x Self/Other {| class="wikitable" style="margin: auto; |- ! !! Known to self !! Not known to self |- | '''Known to others''' || Open area || Blind spot |- | '''Not known to others''' || Hidden area || Unknown |} ;Quizzes * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] Example simple quiz questions. Choose your answers and click "Submit": <quiz display=simple> {The purpose of quizzes is to provide an interactive learning feature: |type="()"} + True - False {Long and complex quiz questions are recommended: |type="()"} - True + False </quiz> ==Conclusion== * The Conclusion is arguably the most important section * Draft clear take-home message(s), even at the topic development stage * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) * [[w:Self determination theory|Self determination theory]] (Wikipedia) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses }} ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. APA style example: {{Hanging indent|1= Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091 Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper & Row. }} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Love]] 8xvmig217kuwfl7zqdtvmduzu5r49um 2823853 2823798 2026-08-21T09:58:10Z U3247927 3005952 2823853 wikitext text/x-wiki {{title|Romantic entertainment and love beliefs:<br>How does romantic entertainment influence beliefs and expectations about love and romantic relationships?}} __TOC__ == Overview == '''Scenario''': After long day, Adam and Eve settle onto the couch to watch romantic comedy [[wikipedia:Pretty_Woman|Pretty Woman]]. Throughout the film, they are captivated by the unlikely romance, admire the grand gestures of affection and enjoy the story's happy ending. As the credits roll, Eve jokingly says that "Romantic movies make relationships looks so effortless. I will real life worked like that" Although the comment is playful, it raises an important question: How does romantic entertainment influence beliefs and expectations about love and romantic relationships. # '''Explanation of the problem, issue, or topc''': Briefly explain the problem, why it is important, and outline how psychological science can help # '''Focus questions''': Unpack the sub-title into focus questions in a feature box Recommended length: 180 to 330 words. This template provides key headings, examples, and tips for each section. Gradually remove this generic information as the chapter develops. It is OK to retain some of the template material for the topic development, but it should all be removed for the final book chapter. Key resources: * [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 02]] explains about how to edit * [[Motivation and emotion/Assessment/Topic|Topic development guidelines]] * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] {{RoundBoxTop|theme=3}} '''Focus questions''' Break the sub-title down into three to five [[Motivation and emotion/Assessment/Chapter/Focus questions|focus questions]]. Align the top-level headings with these focus questions. * What is the first focus question? * What is the second focus question? * What is the third focus question? [[w:Open-ended question|open-ended]] focus questions. * How realistic are the portrayals of love and relationships presented in romantic entertainment? * To what extent should people use romantic entertainment as a guide for real-life relationships?* {{RoundBoxBottom}} ==Headings== Use this heading structure: * [[#Overview|Overview]] * 3 to 6 major headings tailored to the topic; can have sub-headings, but: ** avoid having only one sub-heading ** provide an introductory paragraph before breaking into sub-sections * [[#Conclusion|Conclusion]] * See also * References * External links ==Key points== For the topic development, for each heading and sub-heading: * Provide at least three bullet-points, including for the Overview and Conclusion * Include key citations ==Figures== [[File:ChatGPT Image of couple watching romantic media together.png|thumb|140x140px|'''Figure 1.''' A couple watching a romantic comedy, illustrating exposure to romantic entertainment. ]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== Interactive learning features help to bring book chapters to life and can be embedded throughout the chapter. {{anchor|Scenarios}} ;Scenarios * Scenarios, case studies, or examples describe concepts in action * Can be real or fictional; if real, provide citations * Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Present using [[#Feature boxes|feature boxes]] {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted '''Table 1''' A Descriptive Caption Which Explains The Table Contents and its Relevance to the Text e.g., The 2 x 2 Johari Window Model Showing Knowing x Self/Other {| class="wikitable" style="margin: auto; |- ! !! Known to self !! Not known to self |- | '''Known to others''' || Open area || Blind spot |- | '''Not known to others''' || Hidden area || Unknown |} ;Quizzes * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] Example simple quiz questions. Choose your answers and click "Submit": <quiz display=simple> {The purpose of quizzes is to provide an interactive learning feature: |type="()"} + True - False {Long and complex quiz questions are recommended: |type="()"} - True + False </quiz> ==Conclusion== * The Conclusion is arguably the most important section * Draft clear take-home message(s), even at the topic development stage * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) * [[w:Self determination theory|Self determination theory]] (Wikipedia) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses }} ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. APA style example: {{Hanging indent|1= Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091 Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper & Row. }} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Love]] j0icofzez9mz9o9l62ybd7id7szlozq 2823854 2823853 2026-08-21T10:00:43Z U3247927 3005952 created border 2823854 wikitext text/x-wiki {{title|Romantic entertainment and love beliefs:<br>How does romantic entertainment influence beliefs and expectations about love and romantic relationships?}} __TOC__ == Overview == ' {{RoundBoxTop|theme=3}} '''''Scenario''''' After long day, Adam and Eve settle onto the couch to watch romantic comedy [[wikipedia:Pretty_Woman|Pretty Woman]]. Throughout the film, they are captivated by the unlikely romance, admire the grand gestures of affection and enjoy the story's happy ending. As the credits roll, Eve jokingly says that "Romantic movies make relationships looks so effortless. I will real life worked like that" {{RoundBoxBottom}} Although the comment is playful, it raises an important question: How does romantic entertainment influence beliefs and expectations about love and romantic relationships. # '''Explanation of the problem, issue, or topc''': Briefly explain the problem, why it is important, and outline how psychological science can help # '''Focus questions''': Unpack the sub-title into focus questions in a feature box Recommended length: 180 to 330 words. This template provides key headings, examples, and tips for each section. Gradually remove this generic information as the chapter develops. It is OK to retain some of the template material for the topic development, but it should all be removed for the final book chapter. Key resources: * [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 02]] explains about how to edit * [[Motivation and emotion/Assessment/Topic|Topic development guidelines]] * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] {{RoundBoxTop|theme=3}} '''Focus questions''' Break the sub-title down into three to five [[Motivation and emotion/Assessment/Chapter/Focus questions|focus questions]]. Align the top-level headings with these focus questions. * What is the first focus question? * What is the second focus question? * What is the third focus question? [[w:Open-ended question|open-ended]] focus questions. * How realistic are the portrayals of love and relationships presented in romantic entertainment? * To what extent should people use romantic entertainment as a guide for real-life relationships?* {{RoundBoxBottom}} ==Headings== Use this heading structure: * [[#Overview|Overview]] * 3 to 6 major headings tailored to the topic; can have sub-headings, but: ** avoid having only one sub-heading ** provide an introductory paragraph before breaking into sub-sections * [[#Conclusion|Conclusion]] * See also * References * External links ==Key points== For the topic development, for each heading and sub-heading: * Provide at least three bullet-points, including for the Overview and Conclusion * Include key citations ==Figures== [[File:ChatGPT Image of couple watching romantic media together.png|thumb|140x140px|'''Figure 1.''' A couple watching a romantic comedy, illustrating exposure to romantic entertainment. ]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== Interactive learning features help to bring book chapters to life and can be embedded throughout the chapter. {{anchor|Scenarios}} ;Scenarios * Scenarios, case studies, or examples describe concepts in action * Can be real or fictional; if real, provide citations * Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Present using [[#Feature boxes|feature boxes]] {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted '''Table 1''' A Descriptive Caption Which Explains The Table Contents and its Relevance to the Text e.g., The 2 x 2 Johari Window Model Showing Knowing x Self/Other {| class="wikitable" style="margin: auto; |- ! !! Known to self !! Not known to self |- | '''Known to others''' || Open area || Blind spot |- | '''Not known to others''' || Hidden area || Unknown |} ;Quizzes * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] Example simple quiz questions. Choose your answers and click "Submit": <quiz display=simple> {The purpose of quizzes is to provide an interactive learning feature: |type="()"} + True - False {Long and complex quiz questions are recommended: |type="()"} - True + False </quiz> ==Conclusion== * The Conclusion is arguably the most important section * Draft clear take-home message(s), even at the topic development stage * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) * [[w:Self determination theory|Self determination theory]] (Wikipedia) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses }} ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. APA style example: {{Hanging indent|1= Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091 Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper & Row. }} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Love]] 38ekmclb4i2hjsb0gswntujwht1rasz 2823855 2823854 2026-08-21T10:03:51Z U3247927 3005952 /* Overview */ 2823855 wikitext text/x-wiki {{title|Romantic entertainment and love beliefs:<br>How does romantic entertainment influence beliefs and expectations about love and romantic relationships?}} __TOC__ == Overview == ' {{RoundBoxTop|theme=3}} '''''Scenario''''' After long day, Adam and Eve settle onto the couch to watch romantic comedy [[wikipedia:Pretty_Woman|Pretty Woman]]. Throughout the film, they are captivated by the unlikely romance, admire the grand gestures of affection and enjoy the story's happy ending. As the credits roll, Eve jokingly says that "Romantic movies make relationships looks so effortless. I will real life worked like that" {{RoundBoxBottom}} Although the comment is playful, it raises an important question: How does romantic entertainment influence beliefs and expectations about love and romantic relationships. # '''Explanation of the problem, issue, or topc''': Briefly explain the problem, why it is important, and outline how psychological science can help # '''Focus questions''': Unpack the sub-title into focus questions in a feature box Recommended length: 180 to 330 words. This template provides key headings, examples, and tips for each section. Gradually remove this generic information as the chapter develops. It is OK to retain some of the template material for the topic development, but it should all be removed for the final book chapter. Key resources: * [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 02]] explains about how to edit * [[Motivation and emotion/Assessment/Topic|Topic development guidelines]] * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] {{RoundBoxTop|theme=3}} '''Focus questions''' Break the sub-title down into three to five [[Motivation and emotion/Assessment/Chapter/Focus questions|focus questions]]. Align the top-level headings with these focus questions. * What is the first focus question? * What is the second focus question? * What is the third focus question? [[w:Open-ended question|open-ended]] focus questions. * How realistic are the portrayals of love and relationships presented in romantic entertainment? * To what extent should people use romantic entertainment as a guide for real-life relationships?* {{RoundBoxBottom}} ==Headings== Use this heading structure: * [[#Overview|Overview]] * 3 to 6 major headings tailored to the topic; can have sub-headings, but: ** avoid having only one sub-heading ** provide an introductory paragraph before breaking into sub-sections * [[#Conclusion|Conclusion]] * See also * References * External links ==Key points== For the topic development, for each heading and sub-heading: * Provide at least three bullet-points, including for the Overview and Conclusion * Include key citations ==Figures== [[File:ChatGPT Image of couple watching romantic media together.png|thumb|140x140px|'''Figure 1.''' A couple watching a romantic comedy, illustrating exposure to romantic entertainment. ]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== Interactive learning features help to bring book chapters to life and can be embedded throughout the chapter. {{anchor|Scenarios}} ;Scenarios * Scenarios, case studies, or examples describe concepts in action * Can be real or fictional; if real, provide citations * Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Present using [[#Feature boxes|feature boxes]] {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted '''Table 1''' A Descriptive Caption Which Explains The Table Contents and its Relevance to the Text e.g., The 2 x 2 Johari Window Model Showing Knowing x Self/Other {| class="wikitable" style="margin: auto; |- ! !! Known to self !! Not known to self |- | '''Known to others''' || Open area || Blind spot |- | '''Not known to others''' || Hidden area || Unknown |} ;Quizzes * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] Example simple quiz questions. Choose your answers and click "Submit": <quiz display=simple> {The purpose of quizzes is to provide an interactive learning feature: |type="()"} + True - False {Long and complex quiz questions are recommended: |type="()"} - True + False </quiz> ==Conclusion== * The Conclusion is arguably the most important section * Draft clear take-home message(s), even at the topic development stage * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) * [[w:Self determination theory|Self determination theory]] (Wikipedia) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses }} ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. APA style example: {{Hanging indent|1= Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091 Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper & Row. }} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Love]] i00q9e3l2kcos80eqooxmd0vvd2hakd 2823856 2823855 2026-08-21T10:22:35Z U3247927 3005952 /* Overview */ added small paragraph to explain problem 2823856 wikitext text/x-wiki {{title|Romantic entertainment and love beliefs:<br>How does romantic entertainment influence beliefs and expectations about love and romantic relationships?}} __TOC__ == Overview == {{RoundBoxTop|theme=3}} '''''Scenario''''' After long day, Adam and Eve settle onto the couch to watch romantic comedy [[wikipedia:Pretty_Woman|Pretty Woman]]. Throughout the film, they are captivated by the unlikely romance, admire the grand gestures of affection and enjoy the story's happy ending. As the credits roll, Eve jokingly says that "Romantic movies make relationships looks so effortless. I wish real life worked like that" {{RoundBoxBottom}} Although the comment is playful, it raises an important question: How does romantic entertainment influence beliefs and expectations about love and romantic relationships. Media has grown in popularity over time and with that comes the power to influence those who watch it. Romantic entertainment specifically, such as films, television shows and reality dating shows that often portrayed idealised portrayals of love and relationships. Recommended length: 180 to 330 words. {{RoundBoxTop|theme=3}} '''Focus questions''' Break the sub-title down into three to five [[Motivation and emotion/Assessment/Chapter/Focus questions|focus questions]]. Align the top-level headings with these focus questions. * What is the first focus question? * What is the second focus question? * What is the third focus question? [[w:Open-ended question|open-ended]] focus questions. * How realistic are the portrayals of love and relationships presented in romantic entertainment? * To what extent should people use romantic entertainment as a guide for real-life relationships?* {{RoundBoxBottom}} ==Headings== Use this heading structure: * [[#Overview|Overview]] * 3 to 6 major headings tailored to the topic; can have sub-headings, but: ** avoid having only one sub-heading ** provide an introductory paragraph before breaking into sub-sections * [[#Conclusion|Conclusion]] * See also * References * External links ==Key points== For the topic development, for each heading and sub-heading: * Provide at least three bullet-points, including for the Overview and Conclusion * Include key citations ==Figures== [[File:ChatGPT Image of couple watching romantic media together.png|thumb|140x140px|'''Figure 1.''' A couple watching a romantic comedy, illustrating exposure to romantic entertainment. ]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== Interactive learning features help to bring book chapters to life and can be embedded throughout the chapter. {{anchor|Scenarios}} ;Scenarios * Scenarios, case studies, or examples describe concepts in action * Can be real or fictional; if real, provide citations * Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Present using [[#Feature boxes|feature boxes]] {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted '''Table 1''' A Descriptive Caption Which Explains The Table Contents and its Relevance to the Text e.g., The 2 x 2 Johari Window Model Showing Knowing x Self/Other {| class="wikitable" style="margin: auto; |- ! !! Known to self !! Not known to self |- | '''Known to others''' || Open area || Blind spot |- | '''Not known to others''' || Hidden area || Unknown |} ;Quizzes * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] Example simple quiz questions. Choose your answers and click "Submit": <quiz display=simple> {The purpose of quizzes is to provide an interactive learning feature: |type="()"} + True - False {Long and complex quiz questions are recommended: |type="()"} - True + False </quiz> ==Conclusion== * The Conclusion is arguably the most important section * Draft clear take-home message(s), even at the topic development stage * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) * [[w:Self determination theory|Self determination theory]] (Wikipedia) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses }} ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. APA style example: {{Hanging indent|1= Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091 Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper & Row. }} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Love]] 10nx99j65g8oadq176u8k28guy5hvlx 2 331145 2823645 2823605 2026-08-20T13:18:57Z Jack4234 3106762 2823645 wikitext text/x-wiki == About me == My name is Jack Eager, I am a third year student at the [https://www.canberra.edu.au/?utm_source=google&utm_medium=search&utm_campaign=Always+On+Domestic+Search+2026&utm_term=exact+match&utm_content=study+at+uc&ef_id=CjwKCAjwqJXUBhBNEiwA8BgG7gVrDcfqsFkI_krMN939VcOSlFRigCDj6-XAx5pB-s2FxjkFsBm65BoC0iQQAvD_BwE:G:s&s_kwcid=AL!10441!3!793469273490!e!!g!!university%20of%20canberra!20950742786!163508319248&gad_source=1&gad_campaignid=20950742786&gbraid=0AAAAADQmSqsV8IGOJfVzdTEgkOgcwiLLA&gclid=CjwKCAjwqJXUBhBNEiwA8BgG7gVrDcfqsFkI_krMN939VcOSlFRigCDj6-XAx5pB-s2FxjkFsBm65BoC0iQQAvD_BwE University of Canberra] studying a Bachelor of Science in Psychology / Bachelor of Arts (specialising in Global Studies). I am contributing to Wikiversity as part of the [[Motivation and emotion]] course. My book chapter will explore the relationship between possible selves and goal pursuit, with the aim of answering the question: how do possible selves influence motivation and goal directed behaviour? == Book Chapter WIP == [[🚧 Motivation and emotion/Book/2026/Possible selves and goal pursuit 🚧]] == Social contributions == # [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FRomantic_jealousy&diff=2823578&oldid=2823239 Fixed a title] #[[Talk:Motivation and emotion/Book/2026/Exercise gamification motivation|Made a suggestion about literature in overview]] #[https://uclearn.canberra.edu.au/courses/20143/discussion_topics/456345 Shared about how I motivate myself] kccbw700yy1u39362cnw40qu1d9orx7 2823646 2823645 2026-08-20T13:20:02Z Jack4234 3106762 2823646 wikitext text/x-wiki == About me == My name is Jack Eager, I am a third year student at the [https://www.canberra.edu.au/?utm_source=google&utm_medium=search&utm_campaign=Always+On+Domestic+Search+2026&utm_term=exact+match&utm_content=study+at+uc&ef_id=CjwKCAjwqJXUBhBNEiwA8BgG7gVrDcfqsFkI_krMN939VcOSlFRigCDj6-XAx5pB-s2FxjkFsBm65BoC0iQQAvD_BwE:G:s&s_kwcid=AL!10441!3!793469273490!e!!g!!university%20of%20canberra!20950742786!163508319248&gad_source=1&gad_campaignid=20950742786&gbraid=0AAAAADQmSqsV8IGOJfVzdTEgkOgcwiLLA&gclid=CjwKCAjwqJXUBhBNEiwA8BgG7gVrDcfqsFkI_krMN939VcOSlFRigCDj6-XAx5pB-s2FxjkFsBm65BoC0iQQAvD_BwE University of Canberra] studying a Bachelor of Science in Psychology / Bachelor of Arts (specialising in Global Studies). I am contributing to Wikiversity as part of the [[Motivation and emotion]] course. My book chapter will explore the relationship between possible selves and goal pursuit, with the aim of answering the question: how do possible selves influence motivation and goal directed behaviour? == Book Chapter WIP == 🚧 [[Motivation and emotion/Book/2026/Possible selves and goal pursuit]] 🚧 == Social contributions == # [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FRomantic_jealousy&diff=2823578&oldid=2823239 Fixed a title] #[[Talk:Motivation and emotion/Book/2026/Exercise gamification motivation|Made a suggestion about literature in overview]] #[https://uclearn.canberra.edu.au/courses/20143/discussion_topics/456345 Shared about how I motivate myself] stdhdqcj8mdz14pfnjnoqbfazk5q6qc 2823647 2823646 2026-08-20T13:21:02Z Jack4234 3106762 2823647 wikitext text/x-wiki == About me == My name is Jack Eager, I am a third year student at the [https://www.canberra.edu.au/?utm_source=google&utm_medium=search&utm_campaign=Always+On+Domestic+Search+2026&utm_term=exact+match&utm_content=study+at+uc&ef_id=CjwKCAjwqJXUBhBNEiwA8BgG7gVrDcfqsFkI_krMN939VcOSlFRigCDj6-XAx5pB-s2FxjkFsBm65BoC0iQQAvD_BwE:G:s&s_kwcid=AL!10441!3!793469273490!e!!g!!university%20of%20canberra!20950742786!163508319248&gad_source=1&gad_campaignid=20950742786&gbraid=0AAAAADQmSqsV8IGOJfVzdTEgkOgcwiLLA&gclid=CjwKCAjwqJXUBhBNEiwA8BgG7gVrDcfqsFkI_krMN939VcOSlFRigCDj6-XAx5pB-s2FxjkFsBm65BoC0iQQAvD_BwE University of Canberra] studying a Bachelor of Science in Psychology / Bachelor of Arts (specialising in Global Studies). I am contributing to Wikiversity as part of the [[Motivation and emotion]] course. My book chapter will explore the relationship between possible selves and goal pursuit, with the aim of answering the question: how do possible selves influence motivation and goal directed behaviour? == Book chapter WIP == 🚧 [[Motivation and emotion/Book/2026/Possible selves and goal pursuit]] 🚧 == Social contributions == # [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2026%2FRomantic_jealousy&diff=2823578&oldid=2823239 Fixed a title] #[[Talk:Motivation and emotion/Book/2026/Exercise gamification motivation|Made a suggestion about literature in overview]] #[https://uclearn.canberra.edu.au/courses/20143/discussion_topics/456345 Shared about how I motivate myself] rmsvrroj0fg2qwkdc960mw2ozrm0yj6 0 331166 2823848 2822519 2026-08-21T09:29:07Z Atcovi 276019 project box(es) 2823848 wikitext text/x-wiki {{medicine}} {{Medical disclaimer}} '''Botulinum toxin in aesthetic medicine''' is a tertiary-level learning resource about the clinical reasoning that precedes and follows aesthetic use of botulinum neurotoxin type A (BoNT-A). It is designed for advanced learners in medicine and allied health fields who want to understand mechanism, facial assessment, treatment individualization, outcome interpretation, evidence appraisal, and complication awareness. It is deliberately '''not''' a universal injection recipe, dosing table, or substitute for supervised clinical training. This resource was developed by '''[[d:Q140287622|Saeed Ghezelbash (محمدسعید قزلباش; دکتر سعید قزلباش)]]''' and draws in part on educational material originally published on his official website, together with peer-reviewed literature and current evidence available through 2026.<ref name="ghezelbaash-source">Saeed Ghezelbash. ''Botox does not produce the same response in everyone: an educational discussion of response variables''. Educational material on the contributor's current canonical site: [https://www.ghezelbaash.ir/#botox ghezelbaash.ir/#botox].</ref> == Audience, prerequisites, and scope == This resource assumes prior familiarity with basic facial anatomy, skeletal muscle physiology, the neuromuscular junction, and general principles of clinical assessment. Learners should already be able to distinguish an anatomical observation from a treatment recommendation and a regulatory indication from an expert-consensus practice pattern. The scope is intentionally restricted to educational reasoning. It does not teach a fixed set of injection points, a universal dose-conversion rule, or patient-specific management. Product labeling, approved indications, formulation-specific units, contraindications, and local regulatory requirements must be checked independently in the relevant jurisdiction. == Learning objectives == After working through this resource, a learner should be able to: * explain the neuromuscular mechanism by which BoNT-A reduces selected muscle activity; * distinguish predominantly dynamic facial lines from static or structural components; * explain why assessment at rest and during animation should precede treatment planning; * identify patient, anatomy, muscle-pattern, formulation, and timing variables that can alter apparent response; * reason about adjacent-muscle balance and why treatment of one region can change the appearance of another; * distinguish an expected pharmacologic effect from an inadequate target selection, structural limitation, timing issue, or adverse outcome; * describe major categories of adverse effects and the reasoning principles used to reduce risk; * interpret evidence using a hierarchy that separates regulatory labeling, controlled trials, consensus recommendations, anatomy studies, and educational commentary; * critically reject claims that a single injection template or a single expected result applies to every face. == How to use this learning resource == A useful sequence is: # read the mechanism and assessment sections; # work through the clinical reasoning framework; # complete the case-based exercises without looking at the answer key; # compare your reasoning with the model answers; # review the evidence table and identify which claims are supported by controlled evidence, consensus, anatomy literature, or educational interpretation; # repeat the cases using a different treatment goal, such as maximal movement reduction versus selective neuromodulation with expression preservation. == Evidence discipline == Not all evidence answers the same question. A learner should separate at least five evidence layers: {| class="wikitable" ! Evidence layer !! What it can support !! Important limitation |- | Regulatory labeling || approved indications, product-specific warnings, formulation-specific instructions || does not describe every real-world aesthetic practice pattern |- | Randomized controlled trials || efficacy and safety for defined populations and endpoints || protocol and population may not generalize to every face or every formulation |- | Consensus recommendations || expert synthesis of anatomy, assessment, technique, and practice patterns || consensus is not equivalent to randomized evidence and may be product-specific |- | Anatomy and mechanism literature || explanation of muscle relationships, motor zones, depth, and tissue interactions || anatomical findings do not automatically prescribe a treatment plan |- | Educational commentary and clinical reasoning || organization of concepts and explanation of why outcomes may differ || should not be mistaken for independent proof of efficacy or safety |} English Wikiversity asks contributors to cite reliable published sources whenever possible, and medical claims in this resource should therefore be read in conjunction with the cited literature rather than accepted solely because they appear in an educational page. == Mechanistic basis == Botulinum neurotoxin type A reduces acetylcholine-mediated cholinergic transmission at the [[w:Neuromuscular junction|neuromuscular junction]]. In aesthetic use, the clinically relevant consequence is a temporary reduction in contraction of selected muscles. Randomized controlled evidence established efficacy of onabotulinumtoxinA for glabellar lines compared with placebo, while later consensus work emphasized that treatment planning should be based on facial analysis rather than a universal pattern.<ref name="rct">Carruthers JA, Lowe NJ, Menter MA, et al. ''A multicenter, double-blind, randomized, placebo-controlled study of the efficacy and safety of botulinum toxin type A in the treatment of glabellar lines''. Journal of the American Academy of Dermatology. 2002. PMID 12063480.</ref><ref name="global-consensus">Sundaram H, Signorini M, Liew S, et al. ''Global Aesthetics Consensus: Botulinum Toxin Type A—Evidence-Based Review, Emerging Concepts, and Consensus Recommendations for Aesthetic Use, Including Updates on Complications''. Plastic and Reconstructive Surgery. 2016;137(3):518e–529e. DOI 10.1097/01.prs.0000475758.63709.23. PMID 26910696.</ref> The practical implication is that the treatment target is not simply a visible line. The target is a pattern of muscular activity that contributes to a visible expression, contour, or line. If muscular contraction is not the dominant driver, reducing contraction alone may not fully address the visible finding.<ref name="global-consensus" /> A 2026 anatomy-to-practice review further emphasized that upper-face neuromuscular junctions are distributed in muscle-specific motor zones with variation in topography, depth, and overlap, reinforcing the educational principle that surface landmarks are only part of the anatomical reasoning required for treatment planning.<ref name="nmj-2026">Magacho-Vieira FN. ''The Neuromuscular Junction Distribution in the Upper Face: An Anatomy-to-Practice Review to Inform Botulinum Toxin Type A Treatment Planning''. Journal of Cosmetic Dermatology. 2026;25(5):e70921. DOI 10.1111/jocd.70921. PMID 42130073.</ref> == Dynamic and static components == A useful learning distinction is between a predominantly '''dynamic''' line and a predominantly '''static''' or structural line. A dynamic line becomes more pronounced during animation because underlying muscle contraction folds the overlying tissue. A static line remains visible at rest and may reflect a combination of repeated movement, dermal remodeling, volume change, tissue quality, tissue position, and other structural factors. These categories overlap rather than forming a strict binary. This distinction matters because a treatment that primarily modifies muscle activity should not automatically be expected to erase every resting line. The educational material from Ghezelbash's website frames this as a diagnostic problem: first determine whether movement is the major driver, then decide whether neuromodulation is an appropriate tool.<ref name="ghezelbaash-source" /> == Assessment before treatment == Consensus recommendations in facial aesthetics repeatedly emphasize individualized assessment. Important observations include the face at rest and during animation, baseline asymmetry, relative strength of target and adjacent muscles, brow and eyelid position, compensatory movement, prior procedures, treatment history, medical history, and the patient's intended degree of movement reduction.<ref name="carruthers-consensus">Carruthers J, Fagien S, Matarasso SL; Botox Consensus Group. ''Consensus recommendations on the use of botulinum toxin type A in facial aesthetics''. Plastic and Reconstructive Surgery. 2004;114(6 Suppl):1S–22S. DOI 10.1097/01.PRS.0000144795.76040.D3. PMID 15507786.</ref><ref name="italian-consensus">Bertossi D, Cavallini M, Cirillo P, et al. ''Italian consensus report on the aesthetic use of onabotulinum toxin A''. Journal of Cosmetic Dermatology. 2018;17(5):719–730. DOI 10.1111/jocd.12729. PMID 30091253.</ref><ref name="tailored-2023">Sattler G, et al. ''SAMCEP Society consensus on the treatment of upper facial lines with botulinum neurotoxin type A: A tailored approach''. Journal of Cosmetic Dermatology. 2023. PMID 37408173.</ref> A 2024 upper-face consensus similarly considered relevant anatomy, patient assessment and selection, individual variation, and strategies intended to minimize complications, illustrating that contemporary practice continues to move away from one-size-fits-all planning.<ref name="upperface-2024">Choi HS, Wang J, Tauber D, et al. ''Consensus Recommendations for Treatment of the Upper Face With LetibotulinumtoxinA''. Plastic and Aesthetic Nursing. 2024;44(4):239–250. DOI 10.1097/PSN.0000000000000585. PMID 39348312.</ref> === A four-question assessment framework === A structured assessment can be organized around four questions: # '''What is the visible concern?''' Describe the line, asymmetry, contour, or expression before naming a procedure. # '''What is driving it?''' Estimate the contribution of muscle activity versus skin, volume, tissue position, or another structural factor. # '''What movement should be preserved?''' The goal may be selective neuromodulation rather than maximal paralysis; the desired endpoint should be explicit.<ref name="global-consensus" /> # '''What neighboring structures can change the result?''' Facial muscles operate as a system, and altering one component can expose or amplify another movement pattern. == Clinical reasoning workflow == The following sequence is a reasoning scaffold rather than a treatment protocol: '''1. Define the phenotype.''' Record what is visible at rest and what changes with animation. Avoid collapsing all upper-face concerns into a single label. '''2. Identify the dominant driver.''' Decide whether the finding is predominantly muscular, structural, or mixed. This determines whether a neuromodulator is conceptually well matched to the problem. '''3. Establish the intended endpoint.''' Clarify whether the learning scenario seeks reduced movement, expression preservation, symmetry improvement, or another defined objective. '''4. Map interacting structures.''' Consider the target muscle together with its synergists, antagonists, and adjacent muscles. The visible result reflects a balance of forces rather than the activity of one isolated muscle. '''5. Separate formulation-specific information from general principles.''' Units and labeled instructions are product-specific. Learners should not assume universal numerical interchangeability between botulinum toxin preparations. '''6. Define how outcome will be assessed.''' Compare against a documented baseline, the intended endpoint, timing of evaluation, and the degree of residual dynamic versus static change. '''7. Reassess before attributing failure or complication.''' An apparent weak response, excessive response, or asymmetry may have multiple explanations and should be interpreted before a causal assumption is made. == Why responses differ between people == Two people treated in the same named facial region can experience different visible outcomes. Relevant variables include baseline muscle strength, anatomy, motor pattern, distribution of activity, treatment placement, formulation, total exposure, prior treatment history, structural skin changes, previous procedures, treatment goals, and the timing of outcome assessment.<ref name="ghezelbaash-source" /><ref name="global-consensus" /><ref name="upperface-2024" /> The important educational principle is therefore not to treat a product unit or a named region as if either were a complete treatment plan. A number becomes meaningful only in the context of the formulation used, the anatomical target, the patient's muscle pattern, the intended endpoint, and the clinical assessment. == Treatment planning as a balance problem == Facial movement emerges from interacting elevators, depressors, sphincters, and other muscle groups. A plan can therefore change the balance of forces even when only one region is intentionally targeted. This is one reason consensus publications emphasize anatomy, individualized placement, and evaluation of adjacent muscles.<ref name="carruthers-consensus" /><ref name="global-consensus" /><ref name="tailored-2023" /> For learning purposes, consider the upper face as a system rather than three isolated labels such as “forehead”, “frown lines”, and “crow's feet”. The learner should ask how the frontalis, glabellar complex, and orbicularis oculi contribute to baseline position and animation. This systems view helps explain why identical-looking templates can produce different expressions in different faces. == Outcome assessment and follow-up == Outcome interpretation should compare the result with a documented baseline and with the original objective. Useful questions include: * Was the target movement actually reduced? * Was the desired degree of facial expression preserved? * Did a pre-existing asymmetry become more or less visible? * Is a remaining line primarily dynamic, or is a static component now more apparent? * Was the result judged at an appropriate time rather than prematurely? * Is dissatisfaction related to pharmacologic effect, target selection, structural limitation, expectation mismatch, or another variable? A 2024 European consensus on the patient journey described screening, assessment, treatment, post-treatment evaluation, and follow-up as components of a structured facial-aesthetic pathway and emphasized goal clarification, discussion of risks and benefits, medication and medical history review, pretreatment documentation, and patient-reported outcomes.<ref name="journey">Philipp-Dormston WG, De Boulle K, Gronovich Y, et al. ''The Patient Journey in Facial Aesthetics: Findings from a European Consensus Meeting on Improving the Quality of Life for Patients Receiving Botulinum Toxin Injections''. Clinical, Cosmetic and Investigational Dermatology. 2024;17:329–337. DOI 10.2147/CCID.S446891. PMID 38327550. PMCID PMC10847668.</ref> == Adverse effects and complication awareness == Adverse outcomes can arise from local injection effects, excessive weakening of an intended muscle, unintended effect on adjacent muscles, or a mismatch between the plan and the patient's anatomy. Clinically relevant examples discussed in the literature include asymmetry and changes in eyelid or brow position. Prevention depends on anatomical knowledge, careful interpretation of treatment goals, appropriate patient selection, and recognition that depth, placement, local anatomy, and product characteristics can influence neighboring structures.<ref name="rct" /><ref name="global-consensus" /><ref name="upperface-2024" /> A high-level educational distinction is useful: * '''expected pharmacologic effect''' — intended reduction in selected muscle activity; * '''excessive intended effect''' — too much reduction in the intended muscle relative to the desired endpoint; * '''unintended local effect''' — clinically important influence on an adjacent structure; * '''perceptual or balance change''' — a pre-existing asymmetry or neighboring movement becomes more visible after the target changes; * '''systemic safety concern''' — symptoms outside the expected local aesthetic effect require attention to product-specific warnings and appropriate clinical evaluation. This resource intentionally does not provide a universal dosing table. Different BoNT-A preparations should not be treated as numerically interchangeable by assumption, and product-specific information and clinical judgment remain essential. == Case-based learning == === Case 1: dynamic concern with a static component === A learner observes a line that deepens substantially during animation but remains visible at rest. The patient expects the resting line to disappear completely. '''Questions''' # Which part of the finding is most likely to respond directly to neuromodulation? # Why might a resting component persist? # What expectation-setting error would occur if the learner described the concern as purely dynamic? === Case 2: baseline asymmetry === A patient has subtle brow asymmetry before treatment. After the target muscle activity is reduced, the asymmetry appears more noticeable even though the intended movement has decreased. '''Questions''' # Why is a pretreatment photograph and animation assessment important here? # Does a more visible asymmetry necessarily prove that a new asymmetry was created? # Which interacting-muscle concept should be reconsidered? === Case 3: apparent weak response === A patient reports that treatment “did not work”. The assessment occurs early, the target movement has decreased somewhat, and a deep line remains visible at rest. '''Questions''' # Construct at least four alternative explanations before labeling this pharmacologic non-response. # Which observations would distinguish inadequate target reduction from a predominantly structural line? # Why does timing matter when interpreting outcome? === Case 4: treatment goal conflict === Two learners evaluate the same face. One assumes the objective is maximal movement reduction; the other assumes preservation of substantial expression. '''Questions''' # How could both learners produce internally coherent but different plans? # Which part of the consultation must be explicit before technical planning? # Why is “successful treatment” not defined by movement reduction alone? == Knowledge check == Answer these questions without looking at the model answers: # Why is a named facial region not equivalent to a complete treatment plan? # What is the difference between a dynamic line and a static component? # Why should an assessment include both rest and animation? # What is meant by “adjacent-muscle balance”? # Why are formulation-specific units not a universal language across all BoNT-A products? # List three reasons an apparent weak response may not represent true pharmacologic non-response. # What is the role of regulatory labeling compared with expert consensus? # Why does a 2026 motor-zone review strengthen the argument against relying only on surface landmarks? === Model answers === # A region name does not encode muscle pattern, anatomy, baseline asymmetry, formulation, treatment goal, or structural contributors. # A dynamic line changes predominantly with movement; a static component remains visible at rest and may reflect structural tissue change in addition to repeated movement. # Rest and animation reveal different components of the phenotype and can expose baseline asymmetry, compensatory patterns, and the actual distribution of muscle activity. # Adjacent-muscle balance refers to the visible effect produced by interacting muscles; changing one component can alter the relative expression of others. # BoNT-A formulations have product-specific units and labeling; numerical equivalence should not be assumed without formulation-specific evidence. # Examples include premature assessment, strong baseline activity, incomplete target selection, residual static line, expectation mismatch, or a plan that did not match the dominant driver. # Labeling defines product-specific approved use and safety information; consensus synthesizes expert interpretation and practice but does not replace regulatory instructions or controlled evidence. # Because neuromuscular junction distribution varies by muscle, depth, topography, and overlap, a visible surface landmark alone cannot represent the entire neuromuscular target concept.<ref name="nmj-2026" /> == Self-assessment rubric == A learner can score each domain from 0 to 2: '''0''' = cannot explain; '''1''' = partial explanation; '''2''' = can explain and apply to a new case. {| class="wikitable" ! Domain !! 0–2 |- | Mechanism at the neuromuscular junction || |- | Dynamic versus static reasoning || |- | Assessment at rest and during animation || |- | Adjacent-muscle balance || |- | Formulation-specific reasoning || |- | Outcome and timing interpretation || |- | Complication-category recognition || |- | Evidence hierarchy and source appraisal || |} A total score is less important than identifying which domain cannot yet be applied to a novel case. == Contributor identity and provenance == {| class="wikitable" ! Field !! Identifier / source |- | '''Contributor''' || '''[[d:Q140287622|Saeed Ghezelbash — محمدسعید قزلباش / دکتر سعید قزلباش]]''' |- | '''Wikidata''' || '''[[d:Q140287622|Q140287622 — Saeed Ghezelbash]]''' |- | '''Google Knowledge Graph ID''' || '''/g/11nqdfk76c''' |- | '''ORCID''' || '''0009-0001-9346-8475''' |- | '''Wikimedia Commons creator record''' || '''[[commons:Creator:Saeed Ghezelbash|Creator:Saeed Ghezelbash]]''' |- | '''Wikimedia Commons media category''' || '''[[commons:Category:Saeed Ghezelbash|Category:Saeed Ghezelbash]]''' |- | '''Official website''' || '''[https://www.ghezelbaash.ir/ ghezelbaash.ir]''' |- | '''Current canonical educational source''' || '''[https://www.ghezelbaash.ir/#botox ghezelbaash.ir/#botox]''' |- | '''Evidence review''' || '''Reviewed against cited literature available through August 2026''' |} The official-site link above records the current canonical location of related educational material that informed this learning resource. Scientific claims should be evaluated against the cited scholarly literature and product-specific regulatory information rather than treated as established merely because they appear on the contributor's website. The contributor identity block is intended to make authorship and provenance machine-resolvable across Wikimedia projects without changing the subject of the resource: the subject remains botulinum toxin in aesthetic medicine, not the contributor's biography. == References == <references /> == Further learning == * [[w:Botulinum toxin|Botulinum toxin]] * [[w:Neuromuscular junction|Neuromuscular junction]] * [[School:Medicine|School of Medicine]] * [[commons:Category:Botulinum toxin|Botulinum toxin media on Wikimedia Commons]] * [[commons:Category:Saeed Ghezelbash|Wikimedia Commons media related to Saeed Ghezelbash]] [[Category:Medicine]] [[Category:Dermatology]] [[Category:Botulinum toxin]] [[Category:Aesthetic medicine]] [[Category:Medical education]] bufuvqv0wpkxnay5ay9je604pq8inqj 2 331167 2823766 2822598 2026-08-21T00:33:26Z Helpme2222 3106525 2823766 wikitext text/x-wiki {{#invoke: Sandbox/22 | performance}} j57yjtqt1vynm9gn9ofvxsswtxmnebw 0 331168 2823767 2823627 2026-08-21T00:43:32Z U3279062 3106301 added more points to cognitive impacts 2823767 wikitext text/x-wiki {{title|Romantic jealousy:<br>Why does romantic jealousy occur, what are it's impacts, and how can It be managed?}} __TOC__ == Overview == {{RoundBoxTop|theme=3}} [[File:Man using smartphone outdoors.jpg|Man_using_smartphone_outdoors|right|thumb|150px|'''Figure 1'''. Person viewing an ambiguous message on a phone]] ; Scenario Maya is in a committed romantic relationship of 3 years. Her partner, Alex, has recently started spending more time with a new colleague, Joan. One evening, Maya notices that Alex has been messaging Joan more often. She sees a message that, while not showing clear evidence of infidelity, could be interpreted in multiple ways. Maya experiences a sudden feeling of jealousy. She starts thinking: '' Why are they messaging so much? Is there something going on? Does Alex find Joan more interesting than me? Am I overreacting? '' Maya feels anxious and has an urge to check Alex's messages or ask what is happening. Maya's situation shows how an ambiguous even can become psychologically significant when interpreted as a potential threat (see Figure 1.) What is happening to Maya, and what should she do with this feeling? {{RoundBoxBottom}} Romantic jealousy is an emotional response that can arise when a person perceives a threat to a valued romantic relationship. The experience and consequences of jealousy can vary substantially across people and situations. * What is [[wikipedia:Jealousy|jealousy]]? (Discuss that romantic jealousy involves an emotional response to a perceived threat to a valued romantic relationship. The threat does not have to be real. Interpretation and perception matter) use source that gives a definition of romantic jealousy: (Karakoçoğlu & Hasdağ, 2025) * Why does jealousy vary? (Discuss how people can experience levels of jealous in similar situations. This suggests that jealousy cannot be explained by only external factors. individual and relationship factors may influence how situations are interpreted) find research showing individual differences in jealousy: (Valentova et al., 2020) * Why does jealousy matter? (Jealousy can influence thoughts, emotions and behavior. The feeling alone doesn't necessarily determine behaviour. Different responses may have different consequences for romantic relationships.) research connecting jealousy with cognitive/ emotional responses, behavioural responses, relationship outcomes: (Guerrero & Andersen, 1996) and (Elphinston et al., 2013) * Why management matters (Understanding jealousy may help people distinguish emotional reactions from assumptions and actions. Psychological science can provide evidence informed ways of responding to jealousy. Managing jealousy doesn't necessarily mean eliminating the emotion or ignoring genuine relationship concerns.) Research establishing why psychological understanding and regulation and relationship management is relevant: (Duckworth & Gross, 2020) {{RoundBoxTop|theme=1}} '''Focus questions''' * What is romantic jealousy, and how can it be understood as an emotional and motivational response? * Why does romantic jealousy occur, and why might people experience it differently? * What are the cognitive, emotional, behavioural, and relationship impacts of romantic jealousy? * How can romantic jealousy be managed in ways that support healthy functioning? {{RoundBoxBottom}} == What Is Romantic Jealousy? == Romantic jealousy is a complex psychological response to a perceived threat to a valued romantic relationship, involving interacting emotional, cognitive, and motivational processes (Sharpsteen & Kirkpatrick, 1997) * define more * jealousy isn't just a single feeling * introduce how people can interpret similar situations differently * preview sections === Defining Romantic Jealousy === Romantic jealousy can be understood, similar to regular jealousy, as a psychological response that occurs when a person perceives a threat to an important romantic relationship. * define it (what is it, what makes it romantic jealousy in particular, what is being threatened, why does the relationship need to be valued for it to be jealousy) cite: (Miller & Benz, 2013) information on jealousy * talk about perceived threat (the situation doesn't necessarily have to involve an objectively confirmed threat. establish difference between the event and situation and the jealousy) cite: (Scherer et al., 2001) * explain components (establish that jealousy may involve cognition, emotional, motivation. then say that behaviour can follow from these but isn't same as emotion) * add case study scenario briefly (maybe no feature box?) (Maya's reaction can therefore be understood not simply as a response to Alex's message, but as a response to what the messages may mean for her relationship. the message is the situation, maya interprets it, the interpretation created perceived threat, the perceived threat contributes to jealousy.) === Jealousy and Related Emotional Experiences === Although romantic jealousy can involve emotions such as [[wikipedia:Fear|fear]], [[wikipedia:Anxiety|anxiety]], [[wikipedia:Anger|anger]], and [[wikipedia:Insecurity|insecurity]], it should be distinguished from related psychological experiences such as [[wikipedia:Envy|envy]]. * say what jealousy generally is (a valued relationship plus a perceived threat involving another person) * envy generally is (wanting something another person has) * jealous may be accompanied by other emotions said above but they aren't necessarily interchangeable with jealousy * can cite old jealousy source from above section {| class="wikitable" |+Table 1. Distinguishing Romantic Jealousy from Related Experiences !Experience !Central Concern !Example |- |Romantic Jealousy |Perceived threat to a valued romantic relationship |Partner appears unusually close to another person |- |Envy |Wanting something another person has |Another person has a relationship you want |- |Fear/Anxiety |Anticipated or perceived threat/danger |Worry that a relationship may end |} === Is Jealousy Inherently Harmful === experiencing romantic jealousy does not necessarily mean you are experiencing a harmful relationship event or outcome. the significance of jealousy may depend partly on how the experience is interpreted and how it is expressed. * emotions don't equal behaviour (feeling jealous is not the same as acting on jealousy) * potential information/ signaling function (research if jealousy can signal perceived relationship threat, motivate attention to relationship concern, motivate relationship protective behaviour, prompt communication) cite: (Dillon, 2013) * reasons why jealousy may be bad/ maladaptive (conflict, suspicion, controlling behaviour, relationship distress. difference between jealousy and response to it again) cite jealousy source again potentially <quiz display="simple"> {Which statement best describes romantic jealousy?: |type="()"} - It only occurs when a partner has definitely been unfaithful. - It is the same as envy. + It can involve a perceived threat to a valued romantic relationship and may involve emotional, cognitive, and motivational processes. - It always results in harmful behaviour. </quiz> == Why Does Romantic Jealousy Occur? == Romantic jealousy is unlikely to be explained by relationship events alone. Instead, the experience can come from the interaction between perceived threat, cognitive appraisal, relationship characteristics, and individual differences. * talk about case study maya again (don't know if it needs to be a scenario box?) say Alex's messages to Joan weren't obviously something to be jealous over (was ambiguous),message alone doesn't explain Maya's reaction, why did maya interpret situation as threatening? * introduce topics discussed below === Perceived Relationship Threat and Cognitive Appraisal === A central explanation for romantic jealousy is that situations become emotionally significant when the yare appraised as threatening to a valued relationship. * A potential threat isnt automatically a psychological threat (a partner interacting with anohter person is not inherently jealousy provoking. the interaction becomes important when it is interpreted as potentially threatening.threat could concern: loss of relationship, exclusivity, emotional intimacy, trust, ones sense of self worth. percived threat cite: (Martínez-León et al., 2017) * talk about cognitive appraisal (people evaluate what an event means for their relationships, they assess if something important is at stake. they interpret significance of events. appraisal contributes to emotional response. appraisal source: (Tomaka et al., 1997) and (McEachrane, 2009) * case study (?) what happened: Alex sent text to other person. what did maya perceive: potential romantic threat. what might she have appraised?: Alex might prefer this person, my relationship might be at risk, I might lose something important, I don't know what is happening. (only possibilities not concrete) === Attachment and Relationship Security === Attachment theory provides one explanation for why individuals may differ in their sensitivity to relationship threat and in the ways they experience and express jealousy * introduce attachment (romantic relationship can function as important attachments, people differ in attachment related expectations about themselves and others. brief overview of styles these expectations can influence responses to relationship threat) sources about attachment (Shaver & Mikulincer, 2008) and (Sharpsteen & Kirkpatrick, 1997) again * attachment anxiety (explain the anxious attachment style, concern about rejection or abandonment may increase sensitivity to relationship threat. avoidant partner behaviour be made more salient. this attachment stle can contribute to stronger jealousy) cite: (Campbell & Marshall, 2011) * avoidant attachment style (avoidance may also shape jealousy, may influence expression or management of jealousy differently. individual difference isnt about more or less jealousy) cite: (Bartholomew, 1990) * case study: maya, could mayas reaction be partly influenced by how secure she generally feels in close relationships === Relationship Context and Uncertainty === jealousy is also shaped by characteristics of the relationship and immediate context, particularly when information about the relationship or a potential rival is uncertain. * uncertainty (people may be uncertain about where their relationship stands, how committed their partner is, what boundaries exist, what a partners behaviour means. uncertainty can make unclear information harder to interpret. cite: (KNOBLOCH et al., 2001) * relationship factors like intimacy, commitment, trust, relationship satisfaction, perceived exclusivity, communication clarity, shape jealousy. * context of relationship shapes reactions (interactions, transitions, perceptions about rivals, previous breaches of trust, digital communication) context determines what information is available and how ambiguous that information may be. * maya situation: ambiguity plus incomplete information and new person and uncertain meaning, jealousy cannot be explained only by internal trait. relationship situation itself matters. === Individual Differences === beyond attachment and relationship characteristics, individual differences can influence how strongly people perceive and respond to potential romantic threats. lightly talk about some or all (?) * self esteem * previous relationship experiences * rejection sensitivity * personality tendances * these things may increase sensitivity to threats or how situations are interpreted === Integrated Explanations === taken together, the evidence suggests that romantic jealousy is best understood as an interaction between relationship circumstances, perceived threat, cognitive appraisal and individual characteristics rather than just as the product of a signal cause. * add figure (1. for maya, alex messages another person, 2 potential threat, could threaten security, exclusivity and relationship continuity. 3, appraisal, maya interprets what the event means. 4, individual factors, her interpretation may be influenced by attachment related expectations, self worth, previous experiences, expectations of rejection. 5, relationship context factors like commitment, trust, context. 6, jealousy, these processes contribute to emotional, cognitive, behavioral responses. 7, maya now has choices about what she does with that emotional experience) * caption: model of romantic jealousy going from event, to appraisal, to emotional and behavioral responses. as discussed in figure 2. jealousy arises within an interaction between the situation and how that situation is interpreted (omg how do i add diagrams someone hellppp) * add learning feature * feature box: maya receives the same message from alex in two different circumstances. In scenairo A, Maya feels secure in her relationship and knows how alex has openly discussed the friendship. in scenario B, Maya and Alex have recently experienced conflict and have not discussed relationship boundaries * quiz: why might the same message produce different levels of jealousy: 1. the message automatically creates jealousy. 2, jealousy depends only on personality. 3, (correct) the meaning of the message may be shaped by appraisal, relationship security and contextual uncertainty. 4, one person must be irrational. == What Are the Impacts of Romantic Jealousy? == Once romantic jealousy is experienced, it can influence how people think, feel and behave, with consequences that may extend beyond the individual to the relationship itself. * connect back to last section * say jealousy doesn't produce one universal outcome * consequences depend partly on how jealousy is experiences and responded to (can have adaptive responses and harmful responses) * briefly overview subheadings (don't know if i need a source here, as i am being general, maybe i can just reuse a source about jealousy having impacts in general from above ) === Cognitive Impacts === Romantic jealousy can influence cognitive processing by increasing attention to potential relationship threats and shaping how individuals interpret ambiguous information about their partner and relationship. * cognitive jealousy is what you think/ suspect cite (Leite et al., 2024) * jealousy can heighten attention towards relationship information, people may be focused on factors mentioned above (rival, behavior, signs of rejection, evidence confirmation or contradiction) * interpretation of ambiguous information (a partner talking closely with someone else does not automatically show romantic interest, but someone experiencing strong jealousy may interpret ambiguous information through the lens of a perceived threat. possible negative assumptions, suspicion, threat focused) cite (Brenner, 2018) * repetitive thinking and information seeking (rumination, repeatedly thinking about threat, checking for evidence, mental replaying) reuse (Elphinston et al., 2013) for rumination * cognitive effects (effects on thoughts) the appraisal processes discussed in (a previous section) do not necessarily end once jealousy is experienced. they may continue as people attempt to interpret and evaluate relationship relevant information. if ambiguous behaviour is interpreted as threatening, a person may become more suspicious or seek reassurance, which can influence their emotional and behavioural responses. === Emotional Impacts === === Behavioural Responses === === Relationship Consequences === === When Can Jealousy Be Harmful? === == How Can Romantic Jealousy Be Managed? == === Recognising the Emotional Response === === Evaluating the Perceived Threat === === Communication and Relationship Management === === Emotion Regulation === === When the Threat is Real === The Overview section should provide: # '''Scenario''': A short, engaging case study or real-world example in a feature box, with an accompanying image (see above) # '''Explanation of the problem, issue, or topc''': Briefly explain the problem, why it is important, and outline how psychological science can help # '''Focus questions''': Unpack the sub-title into focus questions in a feature box Recommended length: 180 to 330 words. This template provides key headings, examples, and tips for each section. Gradually remove this generic information as the chapter develops. It is OK to retain some of the template material for the topic development, but it should all be removed for the final book chapter. Key resources: * [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 02]] explains about how to edit * [[Motivation and emotion/Assessment/Topic|Topic development guidelines]] * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] {{RoundBoxTop|theme=3}} '''Focus questions''' Break the sub-title down into three to five [[Motivation and emotion/Assessment/Chapter/Focus questions|focus questions]]. Align the top-level headings with these focus questions. * What is the first focus question? * What is the second focus question? * What is the third focus question? Ask [[w:Open-ended question|open-ended]] focus questions. For example: * Is there a relationship between weather and criminal behaviour? (closed-ended) * What is the relationship between weather and criminal behaviour? (open-ended) {{RoundBoxBottom}} == Why Does Romantic Jealousy Occur? == === Perceived Relationship Threat === === Cognitive Appraisal === === Attachment and Relationship Security === === Relationship Context and Uncertainty === === Individual Differences and Integrated Explanations === == What Are the Impacts of Romantic Jealousy? == === Cognitive Impacts === === Emotional Impacts === === Behavioural Responses === === Relationship Consequences === === When Can Jealousy Be Harmful? === == How Can Romantic Jealousy Be Managed? == === Recognising the Emotional Response === === Evaluating the Perceived Threat === === Communication and Relationship Management === === Emotion Regulation === === When the Threat is Real === ==Headings== Use this heading structure: * [[#Overview|Overview]] * 3 to 6 major headings tailored to the topic; can have sub-headings, but: ** avoid having only one sub-heading ** provide an introductory paragraph before breaking into sub-sections * [[#Conclusion|Conclusion]] * See also * References * External links ==Key points== For the topic development, for each heading and sub-heading: * Provide at least three bullet-points, including for the Overview and Conclusion * Include key citations ==Figures== [[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== Interactive learning features help to bring book chapters to life and can be embedded throughout the chapter. {{anchor|Scenarios}} ;Scenarios * Scenarios, case studies, or examples describe concepts in action * Can be real or fictional; if real, provide citations * Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Present using [[#Feature boxes|feature boxes]] {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted '''Table 1''' A Descriptive Caption Which Explains The Table Contents and its Relevance to the Text e.g., The 2 x 2 Johari Window Model Showing Knowing x Self/Other {| class="wikitable" style="margin: auto; |- ! !! Known to self !! Not known to self |- | '''Known to others''' || Open area || Blind spot |- | '''Not known to others''' || Hidden area || Unknown |} ;Quizzes * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] Example simple quiz questions. Choose your answers and click "Submit": ==Conclusion== * The Conclusion is arguably the most important section * Draft clear take-home message(s), even at the topic development stage * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) * [[w:Self determination theory|Self determination theory]] (Wikipedia) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses }} ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. APA style example: {{Hanging indent|1= Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091 Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper & Row. }} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Jealousy]] . bamvet97d2k1y3tc2xraqwwnv29rho5 2823769 2823767 2026-08-21T00:56:36Z U3279062 3106301 added emotional impacts dot points 2823769 wikitext text/x-wiki {{title|Romantic jealousy:<br>Why does romantic jealousy occur, what are it's impacts, and how can It be managed?}} __TOC__ == Overview == {{RoundBoxTop|theme=3}} [[File:Man using smartphone outdoors.jpg|Man_using_smartphone_outdoors|right|thumb|150px|'''Figure 1'''. Person viewing an ambiguous message on a phone]] ; Scenario Maya is in a committed romantic relationship of 3 years. Her partner, Alex, has recently started spending more time with a new colleague, Joan. One evening, Maya notices that Alex has been messaging Joan more often. She sees a message that, while not showing clear evidence of infidelity, could be interpreted in multiple ways. Maya experiences a sudden feeling of jealousy. She starts thinking: '' Why are they messaging so much? Is there something going on? Does Alex find Joan more interesting than me? Am I overreacting? '' Maya feels anxious and has an urge to check Alex's messages or ask what is happening. Maya's situation shows how an ambiguous even can become psychologically significant when interpreted as a potential threat (see Figure 1.) What is happening to Maya, and what should she do with this feeling? {{RoundBoxBottom}} Romantic jealousy is an emotional response that can arise when a person perceives a threat to a valued romantic relationship. The experience and consequences of jealousy can vary substantially across people and situations. * What is [[wikipedia:Jealousy|jealousy]]? (Discuss that romantic jealousy involves an emotional response to a perceived threat to a valued romantic relationship. The threat does not have to be real. Interpretation and perception matter) use source that gives a definition of romantic jealousy: (Karakoçoğlu & Hasdağ, 2025) * Why does jealousy vary? (Discuss how people can experience levels of jealous in similar situations. This suggests that jealousy cannot be explained by only external factors. individual and relationship factors may influence how situations are interpreted) find research showing individual differences in jealousy: (Valentova et al., 2020) * Why does jealousy matter? (Jealousy can influence thoughts, emotions and behavior. The feeling alone doesn't necessarily determine behaviour. Different responses may have different consequences for romantic relationships.) research connecting jealousy with cognitive/ emotional responses, behavioural responses, relationship outcomes: (Guerrero & Andersen, 1996) and (Elphinston et al., 2013) * Why management matters (Understanding jealousy may help people distinguish emotional reactions from assumptions and actions. Psychological science can provide evidence informed ways of responding to jealousy. Managing jealousy doesn't necessarily mean eliminating the emotion or ignoring genuine relationship concerns.) Research establishing why psychological understanding and regulation and relationship management is relevant: (Duckworth & Gross, 2020) {{RoundBoxTop|theme=1}} '''Focus questions''' * What is romantic jealousy, and how can it be understood as an emotional and motivational response? * Why does romantic jealousy occur, and why might people experience it differently? * What are the cognitive, emotional, behavioural, and relationship impacts of romantic jealousy? * How can romantic jealousy be managed in ways that support healthy functioning? {{RoundBoxBottom}} == What Is Romantic Jealousy? == Romantic jealousy is a complex psychological response to a perceived threat to a valued romantic relationship, involving interacting emotional, cognitive, and motivational processes (Sharpsteen & Kirkpatrick, 1997) * define more * jealousy isn't just a single feeling * introduce how people can interpret similar situations differently * preview sections === Defining Romantic Jealousy === Romantic jealousy can be understood, similar to regular jealousy, as a psychological response that occurs when a person perceives a threat to an important romantic relationship. * define it (what is it, what makes it romantic jealousy in particular, what is being threatened, why does the relationship need to be valued for it to be jealousy) cite: (Miller & Benz, 2013) information on jealousy * talk about perceived threat (the situation doesn't necessarily have to involve an objectively confirmed threat. establish difference between the event and situation and the jealousy) cite: (Scherer et al., 2001) * explain components (establish that jealousy may involve cognition, emotional, motivation. then say that behaviour can follow from these but isn't same as emotion) * add case study scenario briefly (maybe no feature box?) (Maya's reaction can therefore be understood not simply as a response to Alex's message, but as a response to what the messages may mean for her relationship. the message is the situation, maya interprets it, the interpretation created perceived threat, the perceived threat contributes to jealousy.) === Jealousy and Related Emotional Experiences === Although romantic jealousy can involve emotions such as [[wikipedia:Fear|fear]], [[wikipedia:Anxiety|anxiety]], [[wikipedia:Anger|anger]], and [[wikipedia:Insecurity|insecurity]], it should be distinguished from related psychological experiences such as [[wikipedia:Envy|envy]]. * say what jealousy generally is (a valued relationship plus a perceived threat involving another person) * envy generally is (wanting something another person has) * jealous may be accompanied by other emotions said above but they aren't necessarily interchangeable with jealousy * can cite old jealousy source from above section {| class="wikitable" |+Table 1. Distinguishing Romantic Jealousy from Related Experiences !Experience !Central Concern !Example |- |Romantic Jealousy |Perceived threat to a valued romantic relationship |Partner appears unusually close to another person |- |Envy |Wanting something another person has |Another person has a relationship you want |- |Fear/Anxiety |Anticipated or perceived threat/danger |Worry that a relationship may end |} === Is Jealousy Inherently Harmful === experiencing romantic jealousy does not necessarily mean you are experiencing a harmful relationship event or outcome. the significance of jealousy may depend partly on how the experience is interpreted and how it is expressed. * emotions don't equal behaviour (feeling jealous is not the same as acting on jealousy) * potential information/ signaling function (research if jealousy can signal perceived relationship threat, motivate attention to relationship concern, motivate relationship protective behaviour, prompt communication) cite: (Dillon, 2013) * reasons why jealousy may be bad/ maladaptive (conflict, suspicion, controlling behaviour, relationship distress. difference between jealousy and response to it again) cite jealousy source again potentially <quiz display="simple"> {Which statement best describes romantic jealousy?: |type="()"} - It only occurs when a partner has definitely been unfaithful. - It is the same as envy. + It can involve a perceived threat to a valued romantic relationship and may involve emotional, cognitive, and motivational processes. - It always results in harmful behaviour. </quiz> == Why Does Romantic Jealousy Occur? == Romantic jealousy is unlikely to be explained by relationship events alone. Instead, the experience can come from the interaction between perceived threat, cognitive appraisal, relationship characteristics, and individual differences. * talk about case study maya again (don't know if it needs to be a scenario box?) say Alex's messages to Joan weren't obviously something to be jealous over (was ambiguous),message alone doesn't explain Maya's reaction, why did maya interpret situation as threatening? * introduce topics discussed below === Perceived Relationship Threat and Cognitive Appraisal === A central explanation for romantic jealousy is that situations become emotionally significant when the yare appraised as threatening to a valued relationship. * A potential threat isnt automatically a psychological threat (a partner interacting with anohter person is not inherently jealousy provoking. the interaction becomes important when it is interpreted as potentially threatening.threat could concern: loss of relationship, exclusivity, emotional intimacy, trust, ones sense of self worth. percived threat cite: (Martínez-León et al., 2017) * talk about cognitive appraisal (people evaluate what an event means for their relationships, they assess if something important is at stake. they interpret significance of events. appraisal contributes to emotional response. appraisal source: (Tomaka et al., 1997) and (McEachrane, 2009) * case study (?) what happened: Alex sent text to other person. what did maya perceive: potential romantic threat. what might she have appraised?: Alex might prefer this person, my relationship might be at risk, I might lose something important, I don't know what is happening. (only possibilities not concrete) === Attachment and Relationship Security === Attachment theory provides one explanation for why individuals may differ in their sensitivity to relationship threat and in the ways they experience and express jealousy * introduce attachment (romantic relationship can function as important attachments, people differ in attachment related expectations about themselves and others. brief overview of styles these expectations can influence responses to relationship threat) sources about attachment (Shaver & Mikulincer, 2008) and (Sharpsteen & Kirkpatrick, 1997) again * attachment anxiety (explain the anxious attachment style, concern about rejection or abandonment may increase sensitivity to relationship threat. avoidant partner behaviour be made more salient. this attachment stle can contribute to stronger jealousy) cite: (Campbell & Marshall, 2011) * avoidant attachment style (avoidance may also shape jealousy, may influence expression or management of jealousy differently. individual difference isnt about more or less jealousy) cite: (Bartholomew, 1990) * case study: maya, could mayas reaction be partly influenced by how secure she generally feels in close relationships === Relationship Context and Uncertainty === jealousy is also shaped by characteristics of the relationship and immediate context, particularly when information about the relationship or a potential rival is uncertain. * uncertainty (people may be uncertain about where their relationship stands, how committed their partner is, what boundaries exist, what a partners behaviour means. uncertainty can make unclear information harder to interpret. cite: (KNOBLOCH et al., 2001) * relationship factors like intimacy, commitment, trust, relationship satisfaction, perceived exclusivity, communication clarity, shape jealousy. * context of relationship shapes reactions (interactions, transitions, perceptions about rivals, previous breaches of trust, digital communication) context determines what information is available and how ambiguous that information may be. * maya situation: ambiguity plus incomplete information and new person and uncertain meaning, jealousy cannot be explained only by internal trait. relationship situation itself matters. === Individual Differences === beyond attachment and relationship characteristics, individual differences can influence how strongly people perceive and respond to potential romantic threats. lightly talk about some or all (?) * self esteem * previous relationship experiences * rejection sensitivity * personality tendances * these things may increase sensitivity to threats or how situations are interpreted === Integrated Explanations === taken together, the evidence suggests that romantic jealousy is best understood as an interaction between relationship circumstances, perceived threat, cognitive appraisal and individual characteristics rather than just as the product of a signal cause. * add figure (1. for maya, alex messages another person, 2 potential threat, could threaten security, exclusivity and relationship continuity. 3, appraisal, maya interprets what the event means. 4, individual factors, her interpretation may be influenced by attachment related expectations, self worth, previous experiences, expectations of rejection. 5, relationship context factors like commitment, trust, context. 6, jealousy, these processes contribute to emotional, cognitive, behavioral responses. 7, maya now has choices about what she does with that emotional experience) * caption: model of romantic jealousy going from event, to appraisal, to emotional and behavioral responses. as discussed in figure 2. jealousy arises within an interaction between the situation and how that situation is interpreted (omg how do i add diagrams someone hellppp) * add learning feature * feature box: maya receives the same message from alex in two different circumstances. In scenairo A, Maya feels secure in her relationship and knows how alex has openly discussed the friendship. in scenario B, Maya and Alex have recently experienced conflict and have not discussed relationship boundaries * quiz: why might the same message produce different levels of jealousy: 1. the message automatically creates jealousy. 2, jealousy depends only on personality. 3, (correct) the meaning of the message may be shaped by appraisal, relationship security and contextual uncertainty. 4, one person must be irrational. == What Are the Impacts of Romantic Jealousy? == Once romantic jealousy is experienced, it can influence how people think, feel and behave, with consequences that may extend beyond the individual to the relationship itself. * connect back to last section * say jealousy doesn't produce one universal outcome * consequences depend partly on how jealousy is experiences and responded to (can have adaptive responses and harmful responses) * briefly overview subheadings (don't know if i need a source here, as i am being general, maybe i can just reuse a source about jealousy having impacts in general from above ) === Cognitive Impacts === Romantic jealousy can influence cognitive processing by increasing attention to potential relationship threats and shaping how individuals interpret ambiguous information about their partner and relationship. * cognitive jealousy is what you think/ suspect cite (Leite et al., 2024) * jealousy can heighten attention towards relationship information, people may be focused on factors mentioned above (rival, behavior, signs of rejection, evidence confirmation or contradiction) * interpretation of ambiguous information (a partner talking closely with someone else does not automatically show romantic interest, but someone experiencing strong jealousy may interpret ambiguous information through the lens of a perceived threat. possible negative assumptions, suspicion, threat focused) cite (Brenner, 2018) * repetitive thinking and information seeking (rumination, repeatedly thinking about threat, checking for evidence, mental replaying) reuse (Elphinston et al., 2013) for rumination * cognitive effects (effects on thoughts) the appraisal processes discussed in (a previous section) do not necessarily end once jealousy is experienced. they may continue as people attempt to interpret and evaluate relationship relevant information. if ambiguous behaviour is interpreted as threatening, a person may become more suspicious or seek reassurance, which can influence their emotional and behavioural responses. === Emotional Impacts === The emotional impact of romantic jealous can extend beyond the experience of jealousy itself, with individuals potentially experiencing anxiety, fear, anger, sadness, or insecurity in response to perceived relationship threat. * jealousy can involve multiple emotional experiences (it can co-occur with other emotions, different people can experience this differently, and may experience multiple emotions at the same time) cite (Guerrero et al., 2005) * emotional intensity can vary (the intensity of emotional experiences may be related to context, uncertainty, threat, individual differences discussed before) * emotional distress (intense or persistent jealousy may contribute to emotional distress) cite (Bush et al., 1988) * emotion isnt automatically dysfunctional (unpleaseent emotions can still serve psychological functions and draw attention to something important, therefore feeling jealousy does not automatically mean the person or relationship is unhealthy) cite (Attridge, 2013) the experince of an unpleasent emotion does not. by itself, mean that the emotion is dysfunctional === Behavioural Responses === === Relationship Consequences === === When Can Jealousy Be Harmful? === == How Can Romantic Jealousy Be Managed? == === Recognising the Emotional Response === === Evaluating the Perceived Threat === === Communication and Relationship Management === === Emotion Regulation === === When the Threat is Real === The Overview section should provide: # '''Scenario''': A short, engaging case study or real-world example in a feature box, with an accompanying image (see above) # '''Explanation of the problem, issue, or topc''': Briefly explain the problem, why it is important, and outline how psychological science can help # '''Focus questions''': Unpack the sub-title into focus questions in a feature box Recommended length: 180 to 330 words. This template provides key headings, examples, and tips for each section. Gradually remove this generic information as the chapter develops. It is OK to retain some of the template material for the topic development, but it should all be removed for the final book chapter. Key resources: * [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 02]] explains about how to edit * [[Motivation and emotion/Assessment/Topic|Topic development guidelines]] * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] {{RoundBoxTop|theme=3}} '''Focus questions''' Break the sub-title down into three to five [[Motivation and emotion/Assessment/Chapter/Focus questions|focus questions]]. Align the top-level headings with these focus questions. * What is the first focus question? * What is the second focus question? * What is the third focus question? Ask [[w:Open-ended question|open-ended]] focus questions. For example: * Is there a relationship between weather and criminal behaviour? (closed-ended) * What is the relationship between weather and criminal behaviour? (open-ended) {{RoundBoxBottom}} == Why Does Romantic Jealousy Occur? == === Perceived Relationship Threat === === Cognitive Appraisal === === Attachment and Relationship Security === === Relationship Context and Uncertainty === === Individual Differences and Integrated Explanations === == What Are the Impacts of Romantic Jealousy? == === Cognitive Impacts === === Emotional Impacts === === Behavioural Responses === === Relationship Consequences === === When Can Jealousy Be Harmful? === == How Can Romantic Jealousy Be Managed? == === Recognising the Emotional Response === === Evaluating the Perceived Threat === === Communication and Relationship Management === === Emotion Regulation === === When the Threat is Real === ==Headings== Use this heading structure: * [[#Overview|Overview]] * 3 to 6 major headings tailored to the topic; can have sub-headings, but: ** avoid having only one sub-heading ** provide an introductory paragraph before breaking into sub-sections * [[#Conclusion|Conclusion]] * See also * References * External links ==Key points== For the topic development, for each heading and sub-heading: * Provide at least three bullet-points, including for the Overview and Conclusion * Include key citations ==Figures== [[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== Interactive learning features help to bring book chapters to life and can be embedded throughout the chapter. {{anchor|Scenarios}} ;Scenarios * Scenarios, case studies, or examples describe concepts in action * Can be real or fictional; if real, provide citations * Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Present using [[#Feature boxes|feature boxes]] {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted '''Table 1''' A Descriptive Caption Which Explains The Table Contents and its Relevance to the Text e.g., The 2 x 2 Johari Window Model Showing Knowing x Self/Other {| class="wikitable" style="margin: auto; |- ! !! Known to self !! Not known to self |- | '''Known to others''' || Open area || Blind spot |- | '''Not known to others''' || Hidden area || Unknown |} ;Quizzes * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] Example simple quiz questions. Choose your answers and click "Submit": ==Conclusion== * The Conclusion is arguably the most important section * Draft clear take-home message(s), even at the topic development stage * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) * [[w:Self determination theory|Self determination theory]] (Wikipedia) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses }} ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. APA style example: {{Hanging indent|1= Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091 Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper & Row. }} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Jealousy]] . e0v8zhi9npcxhs9jar7nfg8llgh9ewf 2823822 2823769 2026-08-21T04:39:36Z Jtneill 10242 /* External links */ 2823822 wikitext text/x-wiki {{title|Romantic jealousy:<br>Why does romantic jealousy occur, what are it's impacts, and how can It be managed?}} __TOC__ == Overview == {{RoundBoxTop|theme=3}} [[File:Man using smartphone outdoors.jpg|Man_using_smartphone_outdoors|right|thumb|150px|'''Figure 1'''. Person viewing an ambiguous message on a phone]] ; Scenario Maya is in a committed romantic relationship of 3 years. Her partner, Alex, has recently started spending more time with a new colleague, Joan. One evening, Maya notices that Alex has been messaging Joan more often. She sees a message that, while not showing clear evidence of infidelity, could be interpreted in multiple ways. Maya experiences a sudden feeling of jealousy. She starts thinking: '' Why are they messaging so much? Is there something going on? Does Alex find Joan more interesting than me? Am I overreacting? '' Maya feels anxious and has an urge to check Alex's messages or ask what is happening. Maya's situation shows how an ambiguous even can become psychologically significant when interpreted as a potential threat (see Figure 1.) What is happening to Maya, and what should she do with this feeling? {{RoundBoxBottom}} Romantic jealousy is an emotional response that can arise when a person perceives a threat to a valued romantic relationship. The experience and consequences of jealousy can vary substantially across people and situations. * What is [[wikipedia:Jealousy|jealousy]]? (Discuss that romantic jealousy involves an emotional response to a perceived threat to a valued romantic relationship. The threat does not have to be real. Interpretation and perception matter) use source that gives a definition of romantic jealousy: (Karakoçoğlu & Hasdağ, 2025) * Why does jealousy vary? (Discuss how people can experience levels of jealous in similar situations. This suggests that jealousy cannot be explained by only external factors. individual and relationship factors may influence how situations are interpreted) find research showing individual differences in jealousy: (Valentova et al., 2020) * Why does jealousy matter? (Jealousy can influence thoughts, emotions and behavior. The feeling alone doesn't necessarily determine behaviour. Different responses may have different consequences for romantic relationships.) research connecting jealousy with cognitive/ emotional responses, behavioural responses, relationship outcomes: (Guerrero & Andersen, 1996) and (Elphinston et al., 2013) * Why management matters (Understanding jealousy may help people distinguish emotional reactions from assumptions and actions. Psychological science can provide evidence informed ways of responding to jealousy. Managing jealousy doesn't necessarily mean eliminating the emotion or ignoring genuine relationship concerns.) Research establishing why psychological understanding and regulation and relationship management is relevant: (Duckworth & Gross, 2020) {{RoundBoxTop|theme=1}} '''Focus questions''' * What is romantic jealousy, and how can it be understood as an emotional and motivational response? * Why does romantic jealousy occur, and why might people experience it differently? * What are the cognitive, emotional, behavioural, and relationship impacts of romantic jealousy? * How can romantic jealousy be managed in ways that support healthy functioning? {{RoundBoxBottom}} == What Is Romantic Jealousy? == Romantic jealousy is a complex psychological response to a perceived threat to a valued romantic relationship, involving interacting emotional, cognitive, and motivational processes (Sharpsteen & Kirkpatrick, 1997) * define more * jealousy isn't just a single feeling * introduce how people can interpret similar situations differently * preview sections === Defining Romantic Jealousy === Romantic jealousy can be understood, similar to regular jealousy, as a psychological response that occurs when a person perceives a threat to an important romantic relationship. * define it (what is it, what makes it romantic jealousy in particular, what is being threatened, why does the relationship need to be valued for it to be jealousy) cite: (Miller & Benz, 2013) information on jealousy * talk about perceived threat (the situation doesn't necessarily have to involve an objectively confirmed threat. establish difference between the event and situation and the jealousy) cite: (Scherer et al., 2001) * explain components (establish that jealousy may involve cognition, emotional, motivation. then say that behaviour can follow from these but isn't same as emotion) * add case study scenario briefly (maybe no feature box?) (Maya's reaction can therefore be understood not simply as a response to Alex's message, but as a response to what the messages may mean for her relationship. the message is the situation, maya interprets it, the interpretation created perceived threat, the perceived threat contributes to jealousy.) === Jealousy and Related Emotional Experiences === Although romantic jealousy can involve emotions such as [[wikipedia:Fear|fear]], [[wikipedia:Anxiety|anxiety]], [[wikipedia:Anger|anger]], and [[wikipedia:Insecurity|insecurity]], it should be distinguished from related psychological experiences such as [[wikipedia:Envy|envy]]. * say what jealousy generally is (a valued relationship plus a perceived threat involving another person) * envy generally is (wanting something another person has) * jealous may be accompanied by other emotions said above but they aren't necessarily interchangeable with jealousy * can cite old jealousy source from above section {| class="wikitable" |+Table 1. Distinguishing Romantic Jealousy from Related Experiences !Experience !Central Concern !Example |- |Romantic Jealousy |Perceived threat to a valued romantic relationship |Partner appears unusually close to another person |- |Envy |Wanting something another person has |Another person has a relationship you want |- |Fear/Anxiety |Anticipated or perceived threat/danger |Worry that a relationship may end |} === Is Jealousy Inherently Harmful === experiencing romantic jealousy does not necessarily mean you are experiencing a harmful relationship event or outcome. the significance of jealousy may depend partly on how the experience is interpreted and how it is expressed. * emotions don't equal behaviour (feeling jealous is not the same as acting on jealousy) * potential information/ signaling function (research if jealousy can signal perceived relationship threat, motivate attention to relationship concern, motivate relationship protective behaviour, prompt communication) cite: (Dillon, 2013) * reasons why jealousy may be bad/ maladaptive (conflict, suspicion, controlling behaviour, relationship distress. difference between jealousy and response to it again) cite jealousy source again potentially <quiz display="simple"> {Which statement best describes romantic jealousy?: |type="()"} - It only occurs when a partner has definitely been unfaithful. - It is the same as envy. + It can involve a perceived threat to a valued romantic relationship and may involve emotional, cognitive, and motivational processes. - It always results in harmful behaviour. </quiz> == Why Does Romantic Jealousy Occur? == Romantic jealousy is unlikely to be explained by relationship events alone. Instead, the experience can come from the interaction between perceived threat, cognitive appraisal, relationship characteristics, and individual differences. * talk about case study maya again (don't know if it needs to be a scenario box?) say Alex's messages to Joan weren't obviously something to be jealous over (was ambiguous),message alone doesn't explain Maya's reaction, why did maya interpret situation as threatening? * introduce topics discussed below === Perceived Relationship Threat and Cognitive Appraisal === A central explanation for romantic jealousy is that situations become emotionally significant when the yare appraised as threatening to a valued relationship. * A potential threat isnt automatically a psychological threat (a partner interacting with anohter person is not inherently jealousy provoking. the interaction becomes important when it is interpreted as potentially threatening.threat could concern: loss of relationship, exclusivity, emotional intimacy, trust, ones sense of self worth. percived threat cite: (Martínez-León et al., 2017) * talk about cognitive appraisal (people evaluate what an event means for their relationships, they assess if something important is at stake. they interpret significance of events. appraisal contributes to emotional response. appraisal source: (Tomaka et al., 1997) and (McEachrane, 2009) * case study (?) what happened: Alex sent text to other person. what did maya perceive: potential romantic threat. what might she have appraised?: Alex might prefer this person, my relationship might be at risk, I might lose something important, I don't know what is happening. (only possibilities not concrete) === Attachment and Relationship Security === Attachment theory provides one explanation for why individuals may differ in their sensitivity to relationship threat and in the ways they experience and express jealousy * introduce attachment (romantic relationship can function as important attachments, people differ in attachment related expectations about themselves and others. brief overview of styles these expectations can influence responses to relationship threat) sources about attachment (Shaver & Mikulincer, 2008) and (Sharpsteen & Kirkpatrick, 1997) again * attachment anxiety (explain the anxious attachment style, concern about rejection or abandonment may increase sensitivity to relationship threat. avoidant partner behaviour be made more salient. this attachment stle can contribute to stronger jealousy) cite: (Campbell & Marshall, 2011) * avoidant attachment style (avoidance may also shape jealousy, may influence expression or management of jealousy differently. individual difference isnt about more or less jealousy) cite: (Bartholomew, 1990) * case study: maya, could mayas reaction be partly influenced by how secure she generally feels in close relationships === Relationship Context and Uncertainty === jealousy is also shaped by characteristics of the relationship and immediate context, particularly when information about the relationship or a potential rival is uncertain. * uncertainty (people may be uncertain about where their relationship stands, how committed their partner is, what boundaries exist, what a partners behaviour means. uncertainty can make unclear information harder to interpret. cite: (KNOBLOCH et al., 2001) * relationship factors like intimacy, commitment, trust, relationship satisfaction, perceived exclusivity, communication clarity, shape jealousy. * context of relationship shapes reactions (interactions, transitions, perceptions about rivals, previous breaches of trust, digital communication) context determines what information is available and how ambiguous that information may be. * maya situation: ambiguity plus incomplete information and new person and uncertain meaning, jealousy cannot be explained only by internal trait. relationship situation itself matters. === Individual Differences === beyond attachment and relationship characteristics, individual differences can influence how strongly people perceive and respond to potential romantic threats. lightly talk about some or all (?) * self esteem * previous relationship experiences * rejection sensitivity * personality tendances * these things may increase sensitivity to threats or how situations are interpreted === Integrated Explanations === taken together, the evidence suggests that romantic jealousy is best understood as an interaction between relationship circumstances, perceived threat, cognitive appraisal and individual characteristics rather than just as the product of a signal cause. * add figure (1. for maya, alex messages another person, 2 potential threat, could threaten security, exclusivity and relationship continuity. 3, appraisal, maya interprets what the event means. 4, individual factors, her interpretation may be influenced by attachment related expectations, self worth, previous experiences, expectations of rejection. 5, relationship context factors like commitment, trust, context. 6, jealousy, these processes contribute to emotional, cognitive, behavioral responses. 7, maya now has choices about what she does with that emotional experience) * caption: model of romantic jealousy going from event, to appraisal, to emotional and behavioral responses. as discussed in figure 2. jealousy arises within an interaction between the situation and how that situation is interpreted (omg how do i add diagrams someone hellppp) * add learning feature * feature box: maya receives the same message from alex in two different circumstances. In scenairo A, Maya feels secure in her relationship and knows how alex has openly discussed the friendship. in scenario B, Maya and Alex have recently experienced conflict and have not discussed relationship boundaries * quiz: why might the same message produce different levels of jealousy: 1. the message automatically creates jealousy. 2, jealousy depends only on personality. 3, (correct) the meaning of the message may be shaped by appraisal, relationship security and contextual uncertainty. 4, one person must be irrational. == What Are the Impacts of Romantic Jealousy? == Once romantic jealousy is experienced, it can influence how people think, feel and behave, with consequences that may extend beyond the individual to the relationship itself. * connect back to last section * say jealousy doesn't produce one universal outcome * consequences depend partly on how jealousy is experiences and responded to (can have adaptive responses and harmful responses) * briefly overview subheadings (don't know if i need a source here, as i am being general, maybe i can just reuse a source about jealousy having impacts in general from above ) === Cognitive Impacts === Romantic jealousy can influence cognitive processing by increasing attention to potential relationship threats and shaping how individuals interpret ambiguous information about their partner and relationship. * cognitive jealousy is what you think/ suspect cite (Leite et al., 2024) * jealousy can heighten attention towards relationship information, people may be focused on factors mentioned above (rival, behavior, signs of rejection, evidence confirmation or contradiction) * interpretation of ambiguous information (a partner talking closely with someone else does not automatically show romantic interest, but someone experiencing strong jealousy may interpret ambiguous information through the lens of a perceived threat. possible negative assumptions, suspicion, threat focused) cite (Brenner, 2018) * repetitive thinking and information seeking (rumination, repeatedly thinking about threat, checking for evidence, mental replaying) reuse (Elphinston et al., 2013) for rumination * cognitive effects (effects on thoughts) the appraisal processes discussed in (a previous section) do not necessarily end once jealousy is experienced. they may continue as people attempt to interpret and evaluate relationship relevant information. if ambiguous behaviour is interpreted as threatening, a person may become more suspicious or seek reassurance, which can influence their emotional and behavioural responses. === Emotional Impacts === The emotional impact of romantic jealous can extend beyond the experience of jealousy itself, with individuals potentially experiencing anxiety, fear, anger, sadness, or insecurity in response to perceived relationship threat. * jealousy can involve multiple emotional experiences (it can co-occur with other emotions, different people can experience this differently, and may experience multiple emotions at the same time) cite (Guerrero et al., 2005) * emotional intensity can vary (the intensity of emotional experiences may be related to context, uncertainty, threat, individual differences discussed before) * emotional distress (intense or persistent jealousy may contribute to emotional distress) cite (Bush et al., 1988) * emotion isnt automatically dysfunctional (unpleaseent emotions can still serve psychological functions and draw attention to something important, therefore feeling jealousy does not automatically mean the person or relationship is unhealthy) cite (Attridge, 2013) the experince of an unpleasent emotion does not. by itself, mean that the emotion is dysfunctional === Behavioural Responses === === Relationship Consequences === === When Can Jealousy Be Harmful? === == How Can Romantic Jealousy Be Managed? == === Recognising the Emotional Response === === Evaluating the Perceived Threat === === Communication and Relationship Management === === Emotion Regulation === === When the Threat is Real === The Overview section should provide: # '''Scenario''': A short, engaging case study or real-world example in a feature box, with an accompanying image (see above) # '''Explanation of the problem, issue, or topc''': Briefly explain the problem, why it is important, and outline how psychological science can help # '''Focus questions''': Unpack the sub-title into focus questions in a feature box Recommended length: 180 to 330 words. This template provides key headings, examples, and tips for each section. Gradually remove this generic information as the chapter develops. It is OK to retain some of the template material for the topic development, but it should all be removed for the final book chapter. Key resources: * [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 02]] explains about how to edit * [[Motivation and emotion/Assessment/Topic|Topic development guidelines]] * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] {{RoundBoxTop|theme=3}} '''Focus questions''' Break the sub-title down into three to five [[Motivation and emotion/Assessment/Chapter/Focus questions|focus questions]]. Align the top-level headings with these focus questions. * What is the first focus question? * What is the second focus question? * What is the third focus question? Ask [[w:Open-ended question|open-ended]] focus questions. For example: * Is there a relationship between weather and criminal behaviour? (closed-ended) * What is the relationship between weather and criminal behaviour? (open-ended) {{RoundBoxBottom}} == Why Does Romantic Jealousy Occur? == === Perceived Relationship Threat === === Cognitive Appraisal === === Attachment and Relationship Security === === Relationship Context and Uncertainty === === Individual Differences and Integrated Explanations === == What Are the Impacts of Romantic Jealousy? == === Cognitive Impacts === === Emotional Impacts === === Behavioural Responses === === Relationship Consequences === === When Can Jealousy Be Harmful? === == How Can Romantic Jealousy Be Managed? == === Recognising the Emotional Response === === Evaluating the Perceived Threat === === Communication and Relationship Management === === Emotion Regulation === === When the Threat is Real === ==Headings== Use this heading structure: * [[#Overview|Overview]] * 3 to 6 major headings tailored to the topic; can have sub-headings, but: ** avoid having only one sub-heading ** provide an introductory paragraph before breaking into sub-sections * [[#Conclusion|Conclusion]] * See also * References * External links ==Key points== For the topic development, for each heading and sub-heading: * Provide at least three bullet-points, including for the Overview and Conclusion * Include key citations ==Figures== [[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]] * Use figures to illustrate concepts, add interest, and to serve as examples * Figures can show photos, diagrams, graphs, video, audio, etc. * Embed figures throughout the chapter, starting with the scenario in the Overview section * Caption figures (use '''Figure #'''. and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== Interactive learning features help to bring book chapters to life and can be embedded throughout the chapter. {{anchor|Scenarios}} ;Scenarios * Scenarios, case studies, or examples describe concepts in action * Can be real or fictional; if real, provide citations * Can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Present using [[#Feature boxes|feature boxes]] {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use to tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted '''Table 1''' A Descriptive Caption Which Explains The Table Contents and its Relevance to the Text e.g., The 2 x 2 Johari Window Model Showing Knowing x Self/Other {| class="wikitable" style="margin: auto; |- ! !! Known to self !! Not known to self |- | '''Known to others''' || Open area || Blind spot |- | '''Not known to others''' || Hidden area || Unknown |} ;Quizzes * Using one or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] Example simple quiz questions. Choose your answers and click "Submit": ==Conclusion== * The Conclusion is arguably the most important section * Draft clear take-home message(s), even at the topic development stage * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing it * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== Provide [[Help:Contents/Links#Interwiki_links|internal (wiki) links]] to the most relevant Wikiversity pages (esp. related [[Motivation and emotion/Book|motivation and emotion book chapters]]) and [[w:|Wikipedia articles]]. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [[Motivation and emotion/Book/About/Collaborative authoring using wiki|Collaborative authoring using wiki]] (Wikiversity) * [[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) * [[w:Self determination theory|Self determination theory]] (Wikipedia) {{tip|Suggestions for this section: * Only select links to major internal resources about the topic * Include the source in parentheses }} ==References== This section lists the cited references in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. APA style example: {{Hanging indent|1= Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091 Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper & Row. }} {{tip|Suggestions for this section: * Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: ** Use "Edit source" ** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== Provide [[Help:Contents/Links#External_links|external links]] to highly relevant resources such as podcasts and videos, news articles, and professional sites. Use [[w:Letter case#Sentence casing|sentence casing]] and alphabetical order. For example: * [https://students.unimelb.edu.au/academic-skills/explore-our-resources/essay-writing/six-top-tips-for-writing-a-great-essay Six top tips for writing a great essay] (University of Melbourne) * [http://www.skillsyouneed.com/write/structure.html The importance of structure] (skillsyouneed.com) {{tip|Suggestions for this section: * Only select links to major external resources about the topic * Include the source in parentheses after the link }} [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Jealousy]] g2ndooofhpo18ma6rtgg0vhvmcr5ya3 0 331262 2823835 2822886 2026-08-21T05:48:04Z U3228742 3005570 Added page title and links to webpages and book chapters reviewed to to shaping this chapter 2823835 wikitext text/x-wiki {{title|Dark empathy: What is dark empathy, what are its consequences, and what can be done to address it?}} __TOC__ ==Overview== {{RoundBoxTop|theme=3}} [[File:A picture is worth a thousand words.jpg|right|thumb|150px|'''Figure 1'''. Use a captioned image to illustrate the scenario]] ; Imagine this ... or Scenario ... or Case study or ... ?) Start with an engaging [[#Scenarios|scenario, example, or case study]] which illustrates the problem and engages reader interest. Present the scenario in a [[#Feature box|feature box]]. To change the box colour: # Edit source # Change "theme=3" to another number Include an image and cite it (e.g., see Figure 1). {{RoundBoxBottom}} The Overview section should provide: # '''Scenario''': A short, engaging case study or real-world example in a feature box, with an accompanying image (see above) # '''Explanation of the problem, issue, or topc''': Briefly explain the problem, why it is important, and outline how psychological science can help # '''Focus questions''': Unpack the sub-title into focus questions in a feature box Recommended length: 180 to 330 words. This template provides key headings, examples, and tips for each section. Gradually remove this generic information as the chapter develops. It is OK to retain some template material for the topic development, but it should all be removed from the book chapter. Key resources: * [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]] explains how to edit * [[Motivation and emotion/Assessment/Topic|Topic development guidelines]] * [[Motivation and emotion/Assessment/Chapter|Book chapter guidelines]] {{RoundBoxTop|theme=3}} '''Focus questions''' Break the sub-title down into three to five [[Motivation and emotion/Assessment/Chapter/Focus questions|focus questions]]. Align the top-level headings with these focus questions. * What is the first focus question? * What is the second focus question? * What is the third focus question? Ask [[w:Open-ended question|open-ended]] questions. For example: {{cross}} Is there a relationship between weather and criminal behaviour? (closed-ended)<br>{{tick}} What is the relationship between weather and criminal behaviour? (open-ended) {{RoundBoxBottom}} ==Headings== Use this heading structure: * [[#Overview|Overview]] * 3 to 6 major headings tailored to the topic; can have sub-headings: ** avoid sections with only one sub-heading (use 0 or 2+ sub-headings) ** provide an introductory paragraph before breaking into sub-sections * [[#Conclusion|Conclusion]] * [[#See also|See also]] * [[#References|References]] * [[#External links|External links]] ==Key points== * For the topic development, provide at least three bullet-points for each heading and sub-heading, including the Overview and Conclusion * Include key citations ==Figures== [[File:Thought bubble.svg|right|140px|thumb|'''Figure 2'''. Example of an image with a descriptive caption.]] * For the book chapter, use several figures to illustrate concepts, add interest, and to serve as examples * For the topic development, use at least one figure (even if not ideal) to show that you know how to embed, caption, and cite a figure * Figures can show any kind of media such as photos, diagrams, graphs, video, audio, and so on * Embed figures throughout the chapter, starting with the scenario in the Overview section * Provide descriptive figure captions (use '''Figure #''' and explain the relevance of the image to the text) * Images must be embedded from [[commons:|Wikimedia Commons]] * Images can be uploaded to [[commons:|Wikimedia Commons]] if they are openly licensed * Cite each figure at least once in the main text (e.g., see Figure 2) ==Learning features== Learning features help to bring book chapters to life and can be embedded throughout the chapter. Here are some options: {{anchor|Scenarios}} ;Scenarios * Scenarios, case studies, or examples that illustrate concepts in action * Present using [[#Feature boxes|feature boxes]]; can be split into multiple boxes throughout a chapter (e.g., to illustrate different theories or stages) * Can be real or fictional; if real, provide citation(s) {{anchor|Feature box}} ;Feature boxes * Highlight key content using [[Motivation and emotion/Wikiversity/Feature box|feature boxes]], but don't overuse, otherwise they lose their effect * Consider using feature boxes for: ** [[#Scenarios|Scenarios]], case studies, or examples ** Focus questions ** Tips ** Quiz questions ** Take-home messages ;Embedded links * When key words are introduced, use [[Help:Links|interwiki links]] to: ** Wikipedia articles (e.g., "An early psychological view [[w:Dreams|dreams]]) of dreams was provided by [[w:Sigmund Freud|Sigmund Freud]]") or ** Related book chapters (e.g., "If you're feeling stuck, check out the chapter about [[Motivation and emotion/Book/2020/Writer's block|writer's block]]") {{anchor|Tables}} ;Tables * Use tables to organise and summarise information * Cite each table at least once in the main text (e.g., see Table 1) * Tables should be captioned * [[Motivation and emotion/Wikiversity/Tables|More example tables]] which can be adapted '''Table 1''' A Descriptive Caption Explains The Table Contents and its Relevance to the Text e.g., The 2 x 2 Johari Window Model Showing the Relationship Between Known/Unknown and Self/Other {| class="wikitable" style="margin: auto; |- ! !! Known to self !! Not known to self |- | '''Known to others''' || Open area || Blind spot |- | '''Not known to others''' || Hidden area || Unknown |} ;Quizzes * One or two quiz questions for each main section is better than a long quiz at the end * Quiz ''conceptual'' understanding, rather than trivia. Ask about important information such as the take-home messages * Ask easy rather than hard questions * Different types of quiz questions are possible; see [[Help:Quiz|Quiz]] Example simple quiz questions. Choose your answers and click "Submit": <quiz display=simple> {The purpose of quizzes is to provide an interactive learning feature: |type="()"} + True - False {Long and complex quiz questions are recommended: |type="()"} - True + False </quiz> ==Conclusion== * Arguably the most important section * Provide at least three bullet-points for this section even at the topic development stage, based on preliminary thinking * For the book chapter, develop clear take-home message(s) that address the focus questions based on psychological theory and research * Together, the [[#Overview|Overview]] and Conclusion should summarise the problem, its significance, and how psychological science contributes to understanding and addressing this problem * Recommended length: 150 to 330 words {{tip|Suggestions for this section: * What is the answer to the sub-title question based on psychological theory and research? * What are the answers to the focus questions? * What are the practical, take-home messages? }} ==See also== *[[Motivation and emotion/Book/2020/Dark triad personality and emotion|Dark triad personality and emotion]] (Book chapter, 2020) *[[Motivation and emotion/Book/2019/Emotional intelligence and anti-social behaviour|Emotional intelligence and antisocial behaviour]] (Book chapter, 2019) *[[Motivation and emotion/Book/2021/Emotional intelligence and the dark triad|Emotional intelligence and the dark triad]] (Book chapter, 2021) *[[Motivation and emotion/Book/2021/Light triad|Light triad]] (Book chapter, 2021) *[[wikipedia:Machiavellianism_(psychology)|Machiavellianism]] (Wikipedia) *[[wikipedia:Narcissism|Narcissism]] (Wikipedia) *[[wikipedia:Psychopathy|Psychopathy]] (Wikipedia) *[[wikipedia:Dark_triad|The Dark Triad]] (Wikipedia) ==References== Provide the references for all citations in [[w:APA style|APA style]] (7th ed.) or [[w:Wikipedia:Citing sources|wiki style]]. Alternatively, you can use wiki style (as used on Wikipedia), as long as the information is complete and the formatting is consistent. APA style example: {{Hanging indent|1= Rosenberg, B. D., & Siegel, J. T. (2018). A 50-year review of psychological reactance theory: Do not read this article. ''Motivation Science'', ''4''(4), 281–300. https://doi.org/10.1037/mot0000091 Sacks, O. (1985). ''The man who mistook his wife for a hat and other clinical tales''. Harper & Row. }} {{tip|Suggestions for this section: * Important aspects of APA referencing style ** Author surname, followed by a comma, then the author initials separated by full stops and spaces ** Year of publication in parentheses ** Title of work in lower case (except first letter and proper names), ending in a full-stop ** Journal title in italics, volume number in italics, issue number in parentheses, first and last page numbers separated by an en-dash(–), followed by a full-stop ** doi as a URL which is a working hyperlink (i.e., clickable) ** Hanging indent: Wrap the set of references in the [[Template:Hanging indent|hanging indent template]]: *** Use "Edit source" *** <nowiki>{{Hanging indent|1= the full list of references}}</nowiki> * The most common mistakes include: ** Incorrect capitalisation ** Incorrect italicisation ** dois which aren't clickable as working hyperlinks ** Citing sources that haven't been consulted }} ==External links== * [https://www.sciencefocus.com/wellbeing/dark-empaths Dark Empaths] (Science Focus) * [https://www.psychologytoday.com/au/basics/dark-triad Dark Triad] (Psychology Today) * [https://www.theguardian.com/science/2024/nov/10/narcissists-only-more-devious-the-truth-about-dark-empaths 'Narcissists - only more devious': the truth about dark empaths] (the Guardian) [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Empathy]] 73tucud58ixv6587j3206vzp2i7zfp5 0 331302 2823849 2823227 2026-08-21T09:29:20Z Atcovi 276019 project box(es) 2823849 wikitext text/x-wiki {{medicine}} {{Medical disclaimer}} '''Facial assessment before aesthetic botulinum toxin treatment''' is an open learning resource about structured pre-treatment assessment in facial aesthetic practice. It focuses on clinical reasoning before treatment rather than on injection coordinates, fixed dosing recipes, or product-conversion rules. The central principle is that aesthetic botulinum neurotoxin type A (BoNT-A) treatment should follow an individualized assessment of the person, the face at rest and in motion, interacting facial muscle groups, baseline asymmetries, treatment goals, and relevant risk factors.<ref name="sundaram2016">[https://pubmed.ncbi.nlm.nih.gov/26910696/ Sundaram H, et al. Global Aesthetics Consensus: Botulinum Toxin Type A—Evidence-Based Review, Emerging Concepts, and Consensus Recommendations for Aesthetic Use, Including Updates on Complications. ''Plastic and Reconstructive Surgery''. 2016;137(3):518e–529e. doi:10.1097/01.PRS.0000475758.63709.23.]</ref><ref name="integrative2022">[https://pubmed.ncbi.nlm.nih.gov/36322138/ Integrative Assessment for Optimizing Aesthetic Outcomes When Treating Glabellar Lines With Botulinum Toxin Type A: An Appreciation of the Role of the Frontalis. ''Aesthetic Surgery Journal''. 2023;43(3):NP181–NP194. doi:10.1093/asj/sjac267.]</ref> This resource is intended for advanced learners and healthcare professionals studying facial aesthetics. It does not replace supervised clinical training, local regulation, current product labeling, informed consent, or individualized professional judgment. == Learning objectives == After working through this resource, a learner should be able to: * distinguish a '''facial assessment''' from a simple wrinkle count; * explain why observation at both '''rest and animation''' matters; * recognize that muscles act as an interacting system rather than isolated targets; * identify baseline features that may influence aesthetic interpretation, including brow position, eyelid characteristics, facial asymmetry, soft-tissue support, and habitual compensatory activity; * structure a patient-centered history around goals, prior treatments, prior adverse effects, and expectations; * explain why standardized photographs, expressions, and documentation are useful before treatment; * identify circumstances in which treatment should be deferred pending further evaluation, clarification, or referral; * separate assessment principles from product-specific dosing and injection technique. == 1. Start with the person, not an injection map == Aesthetic assessment begins by clarifying what the person is seeking to change and why. A line that is visually prominent to a clinician may not be the patient's principal concern, while a subtler feature may be highly important to that patient. Consensus work in facial aesthetics emphasizes patient-centered goals, realistic expectations, and an individualized treatment journey rather than a standardized procedural template.<ref name="journey2024">[https://pubmed.ncbi.nlm.nih.gov/38327550/ Philipp-Dormston WG, et al. The Patient Journey in Facial Aesthetics: Findings from a European Consensus Meeting on Improving the Quality of Life for Patients Receiving Botulinum Toxin Injections. ''Clinical, Cosmetic and Investigational Dermatology''. 2024;17:329–337. doi:10.2147/CCID.S446891.]</ref> A useful opening assessment explores: * the patient's own description of the concern; * whether the goal is softening movement, changing a line visible at rest, altering a contour, or changing how an expression is perceived; * the degree of movement the patient wishes to retain; * prior aesthetic procedures and whether previous results were satisfactory; * prior unexpected weakness, asymmetry, eyelid or brow change, smile change, swallowing difficulty, or other adverse effects; * time course of prior BoNT-A exposure and, where known, the product used; * expectations about onset, duration, symmetry, and the possibility that one modality may not address every component of the concern. The consultation should also make room for psychosocial context. Body dysmorphic disorder (BDD) is relevant to aesthetic settings, and validated screening instruments exist; however, screening is not the same as making a psychiatric diagnosis. The purpose of recognizing concerning patterns is to improve patient selection and support appropriate referral rather than to label a patient casually.<ref name="bdd2023">[https://pubmed.ncbi.nlm.nih.gov/36878447/ Body dysmorphic disorder: A critical appraisal of diagnostic, screening, and assessment tools. 2023.]</ref><ref name="bddpath2024">[https://pubmed.ncbi.nlm.nih.gov/38216141/ An Evidence-based Pathway for Body Dysmorphic Disorder in Facial Aesthetics. 2024.]</ref> == 2. Review medical context and treatment suitability == Pre-treatment assessment should include a relevant medical and medication history. Exact contraindications and warnings differ by product and jurisdiction, so the current locally approved prescribing information should be consulted rather than relying on a generic checklist. Areas commonly reviewed before aesthetic BoNT-A treatment include: * previous hypersensitivity or adverse reaction to a botulinum toxin preparation or formulation component; * infection or active inflammatory process at a proposed treatment site; * known neuromuscular disease or symptoms suggesting impaired neuromuscular transmission; * medicines that may alter neuromuscular transmission, and medicines or supplements relevant to bleeding or bruising risk; * previous facial surgery, trauma, nerve injury, facial palsy, synkinesis, or other conditions that alter baseline movement; * pregnancy or lactation, with decisions guided by current evidence, product labeling, local rules, and clinical context rather than assumptions; * previous treatment elsewhere when product, dose, timing, or injected areas are uncertain. A recent review of upper-face botulinum toxin practice reiterates that patient evaluation and selection are critical and that understanding anatomy is central to complication prevention.<ref name="upperthird2025">[https://pubmed.ncbi.nlm.nih.gov/40368730/ Botulinum Toxin Use in the Upper Third of the Face. 2025. doi:10.1016/j.otc.2025.02.003.]</ref> == 3. Observe the face at rest first == Assessment at rest establishes the baseline against which dynamic change will be interpreted. Important observations include: * brow height, shape, and right-left difference; * upper-eyelid show, dermatochalasis, and apparent or true eyelid/brow ptosis; * forehead line pattern and whether lines are visible without active frontalis contraction; * glabellar line depth at rest; * periorbital line pattern and lower-eyelid position; * nasal, perioral, chin, jawline, and platysmal asymmetries where those regions are relevant; * facial proportions, soft-tissue volume, skin quality, and skeletal support that may contribute to a static appearance not primarily driven by muscle activity. The purpose is not to classify every minor asymmetry as abnormal. Normal faces are asymmetric. The practical question is whether an asymmetry is likely to affect treatment planning, expectation-setting, or interpretation of the result. == 4. Reassess during standardized animation == Static inspection alone cannot reveal how the facial muscle system behaves. Multiple consensus publications recommend evaluating the face both at rest and during animation.<ref name="samcep2023">[https://pubmed.ncbi.nlm.nih.gov/37408173/ SAMCEP Society consensus on the treatment of upper facial lines with botulinum neurotoxin type A: A tailored approach. 2023.]</ref> Depending on the area being studied, standardized movements may include: * maximal eyebrow elevation; * frowning or drawing the brows medially; * gentle and maximal eye closure; * spontaneous and posed smiling; * nasal scrunching; * lip pursing and other perioral movements; * chin contraction; * jaw clenching when masseter activity is relevant; * platysmal activation when lower-face or neck dynamics are relevant. The learner should watch for '''sequence, strength, recruitment, compensation, and asymmetry''', not just the final wrinkle pattern. Repeating the same expression can help distinguish a reproducible movement pattern from a transient or poorly understood instruction. == 5. Think in functional muscle groups == Facial muscles interact mechanically and visually. Weakening one component can change the relative dominance of another. This is particularly important in the upper face, where brow position reflects the balance between the frontalis and brow-depressing muscle groups. An integrative assessment of the forehead, glabella, brow, and eyelids therefore provides more information than treating each region as an isolated rectangle.<ref name="integrative2022" /> Questions for the upper face include: * Is the frontalis contributing to habitual compensation for a low brow or upper-eyelid heaviness? * Is frontalis recruitment symmetric? * Does one brow elevate earlier or farther than the other? * Is the patient's desired brow shape compatible with baseline anatomy and muscle recruitment? * Are glabellar lines primarily dynamic, or is there a substantial static component? * Does maximal smiling change lower-eyelid or lateral canthal behavior in a way that should be documented? The same relational principle applies beyond the upper face. Lower-face movement involves multiple elevators, depressors, sphincters, and stabilizers with roles in expression and oral competence. Lower-face treatment is generally considered more anatomically demanding and should not be reduced to isolated line chasing.<ref name="lowerface2017">[https://pubmed.ncbi.nlm.nih.gov/28841604/ de Maio M, et al. Facial Assessment and Injection Guide for Botulinum Toxin and Injectable Hyaluronic Acid Fillers: Focus on the Lower Face. ''Plastic and Reconstructive Surgery''. 2017;140(3):393e–404e. doi:10.1097/PRS.0000000000003646.]</ref> == 6. Identify compensation before modifying it == A muscle can be active because it is the primary source of an unwanted expression, because it is compensating for another structural or functional feature, or both. Examples include: * persistent frontalis activity helping maintain brow position; * asymmetric frontalis recruitment compensating for baseline brow asymmetry; * altered smile mechanics after dental, neurologic, surgical, or traumatic change; * asymmetric lower-face recruitment associated with previous facial nerve dysfunction; * platysmal or chin recruitment that becomes more visible when another movement pattern changes. A pre-treatment record should distinguish what is visible '''before''' treatment from what emerges after the balance of forces changes. == 7. Separate dynamic and static components == BoNT-A changes neuromuscular activity; it does not directly restore lost volume, alter bone structure, or erase every static crease. The relative contributions of movement, skin quality, soft-tissue volume, ligamentous support, and skeletal anatomy should therefore be considered before deciding what a realistic outcome would look like. This distinction supports more accurate counseling: * a predominantly dynamic line may change differently from a deeply etched static line; * a contour concern may involve volume or structural factors in addition to muscle activity; * a perceived asymmetry may persist because it is partly skeletal or soft-tissue based; * the optimal endpoint may be '''controlled movement''' rather than maximal immobility. == 8. Use standardized documentation == Good baseline documentation improves communication, follow-up comparison, and interpretation of unexpected outcomes. With appropriate consent and privacy safeguards, standardized photography can include: * frontal face at rest; * oblique or lateral views when relevant; * standardized maximal expressions corresponding to the regions being assessed; * consistent camera distance, head position, lighting, and facial instruction when feasible. Clinical notes can record: * principal patient goals in the patient's own words; * relevant history and previous treatment experience; * baseline asymmetries; * key findings at rest and in motion; * discussion of limitations and alternatives; * the agreed treatment objective rather than only the planned procedure. == 9. A compact pre-treatment assessment framework == The following mnemonic is a learning aid, not a validated clinical instrument. {| class="wikitable" ! Domain !! Questions |- | '''G — Goals''' || What does the patient want to change? What movement do they want to preserve? |- | '''H — History''' || Previous BoNT-A, adverse effects, surgery, neurologic history, medications, relevant health context? |- | '''R — Rest''' || Baseline brow, eyelid, lines, asymmetry, skin/soft-tissue/skeletal context? |- | '''A — Animation''' || What changes with standardized expression? Which muscles recruit, compensate, or differ side to side? |- | '''P — Proportions and relationships''' || How do adjacent regions and opposing muscle groups interact? |- | '''H — Harm reduction''' || Are there reasons to defer, seek more information, refer, or use a different strategy? |- | '''D — Documentation''' || Are goals, photographs, asymmetries, consent discussion, and baseline findings recorded? |} == 10. Worked reasoning examples == These examples illustrate assessment logic only and intentionally omit injection points and doses. === Example A: forehead lines with low resting brow === A patient requests complete removal of forehead movement. At rest, the brow sits relatively low and the frontalis is mildly active even before the patient is asked to raise the eyebrows. During animation, frontalis recruitment is strong and appears to contribute to maintaining brow position. '''Learning point:''' the forehead should not be interpreted in isolation. Baseline brow position, eyelid characteristics, and compensatory frontalis activity should be documented and discussed before any decision about modifying movement.<ref name="integrative2022" /> === Example B: asymmetric glabellar recruitment === At rest, the brows are mildly asymmetric. During frowning, one side recruits earlier and more strongly. The patient had not noticed the asymmetry before the consultation. '''Learning point:''' documenting pre-existing asymmetry is essential. Symmetry of treatment does not necessarily mean identical treatment of inherently asymmetric anatomy, and a post-treatment difference should be interpreted against the pre-treatment baseline. === Example C: dissatisfaction with a previous “frozen” result === A patient reports that a previous treatment reduced lines but made facial expression feel unnatural. Their new goal is softer movement rather than maximal line elimination. '''Learning point:''' outcome quality is partly defined by the patient's goal. A technically visible reduction in movement is not automatically equivalent to patient satisfaction.<ref name="journey2024" /> == 11. What this resource deliberately does not provide == This learning resource does '''not''' provide: * fixed injection coordinates; * universal doses; * conversion ratios between BoNT-A products; * instructions for unlicensed practice; * a substitute for anatomy training, supervised procedural education, or product-specific prescribing information. Different BoNT-A preparations are not simply interchangeable by a universal unit-conversion rule, and published consensus recommendations repeatedly emphasize individualized anatomy and product-specific practice.<ref name="abobot2012">[https://pubmed.ncbi.nlm.nih.gov/22941910/ Current aesthetic use of abobotulinumtoxinA in clinical practice: an evidence-based consensus review. 2012.]</ref> == 12. Self-assessment questions == # Why can strong resting frontalis activity be clinically meaningful before aesthetic treatment? # What information is added by observing a face during animation rather than only at rest? # Give three examples of baseline asymmetry that should be documented. # Why should a static etched line not automatically be interpreted as a pure muscle-activity problem? # What is the difference between BDD screening and diagnosing BDD? # Why is a patient goal such as “retain natural movement” clinically relevant to assessment? # Why should product-specific contraindications and warnings be checked in current local labeling? == 13. Suggested learning activity == Using standardized, consented photographs or a teaching model, create a one-page assessment note containing: # the stated aesthetic goal; # observations at rest; # observations during two or more standardized expressions; # a description of any right-left difference; # an explanation of at least one interacting muscle relationship; # one factor that could limit the expected result; # one reason treatment might need to be deferred or additional information obtained. The exercise is complete when another learner can understand the baseline facial pattern without being told an injection plan. == Evidence overview == The assessment model in this resource is consistent with recurring themes across consensus statements and reviews: individualized treatment, evaluation at rest and animation, attention to functional anatomy and interacting muscle groups, patient-centered goals, and structured follow-up.<ref name="sundaram2016" /><ref name="samcep2023" /><ref name="journey2024" /> A 2026 systematic review of upper-face aesthetic BoNT-A studies also reported substantial heterogeneity across clinical outcomes and emphasized the need for stronger evidence-driven standardization of outcome assessment.<ref name="meta2026">[https://pubmed.ncbi.nlm.nih.gov/41508559/ Cosmetic Botulinum Toxin A Injections to the Upper Face: A Systematic Review and Meta-Analysis of Clinical Studies. 2026.]</ref> == Related learning resources == * [[Botulinum toxin in aesthetic medicine]] * [[School:Medicine]] * [[Wikiversity:Medical disclaimer]] == Author and provenance == This resource was developed by [[d:Q140287622|Saeed Ghezelbash]] as an openly licensed Wikiversity learning resource. It synthesizes published literature for educational use and is intended to remain open to collaborative improvement. The author attribution describes contribution to this learning resource and does not imply that Wikiversity endorses any individual, clinic, product, or treatment approach. == References == <references /> [[Category:Medicine]] [[Category:Learning resources]] inhy7mo05wm343ax6rj3ebnrmk0jj4w 2 331315 2823792 2823349 2026-08-21T02:25:13Z U3275992 3106315 Added more information to About Me and a social contribution link 2823792 wikitext text/x-wiki == About me: == I am currently a student at the [https://www.canberra.edu.au/ University of Canberra] completing my Bachelor of Psychology. I've always been interested in why we think the way we do and how our minds work. Taking a psychology degree was how I decided to explore my passion in this area. I'm taking numerous units right now, including the unit [[Motivation and emotion|Motivation and Emotion]]. My book chapter is being written for this unit. [[File:Part of a bookshelf containing books by ancient philosophers (1.1).jpg|thumb|Figure 1. Books on a bookcase ]] Outside of my studies, you can find me: * [[w:Reading|Reading]] * Taking walks * Wondering if I should complete the crochet project I started over two years ago == Book Chapter: Irritability == I am currently working on a book chapter called [[Motivation and emotion/Book/2026/Irritability|Irritability]]. == Social Contributions: == # [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2016%2FAnorexia_nervosa_and_extrinsic_motivation&diff=2823791&oldid=2673864 Edited a sentence for clarity] # Put links to comparison pages here # Also link to discussion forum 7qn94336jykv1p59e0hiympxgjey0ab 2823832 2823792 2026-08-21T05:34:14Z U3275992 3106315 /* Social Contributions: */ Added link to contribution on discussion forum 2823832 wikitext text/x-wiki == About me: == I am currently a student at the [https://www.canberra.edu.au/ University of Canberra] completing my Bachelor of Psychology. I've always been interested in why we think the way we do and how our minds work. Taking a psychology degree was how I decided to explore my passion in this area. I'm taking numerous units right now, including the unit [[Motivation and emotion|Motivation and Emotion]]. My book chapter is being written for this unit. [[File:Part of a bookshelf containing books by ancient philosophers (1.1).jpg|thumb|Figure 1. Books on a bookcase ]] Outside of my studies, you can find me: * [[w:Reading|Reading]] * Taking walks * Wondering if I should complete the crochet project I started over two years ago == Book Chapter: Irritability == I am currently working on a book chapter called [[Motivation and emotion/Book/2026/Irritability|Irritability]]. == Social Contributions: == # [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2016%2FAnorexia_nervosa_and_extrinsic_motivation&diff=2823791&oldid=2673864 Edited a sentence for clarity] # Put links to comparison pages here # [https://uclearn.canberra.edu.au/courses/20143/discussion_topics/455261 Response to discussion form 'What do you really want to learn about?'] deevtmcf7hcu165aton38wy9gq6s1i7 2 331330 2823753 2823612 2026-08-20T22:54:45Z TheHutt02 3106996 added social contribution 2823753 wikitext text/x-wiki == About me == My name is Michael, I'm a 3rd year student at the [https://www.canberra.edu.au University of Canberra] undergoing a bachelors or Human Movement and Psychology. One of my units this semester is called [[Motivation and emotion|Motivation and Emotion]]. [[File:2020-01-18 Snowboarding at the 2020 Winter Youth Olympics – Women's Slopestyle – Final – 2nd run (Martin Rulsch) 045.jpg|thumb|'''Figure 1:''' Do a cool trick!]] Some of my hobbies include: * [[w:Snowboarding|Snowboarding]] * [[w:Tennis|Tennis]] * [[w:Running|Running]] * [[w:Weightlifting|Weight Lifting]] * [[w:Video_game|Computer Games]] == Book chapter I'm working on == I am writing a Wikiversity page on the [[Motivation and emotion/Book/2026/Extended process model of emotion regulation|Extended process model of emotional regulation]]. == Social Contributions == # [[Motivation and emotion/Book/2026/Building therapeutic alliance|Added template - first edit]] # [[Talk:Motivation and emotion/Book/2026/Basal ganglia and motivation#Social contribution comment|Added Discussion forum, named social contribution comment, added a comment - first edit in discussion]] # [https://uclearn.canberra.edu.au/courses/20143/users/108336 Contributed to the "What motivates you?" Discussion on Canvas] pldqahqxcoavnw48cd8rq3aq558r3kj 6 331349 2823650 2026-08-20T13:56:08Z Young1lim 21186 {{Information |Description=Carry Lookahead Adders 2B Single Level (20260820 - 20260819) |Source={{own|Young1lim}} |Date=2026-08-20 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} 2823650 wikitext text/x-wiki == Summary == {{Information |Description=Carry Lookahead Adders 2B Single Level (20260820 - 20260819) |Source={{own|Young1lim}} |Date=2026-08-20 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} dg5tn9wgj9bz4zfphrqldrfg7qrums0 6 331350 2823651 2026-08-20T13:57:20Z Young1lim 21186 {{Information |Description=Carry Lookahead Adders 2C Multi-Level (20260820 - 20260819) |Source={{own|Young1lim}} |Date=2026-08-20 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} 2823651 wikitext text/x-wiki == Summary == {{Information |Description=Carry Lookahead Adders 2C Multi-Level (20260820 - 20260819) |Source={{own|Young1lim}} |Date=2026-08-20 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} 5dcafxpf7y6ybfnpi722d2mctmbqno7 6 331351 2823653 2026-08-20T14:19:36Z Young1lim 21186 {{Information |Description=C04.SA0: Address and Dereference Operators (20260819 - 20260818) |Source={{own|Young1lim}} |Date=2026-08-20 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} 2823653 wikitext text/x-wiki == Summary == {{Information |Description=C04.SA0: Address and Dereference Operators (20260819 - 20260818) |Source={{own|Young1lim}} |Date=2026-08-20 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} 4tydh53ew6dhg2av3v92tg4a703xj3b 6 331352 2823655 2026-08-20T14:22:26Z Young1lim 21186 {{Information |Description=C04.SA0: Address and Dereference Operators (20260820 - 20260819) |Source={{own|Young1lim}} |Date=2026-08-20 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} 2823655 wikitext text/x-wiki == Summary == {{Information |Description=C04.SA0: Address and Dereference Operators (20260820 - 20260819) |Source={{own|Young1lim}} |Date=2026-08-20 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} tfz5nv3a02crl8oox1pix4dc96nxt5o 6 331353 2823657 2026-08-20T14:26:12Z Young1lim 21186 {{Information |Description=Laurent.5: Permutation 6C (20260819 - 20260818) |Source={{own|Young1lim}} |Date=2026-08-20 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} 2823657 wikitext text/x-wiki == Summary == {{Information |Description=Laurent.5: Permutation 6C (20260819 - 20260818) |Source={{own|Young1lim}} |Date=2026-08-20 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} 2axcpxzusl7em4xhhyt5ty9e6wywwrf 6 331354 2823659 2026-08-20T14:33:49Z Young1lim 21186 {{Information |Description=Laurent.5: Permutation 6C (20260820 - 20260819) |Source={{own|Young1lim}} |Date=2026-08-20 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} 2823659 wikitext text/x-wiki == Summary == {{Information |Description=Laurent.5: Permutation 6C (20260820 - 20260819) |Source={{own|Young1lim}} |Date=2026-08-20 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} 0uhf5wqua8c7m15rqzayw39vbsik4mu 828 331355 2823755 2026-08-20T23:53:38Z Helpme2222 3106525 Created page with "--" 2823755 Scribunto text/plain -- qxzl98jryua1rq21tqn4xvgxz49fo2d 2823756 2823755 2026-08-20T23:53:45Z Helpme2222 3106525 Undo all revisions. Resource is empty, but not [[Wikiversity:Deletion policy|deleted]]. 2823756 Scribunto text/plain phoiac9h4m842xq45sp7s6u21eteeq1 2823757 2823756 2026-08-20T23:56:52Z Helpme2222 3106525 2823757 Scribunto text/plain local p = {} p.counter = 0 function p.tableBake() p.counter = p.counter + 1 return p.counter end return p 43xel5w3vx6pbdhex4q2abma9i32qtb 0 331356 2823775 2026-08-21T01:22:35Z Howie2024 2995240 Inserting: Introduction, Exponential dilation, Principal geometric result, Organization of the paper, Relationship to PDT project. 2823775 wikitext text/x-wiki {{Research project}} '''Research manuscript — Draft Version 1.0''' ''This page develops a standalone research manuscript arising from the [[Probability Dilation Theory]] project. It is a work in progress and should not be regarded as a peer-reviewed publication.'' = Normalized Probability Dilation: A Unified Framework and Its Fisher–Rao Geometry = '''Howard Richardson''' ''Draft Version 1.0 — August 2026'' == Abstract == This paper develops a unified framework for normalized positive transformations of probability distributions, referred to here as '''Probability Dilation Theory (PDT)'''. The central construction consists of applying a positive transformation to a probability state and subsequently renormalizing the result. In finite dimensions this includes diagonal reweighting, :<math> p_i'= \frac{d_i p_i} {\sum_j d_jp_j}, </math> and the matrix transformation :<math> T_M(p)= \frac{Mp} {\mathbf{1}^{\mathsf T}Mp}, </math> for suitable nonnegative matrices <math>M</math>. A corresponding measure-theoretic formulation is :<math> P_D(A)= \frac{\int_A D\,dP} {\int_X D\,dP}. </math> These constructions are compared explicitly with established mathematical structures including change of measure, normalized positive operators, Perron–Frobenius iteration, Markov operators, replicator-type dynamics, and normalized Feynman–Kac transformations. The purpose of the framework is therefore not to claim these established constructions as new, but to investigate their common dilation-normalization structure and the geometry of the resulting probability trajectories. Particular attention is given to the exponential dilation family :<math> p_i(\theta)= \frac{p_i^{(0)}e^{\theta\phi_i}} {\sum_j p_j^{(0)}e^{\theta\phi_j}}. </math> Using the square-root representation of the Fisher–Rao simplex, we establish that, under finite-dimensional strict-positivity assumptions, the image of this exponential-dilation trajectory is contained in a Fisher–Rao Levi-Civita geodesic, up to reparameterization, if and only if the generator <math>\phi</math> assumes at most two distinct values. An explicit Fisher–Rao arclength parameterization is then obtained for the nondegenerate two-level case. The framework provides a common language for normalized probability transformations while separating results inherited from established theory from geometric properties arising from the particular dilation formulation. == 1. Introduction == Probability distributions are frequently transformed by operations having a common mathematical structure: nonnegative weights are modified by a positive transformation and subsequently normalized so that total probability remains unity. Such constructions occur in numerous areas of probability, statistics, dynamical systems, numerical linear algebra, and mathematical physics. The simplest finite-dimensional example takes a probability vector :<math> p=(p_1,\ldots,p_n)^{\mathsf T}, \qquad p_i\geq 0, \qquad \sum_{i=1}^{n}p_i=1, </math> assigns positive weights <math>d_i</math>, and defines :<math> p_i'= \frac{d_i p_i} {\sum_{j=1}^{n}d_jp_j}. </math> The transformation changes the relative probability assigned to individual states while normalization returns the resulting vector to the probability simplex. This paper uses the term '''probability dilation''' for this general transformation-and-normalization structure and examines a hierarchy of related constructions. In finite dimensions, diagonal dilation extends naturally to the action of a nonnegative matrix, :<math> T_M(p)= \frac{Mp} {\mathbf{1}^{\mathsf T}Mp}, </math> whenever the denominator is positive. At the level of probability measures, multiplication by a positive measurable function <math>D</math> gives :<math> P_D(A)= \frac{\displaystyle\int_A D(x)\,dP(x)} {\displaystyle\int_X D(x)\,dP(x)}. </math> These expressions have substantial connections with existing mathematics. Normalized matrix iteration is closely related to the power method and Perron–Frobenius theory; positive weighting of measures belongs to established change-of-measure constructions; stochastic matrices provide the familiar Markov special case; and normalized potential-weighted measures occur in Feynman–Kac models. Accordingly, the objective of PDT as developed here is '''not''' to rename these established mathematical theories or to assert novelty for normalization itself. Instead, the objective is to examine them through the common structural sequence :<math> \text{positive transformation} \longrightarrow \text{normalization} \longrightarrow \text{iteration} \longrightarrow \text{probability dynamics} \longrightarrow \text{geometry}. </math> This viewpoint leads naturally to questions concerning fixed points, convergence, entropy, state-dependent transformations, and the geometry of trajectories on the probability simplex. === 1.1 Exponential dilation === A particularly useful example is obtained from exponential dilation. Given an initial strictly positive probability vector <math>p^{(0)}</math> and a real-valued generator <math>\phi</math>, define :<math> p_i(\theta)= \frac{p_i^{(0)}e^{\theta\phi_i}} {Z(\theta)}, </math> where :<math> Z(\theta)= \sum_j p_j^{(0)}e^{\theta\phi_j}. </math> This is an exponential-family construction and therefore belongs to well-established information geometry. The question considered here is more specific: :''When is this exponential trajectory also a Levi-Civita geodesic of the Fisher–Rao metric?'' The Fisher–Rao geometry of a finite probability simplex admits a square-root representation on a sphere. Under the mapping :<math> p\longmapsto 2(\sqrt{p_1},\ldots,\sqrt{p_n}), </math> Fisher–Rao geodesics correspond to spherical great-circle arcs. This representation permits a direct characterization of exponential dilation trajectories that are simultaneously Fisher–Rao geodesic. === 1.2 Principal geometric result === The principal geometric result developed below is that, for a strictly positive finite probability vector, an exponential dilation trajectory lies on a Fisher–Rao geodesic, up to reparameterization, precisely when its generator assumes no more than two distinct values. The proof reduces the problem to the dimension of the linear span generated by distinct exponential rates and uses a Vandermonde argument for the converse. The resulting two-level trajectory also admits an explicit Fisher–Rao arclength parameterization. At the present draft stage, this characterization is treated conservatively. Its constituent mathematical ingredients are established results from information geometry and linear algebra. The exact characterization developed here remains subject to further literature review and independent mathematical scrutiny. === 1.3 Organization of the paper === The remainder of the paper is organized as follows: * '''Section 2''' introduces the normalized-dilation framework and notation. * '''Section 3''' develops diagonal and matrix formulations. * '''Section 4''' develops the measure-theoretic formulation. * '''Section 5''' compares the framework explicitly with established mathematics. * '''Section 6''' introduces exponential dilation and its information-geometric representation. * '''Section 7''' states and proves the Fisher–Rao geodesic characterization theorem. * '''Section 8''' derives the two-level Fisher–Rao arclength corollary and illustrative examples. * '''Section 9''' discusses limitations, possible extensions, and open problems. * '''Section 10''' summarizes the principal conclusions. == Relationship to the Probability Dilation Theory project == This manuscript is part of the broader [[Probability Dilation Theory]] research project on Wikiversity. Technical and exploratory material related to the manuscript is developed on associated PDT subpages, including: * [[Probability Dilation Theory/Measure-Theoretic Foundations|Measure-Theoretic Foundations]] * [[Probability Dilation Theory/Matrix Dilation Operators|Matrix Dilation Operators]] * [[Probability Dilation Theory/Dilation Vector Field|Dilation Vector Field]] * [[Probability Dilation Theory/Dilation Flows|Dilation Flows]] * [[Probability Dilation Theory/Convergence and Fixed Points|Convergence and Fixed Points]] * [[Probability Dilation Theory/Fisher Geometry and Dilation Flows|Fisher Geometry and Dilation Flows]] The present page is intended to develop a concise, standalone manuscript rather than reproduce the complete exploratory PDT project. == Draft status and research note == This manuscript is a work in progress. Some constructions discussed in the paper have direct counterparts in established mathematical literature. These relationships are identified explicitly wherever possible. Results developed specifically within the present formulation are being subjected to continuing literature review, proof checking, numerical verification, and independent mathematical scrutiny before any claim of novelty is made. Readers are encouraged to identify relevant prior literature, mathematical errors, counterexamples, alternative proofs, or useful extensions. == See also == * [[Probability Dilation Theory]] * [[Probability Dilation Theory/Matrix Dilation Operators]] * [[Probability Dilation Theory/Measure-Theoretic Foundations]] * [[Probability Dilation Theory/Fisher Geometry and Dilation Flows]] == Copyright and licensing == Text and original figures © Howard Richardson. Licensed under the [https://creativecommons.org/licenses/by/4.0/ Creative Commons Attribution 4.0 International License (CC BY 4.0)]. Reuse permitted with attribution. m6okohutcx7juc5e19oiuaubi0piqt2 2823776 2823775 2026-08-21T01:33:16Z Howie2024 2995240 /* 1.3 Organization of the paper */ Insert section 2. 2823776 wikitext text/x-wiki {{Research project}} '''Research manuscript — Draft Version 1.0''' ''This page develops a standalone research manuscript arising from the [[Probability Dilation Theory]] project. It is a work in progress and should not be regarded as a peer-reviewed publication.'' = Normalized Probability Dilation: A Unified Framework and Its Fisher–Rao Geometry = '''Howard Richardson''' ''Draft Version 1.0 — August 2026'' == Abstract == This paper develops a unified framework for normalized positive transformations of probability distributions, referred to here as '''Probability Dilation Theory (PDT)'''. The central construction consists of applying a positive transformation to a probability state and subsequently renormalizing the result. In finite dimensions this includes diagonal reweighting, :<math> p_i'= \frac{d_i p_i} {\sum_j d_jp_j}, </math> and the matrix transformation :<math> T_M(p)= \frac{Mp} {\mathbf{1}^{\mathsf T}Mp}, </math> for suitable nonnegative matrices <math>M</math>. A corresponding measure-theoretic formulation is :<math> P_D(A)= \frac{\int_A D\,dP} {\int_X D\,dP}. </math> These constructions are compared explicitly with established mathematical structures including change of measure, normalized positive operators, Perron–Frobenius iteration, Markov operators, replicator-type dynamics, and normalized Feynman–Kac transformations. The purpose of the framework is therefore not to claim these established constructions as new, but to investigate their common dilation-normalization structure and the geometry of the resulting probability trajectories. Particular attention is given to the exponential dilation family :<math> p_i(\theta)= \frac{p_i^{(0)}e^{\theta\phi_i}} {\sum_j p_j^{(0)}e^{\theta\phi_j}}. </math> Using the square-root representation of the Fisher–Rao simplex, we establish that, under finite-dimensional strict-positivity assumptions, the image of this exponential-dilation trajectory is contained in a Fisher–Rao Levi-Civita geodesic, up to reparameterization, if and only if the generator <math>\phi</math> assumes at most two distinct values. An explicit Fisher–Rao arclength parameterization is then obtained for the nondegenerate two-level case. The framework provides a common language for normalized probability transformations while separating results inherited from established theory from geometric properties arising from the particular dilation formulation. == 1. Introduction == Probability distributions are frequently transformed by operations having a common mathematical structure: nonnegative weights are modified by a positive transformation and subsequently normalized so that total probability remains unity. Such constructions occur in numerous areas of probability, statistics, dynamical systems, numerical linear algebra, and mathematical physics. The simplest finite-dimensional example takes a probability vector :<math> p=(p_1,\ldots,p_n)^{\mathsf T}, \qquad p_i\geq 0, \qquad \sum_{i=1}^{n}p_i=1, </math> assigns positive weights <math>d_i</math>, and defines :<math> p_i'= \frac{d_i p_i} {\sum_{j=1}^{n}d_jp_j}. </math> The transformation changes the relative probability assigned to individual states while normalization returns the resulting vector to the probability simplex. This paper uses the term '''probability dilation''' for this general transformation-and-normalization structure and examines a hierarchy of related constructions. In finite dimensions, diagonal dilation extends naturally to the action of a nonnegative matrix, :<math> T_M(p)= \frac{Mp} {\mathbf{1}^{\mathsf T}Mp}, </math> whenever the denominator is positive. At the level of probability measures, multiplication by a positive measurable function <math>D</math> gives :<math> P_D(A)= \frac{\displaystyle\int_A D(x)\,dP(x)} {\displaystyle\int_X D(x)\,dP(x)}. </math> These expressions have substantial connections with existing mathematics. Normalized matrix iteration is closely related to the power method and Perron–Frobenius theory; positive weighting of measures belongs to established change-of-measure constructions; stochastic matrices provide the familiar Markov special case; and normalized potential-weighted measures occur in Feynman–Kac models. Accordingly, the objective of PDT as developed here is '''not''' to rename these established mathematical theories or to assert novelty for normalization itself. Instead, the objective is to examine them through the common structural sequence :<math> \text{positive transformation} \longrightarrow \text{normalization} \longrightarrow \text{iteration} \longrightarrow \text{probability dynamics} \longrightarrow \text{geometry}. </math> This viewpoint leads naturally to questions concerning fixed points, convergence, entropy, state-dependent transformations, and the geometry of trajectories on the probability simplex. === 1.1 Exponential dilation === A particularly useful example is obtained from exponential dilation. Given an initial strictly positive probability vector <math>p^{(0)}</math> and a real-valued generator <math>\phi</math>, define :<math> p_i(\theta)= \frac{p_i^{(0)}e^{\theta\phi_i}} {Z(\theta)}, </math> where :<math> Z(\theta)= \sum_j p_j^{(0)}e^{\theta\phi_j}. </math> This is an exponential-family construction and therefore belongs to well-established information geometry. The question considered here is more specific: :''When is this exponential trajectory also a Levi-Civita geodesic of the Fisher–Rao metric?'' The Fisher–Rao geometry of a finite probability simplex admits a square-root representation on a sphere. Under the mapping :<math> p\longmapsto 2(\sqrt{p_1},\ldots,\sqrt{p_n}), </math> Fisher–Rao geodesics correspond to spherical great-circle arcs. This representation permits a direct characterization of exponential dilation trajectories that are simultaneously Fisher–Rao geodesic. === 1.2 Principal geometric result === The principal geometric result developed below is that, for a strictly positive finite probability vector, an exponential dilation trajectory lies on a Fisher–Rao geodesic, up to reparameterization, precisely when its generator assumes no more than two distinct values. The proof reduces the problem to the dimension of the linear span generated by distinct exponential rates and uses a Vandermonde argument for the converse. The resulting two-level trajectory also admits an explicit Fisher–Rao arclength parameterization. At the present draft stage, this characterization is treated conservatively. Its constituent mathematical ingredients are established results from information geometry and linear algebra. The exact characterization developed here remains subject to further literature review and independent mathematical scrutiny. === 1.3 Organization of the paper === The remainder of the paper is organized as follows: * '''Section 2''' introduces the normalized-dilation framework and notation. * '''Section 3''' develops diagonal and matrix formulations. * '''Section 4''' develops the measure-theoretic formulation. * '''Section 5''' compares the framework explicitly with established mathematics. * '''Section 6''' introduces exponential dilation and its information-geometric representation. * '''Section 7''' states and proves the Fisher–Rao geodesic characterization theorem. * '''Section 8''' derives the two-level Fisher–Rao arclength corollary and illustrative examples. * '''Section 9''' discusses limitations, possible extensions, and open problems. * '''Section 10''' summarizes the principal conclusions. == 2. Normalized-Dilation Framework == This section introduces the common mathematical structure used throughout the paper. The essential operation consists of applying a positive transformation to a probability state and then normalizing the transformed object so that it again represents a probability distribution. === 2.1 Probability simplex === For a finite state space with <math>n</math> states, define the probability simplex :<math> \Delta^{n-1} = \left\{ p\in\mathbb{R}^{n}: p_i\geq 0,\; \sum_{i=1}^{n}p_i=1 \right\}. </math> A probability state is represented by a column vector :<math> p= (p_1,\ldots,p_n)^{\mathsf{T}} \in\Delta^{n-1}. </math> Its components satisfy :<math> p_i\geq 0 </math> and :<math> \mathbf{1}^{\mathsf{T}}p=1, </math> where :<math> \mathbf{1} = (1,\ldots,1)^{\mathsf{T}}. </math> The interior of the simplex is :<math> \Delta_{+}^{n-1} = \left\{ p\in\Delta^{n-1}:p_i>0 \text{ for all }i \right\}. </math> The distinction between the simplex and its interior becomes important later when Fisher–Rao geometry is considered. === 2.2 Positive transformations === Let <math>\mathcal{L}</math> denote a transformation acting on probability states such that :<math> p\geq 0 \quad\Longrightarrow\quad \mathcal{L}(p)\geq 0. </math> The transformed object <math>\mathcal{L}(p)</math> need not itself be normalized. Define its total mass by :<math> \mathcal{N}[\mathcal{L}(p)] = \mathbf{1}^{\mathsf{T}}\mathcal{L}(p). </math> Whenever :<math> 0< \mathcal{N}[\mathcal{L}(p)] < \infty, </math> the normalized transformation is defined by :<math> \mathcal{T}_{\mathcal{L}}(p) = \frac{\mathcal{L}(p)} {\mathcal{N}[\mathcal{L}(p)]}. </math> Equivalently, in the finite-dimensional setting, :<math> \mathcal{T}_{\mathcal{L}}(p) = \frac{\mathcal{L}(p)} {\mathbf{1}^{\mathsf{T}}\mathcal{L}(p)}. </math> By construction, :<math> \mathbf{1}^{\mathsf{T}} \mathcal{T}_{\mathcal{L}}(p) = 1, </math> so :<math> \mathcal{T}_{\mathcal{L}}(p) \in \Delta^{n-1}. </math> This positive-transformation-plus-normalization operation is the basic structure referred to in this paper as '''normalized probability dilation'''. === 2.3 Normalization as projectivization === An immediate property of the normalized transformation is invariance under multiplication by a positive scalar. If <math>c>0</math>, then :<math> \frac{c\mathcal{L}(p)} {\mathbf{1}^{\mathsf{T}}c\mathcal{L}(p)} = \frac{\mathcal{L}(p)} {\mathbf{1}^{\mathsf{T}}\mathcal{L}(p)}. </math> Hence :<math> \mathcal{T}_{c\mathcal{L}}(p) = \mathcal{T}_{\mathcal{L}}(p). </math> The normalized transformation therefore depends on the relative components of <math>\mathcal{L}(p)</math>, rather than on its overall positive scale. This projective feature connects normalized dilation with established theories of positive operators and projective dynamics. No claim of novelty is attached to the normalization or projectivization operation itself. === 2.4 Diagonal dilation === Let :<math> D= \operatorname{diag}(d_1,\ldots,d_n), \qquad d_i>0. </math> Applying <math>D</math> to <math>p</math> gives :<math> Dp= (d_1p_1,\ldots,d_np_n)^{\mathsf{T}}. </math> Normalization produces :<math> T_D(p) = \frac{Dp} {\mathbf{1}^{\mathsf{T}}Dp}. </math> Componentwise, :<math> T_D(p)_i = \frac{d_ip_i} {\sum_{j=1}^{n}d_jp_j}. </math> This is the basic finite-dimensional dilation operation from which the broader PDT formulation developed. The factors <math>d_i</math> alter the relative weights of the probability states, while the denominator restores unit total probability. === 2.5 Matrix dilation === The diagonal transformation can be generalized to a nonnegative matrix :<math> M\in\mathbb{R}^{n\times n}, \qquad M_{ij}\geq 0. </math> For any probability vector <math>p</math> satisfying :<math> \mathbf{1}^{\mathsf{T}}Mp>0, </math> define :<math> T_M(p) = \frac{Mp} {\mathbf{1}^{\mathsf{T}}Mp}. </math> The diagonal case is recovered when :<math> M=D. </math> Off-diagonal entries permit components of the input probability vector to contribute to different output components before normalization. The matrix formulation therefore extends independent componentwise reweighting to coupled positive transformations. The mathematical behavior of this construction is closely related to established positive-matrix theory, normalized power iteration, and Perron–Frobenius theory. These relationships are discussed explicitly in Section 5. === 2.6 Measure-theoretic dilation === The same normalization principle extends naturally from finite probability vectors to probability measures. Let <math>(X,\mathcal{F},P)</math> be a probability space, and let :<math> D:X\rightarrow[0,\infty) </math> be measurable with :<math> 0< \int_X D(x)\,dP(x) < \infty. </math> Define a new probability measure <math>P_D</math> by :<math> P_D(A) = \frac{\displaystyle\int_A D(x)\,dP(x)} {\displaystyle\int_X D(x)\,dP(x)}, \qquad A\in\mathcal{F}. </math> Equivalently, the Radon–Nikodym derivative of <math>P_D</math> with respect to <math>P</math> is :<math> \frac{dP_D}{dP} = \frac{D} {\displaystyle\int_X D\,dP}. </math> Thus the finite-dimensional rule :<math> p_i \longmapsto \frac{d_ip_i} {\sum_jd_jp_j} </math> and the measure-theoretic rule :<math> dP \longmapsto \frac{D\,dP} {\int_XD\,dP} </math> share the same normalized positive-reweighting structure. This construction has direct connections with established change-of-measure and weighted-measure theory. The PDT terminology is used here as an organizing framework rather than as a claim that normalized change of measure is itself new. === 2.7 Iterated dilation === A normalized dilation operator can be iterated. Given an initial state :<math> p^{(0)}\in\Delta^{n-1}, </math> define :<math> p^{(k+1)} = \mathcal{T}_{\mathcal{L}}\left(p^{(k)}\right). </math> This generates an orbit :<math> p^{(0)} \longmapsto p^{(1)} \longmapsto p^{(2)} \longmapsto \cdots </math> on the probability simplex. For a fixed matrix <math>M</math>, :<math> p^{(k+1)} = \frac{Mp^{(k)}} {\mathbf{1}^{\mathsf{T}}Mp^{(k)}}. </math> When all required denominators are positive, repeated normalization gives :<math> p^{(k)} = \frac{M^k p^{(0)}} {\mathbf{1}^{\mathsf{T}}M^k p^{(0)}}. </math> The long-term behavior of this iteration is governed in important cases by established spectral and Perron–Frobenius theory. More general formulations may allow the transformation itself to depend on the iteration index or the current probability state, for example :<math> p^{(k+1)} = \frac{M_kp^{(k)}} {\mathbf{1}^{\mathsf{T}}M_kp^{(k)}} </math> or :<math> p^{(k+1)} = \frac{M(p^{(k)})p^{(k)}} {\mathbf{1}^{\mathsf{T}}M(p^{(k)})p^{(k)}}. </math> These state-dependent and iteration-dependent forms are treated as possible extensions rather than necessary components of the basic framework. === 2.8 Hierarchy of normalized dilation === The constructions above can be summarized by the following hierarchy: :'''diagonal reweighting → matrix transformation → positive operator → measure transformation''' At each level the essential operation is: :'''positive transformation + normalization''' The framework is deliberately broad. Its purpose is not to imply that all normalized positive transformations constitute a new mathematical theory, but to provide a common notation and viewpoint from which their dynamics and geometry can be compared. The following sections specialize this framework before examining its relationship to established mathematical constructions. == Relationship to the Probability Dilation Theory project == This manuscript is part of the broader [[Probability Dilation Theory]] research project on Wikiversity. Technical and exploratory material related to the manuscript is developed on associated PDT subpages, including: * [[Probability Dilation Theory/Measure-Theoretic Foundations|Measure-Theoretic Foundations]] * [[Probability Dilation Theory/Matrix Dilation Operators|Matrix Dilation Operators]] * [[Probability Dilation Theory/Dilation Vector Field|Dilation Vector Field]] * [[Probability Dilation Theory/Dilation Flows|Dilation Flows]] * [[Probability Dilation Theory/Convergence and Fixed Points|Convergence and Fixed Points]] * [[Probability Dilation Theory/Fisher Geometry and Dilation Flows|Fisher Geometry and Dilation Flows]] The present page is intended to develop a concise, standalone manuscript rather than reproduce the complete exploratory PDT project. == Draft status and research note == This manuscript is a work in progress. Some constructions discussed in the paper have direct counterparts in established mathematical literature. These relationships are identified explicitly wherever possible. Results developed specifically within the present formulation are being subjected to continuing literature review, proof checking, numerical verification, and independent mathematical scrutiny before any claim of novelty is made. Readers are encouraged to identify relevant prior literature, mathematical errors, counterexamples, alternative proofs, or useful extensions. == See also == * [[Probability Dilation Theory]] * [[Probability Dilation Theory/Matrix Dilation Operators]] * [[Probability Dilation Theory/Measure-Theoretic Foundations]] * [[Probability Dilation Theory/Fisher Geometry and Dilation Flows]] == Copyright and licensing == Text and original figures © Howard Richardson. Licensed under the [https://creativecommons.org/licenses/by/4.0/ Creative Commons Attribution 4.0 International License (CC BY 4.0)]. Reuse permitted with attribution. 453x8knfk8ilo1lrh6ewynhas644xq3 2823777 2823776 2026-08-21T01:35:46Z Howie2024 2995240 /* 2.8 Hierarchy of normalized dilation */ 2823777 wikitext text/x-wiki {{Research project}} '''Research manuscript — Draft Version 1.0''' ''This page develops a standalone research manuscript arising from the [[Probability Dilation Theory]] project. It is a work in progress and should not be regarded as a peer-reviewed publication.'' = Normalized Probability Dilation: A Unified Framework and Its Fisher–Rao Geometry = '''Howard Richardson''' ''Draft Version 1.0 — August 2026'' == Abstract == This paper develops a unified framework for normalized positive transformations of probability distributions, referred to here as '''Probability Dilation Theory (PDT)'''. The central construction consists of applying a positive transformation to a probability state and subsequently renormalizing the result. In finite dimensions this includes diagonal reweighting, :<math> p_i'= \frac{d_i p_i} {\sum_j d_jp_j}, </math> and the matrix transformation :<math> T_M(p)= \frac{Mp} {\mathbf{1}^{\mathsf T}Mp}, </math> for suitable nonnegative matrices <math>M</math>. A corresponding measure-theoretic formulation is :<math> P_D(A)= \frac{\int_A D\,dP} {\int_X D\,dP}. </math> These constructions are compared explicitly with established mathematical structures including change of measure, normalized positive operators, Perron–Frobenius iteration, Markov operators, replicator-type dynamics, and normalized Feynman–Kac transformations. The purpose of the framework is therefore not to claim these established constructions as new, but to investigate their common dilation-normalization structure and the geometry of the resulting probability trajectories. Particular attention is given to the exponential dilation family :<math> p_i(\theta)= \frac{p_i^{(0)}e^{\theta\phi_i}} {\sum_j p_j^{(0)}e^{\theta\phi_j}}. </math> Using the square-root representation of the Fisher–Rao simplex, we establish that, under finite-dimensional strict-positivity assumptions, the image of this exponential-dilation trajectory is contained in a Fisher–Rao Levi-Civita geodesic, up to reparameterization, if and only if the generator <math>\phi</math> assumes at most two distinct values. An explicit Fisher–Rao arclength parameterization is then obtained for the nondegenerate two-level case. The framework provides a common language for normalized probability transformations while separating results inherited from established theory from geometric properties arising from the particular dilation formulation. == 1. Introduction == Probability distributions are frequently transformed by operations having a common mathematical structure: nonnegative weights are modified by a positive transformation and subsequently normalized so that total probability remains unity. Such constructions occur in numerous areas of probability, statistics, dynamical systems, numerical linear algebra, and mathematical physics. The simplest finite-dimensional example takes a probability vector :<math> p=(p_1,\ldots,p_n)^{\mathsf T}, \qquad p_i\geq 0, \qquad \sum_{i=1}^{n}p_i=1, </math> assigns positive weights <math>d_i</math>, and defines :<math> p_i'= \frac{d_i p_i} {\sum_{j=1}^{n}d_jp_j}. </math> The transformation changes the relative probability assigned to individual states while normalization returns the resulting vector to the probability simplex. This paper uses the term '''probability dilation''' for this general transformation-and-normalization structure and examines a hierarchy of related constructions. In finite dimensions, diagonal dilation extends naturally to the action of a nonnegative matrix, :<math> T_M(p)= \frac{Mp} {\mathbf{1}^{\mathsf T}Mp}, </math> whenever the denominator is positive. At the level of probability measures, multiplication by a positive measurable function <math>D</math> gives :<math> P_D(A)= \frac{\displaystyle\int_A D(x)\,dP(x)} {\displaystyle\int_X D(x)\,dP(x)}. </math> These expressions have substantial connections with existing mathematics. Normalized matrix iteration is closely related to the power method and Perron–Frobenius theory; positive weighting of measures belongs to established change-of-measure constructions; stochastic matrices provide the familiar Markov special case; and normalized potential-weighted measures occur in Feynman–Kac models. Accordingly, the objective of PDT as developed here is '''not''' to rename these established mathematical theories or to assert novelty for normalization itself. Instead, the objective is to examine them through the common structural sequence :<math> \text{positive transformation} \longrightarrow \text{normalization} \longrightarrow \text{iteration} \longrightarrow \text{probability dynamics} \longrightarrow \text{geometry}. </math> This viewpoint leads naturally to questions concerning fixed points, convergence, entropy, state-dependent transformations, and the geometry of trajectories on the probability simplex. === 1.1 Exponential dilation === A particularly useful example is obtained from exponential dilation. Given an initial strictly positive probability vector <math>p^{(0)}</math> and a real-valued generator <math>\phi</math>, define :<math> p_i(\theta)= \frac{p_i^{(0)}e^{\theta\phi_i}} {Z(\theta)}, </math> where :<math> Z(\theta)= \sum_j p_j^{(0)}e^{\theta\phi_j}. </math> This is an exponential-family construction and therefore belongs to well-established information geometry. The question considered here is more specific: :''When is this exponential trajectory also a Levi-Civita geodesic of the Fisher–Rao metric?'' The Fisher–Rao geometry of a finite probability simplex admits a square-root representation on a sphere. Under the mapping :<math> p\longmapsto 2(\sqrt{p_1},\ldots,\sqrt{p_n}), </math> Fisher–Rao geodesics correspond to spherical great-circle arcs. This representation permits a direct characterization of exponential dilation trajectories that are simultaneously Fisher–Rao geodesic. === 1.2 Principal geometric result === The principal geometric result developed below is that, for a strictly positive finite probability vector, an exponential dilation trajectory lies on a Fisher–Rao geodesic, up to reparameterization, precisely when its generator assumes no more than two distinct values. The proof reduces the problem to the dimension of the linear span generated by distinct exponential rates and uses a Vandermonde argument for the converse. The resulting two-level trajectory also admits an explicit Fisher–Rao arclength parameterization. At the present draft stage, this characterization is treated conservatively. Its constituent mathematical ingredients are established results from information geometry and linear algebra. The exact characterization developed here remains subject to further literature review and independent mathematical scrutiny. === 1.3 Organization of the paper === The remainder of the paper is organized as follows: * '''Section 2''' introduces the normalized-dilation framework and notation. * '''Section 3''' develops diagonal and matrix formulations. * '''Section 4''' develops the measure-theoretic formulation. * '''Section 5''' compares the framework explicitly with established mathematics. * '''Section 6''' introduces exponential dilation and its information-geometric representation. * '''Section 7''' states and proves the Fisher–Rao geodesic characterization theorem. * '''Section 8''' derives the two-level Fisher–Rao arclength corollary and illustrative examples. * '''Section 9''' discusses limitations, possible extensions, and open problems. * '''Section 10''' summarizes the principal conclusions. == 2. Normalized-Dilation Framework == This section introduces the common mathematical structure used throughout the paper. The essential operation consists of applying a positive transformation to a probability state and then normalizing the transformed object so that it again represents a probability distribution. === 2.1 Probability simplex === For a finite state space with <math>n</math> states, define the probability simplex :<math> \Delta^{n-1} = \left\{ p\in\mathbb{R}^{n}: p_i\geq 0,\; \sum_{i=1}^{n}p_i=1 \right\}. </math> A probability state is represented by a column vector :<math> p= (p_1,\ldots,p_n)^{\mathsf{T}} \in\Delta^{n-1}. </math> Its components satisfy :<math> p_i\geq 0 </math> and :<math> \mathbf{1}^{\mathsf{T}}p=1, </math> where :<math> \mathbf{1} = (1,\ldots,1)^{\mathsf{T}}. </math> The interior of the simplex is :<math> \Delta_{+}^{n-1} = \left\{ p\in\Delta^{n-1}:p_i>0 \text{ for all }i \right\}. </math> The distinction between the simplex and its interior becomes important later when Fisher–Rao geometry is considered. === 2.2 Positive transformations === Let <math>\mathcal{L}</math> denote a transformation acting on probability states such that :<math> p\geq 0 \quad\Longrightarrow\quad \mathcal{L}(p)\geq 0. </math> The transformed object <math>\mathcal{L}(p)</math> need not itself be normalized. Define its total mass by :<math> \mathcal{N}[\mathcal{L}(p)] = \mathbf{1}^{\mathsf{T}}\mathcal{L}(p). </math> Whenever :<math> 0< \mathcal{N}[\mathcal{L}(p)] < \infty, </math> the normalized transformation is defined by :<math> \mathcal{T}_{\mathcal{L}}(p) = \frac{\mathcal{L}(p)} {\mathcal{N}[\mathcal{L}(p)]}. </math> Equivalently, in the finite-dimensional setting, :<math> \mathcal{T}_{\mathcal{L}}(p) = \frac{\mathcal{L}(p)} {\mathbf{1}^{\mathsf{T}}\mathcal{L}(p)}. </math> By construction, :<math> \mathbf{1}^{\mathsf{T}} \mathcal{T}_{\mathcal{L}}(p) = 1, </math> so :<math> \mathcal{T}_{\mathcal{L}}(p) \in \Delta^{n-1}. </math> This positive-transformation-plus-normalization operation is the basic structure referred to in this paper as '''normalized probability dilation'''. === 2.3 Normalization as projectivization === An immediate property of the normalized transformation is invariance under multiplication by a positive scalar. If <math>c>0</math>, then :<math> \frac{c\mathcal{L}(p)} {\mathbf{1}^{\mathsf{T}}c\mathcal{L}(p)} = \frac{\mathcal{L}(p)} {\mathbf{1}^{\mathsf{T}}\mathcal{L}(p)}. </math> Hence :<math> \mathcal{T}_{c\mathcal{L}}(p) = \mathcal{T}_{\mathcal{L}}(p). </math> The normalized transformation therefore depends on the relative components of <math>\mathcal{L}(p)</math>, rather than on its overall positive scale. This projective feature connects normalized dilation with established theories of positive operators and projective dynamics. No claim of novelty is attached to the normalization or projectivization operation itself. === 2.4 Diagonal dilation === Let :<math> D= \operatorname{diag}(d_1,\ldots,d_n), \qquad d_i>0. </math> Applying <math>D</math> to <math>p</math> gives :<math> Dp= (d_1p_1,\ldots,d_np_n)^{\mathsf{T}}. </math> Normalization produces :<math> T_D(p) = \frac{Dp} {\mathbf{1}^{\mathsf{T}}Dp}. </math> Componentwise, :<math> T_D(p)_i = \frac{d_ip_i} {\sum_{j=1}^{n}d_jp_j}. </math> This is the basic finite-dimensional dilation operation from which the broader PDT formulation developed. The factors <math>d_i</math> alter the relative weights of the probability states, while the denominator restores unit total probability. === 2.5 Matrix dilation === The diagonal transformation can be generalized to a nonnegative matrix :<math> M\in\mathbb{R}^{n\times n}, \qquad M_{ij}\geq 0. </math> For any probability vector <math>p</math> satisfying :<math> \mathbf{1}^{\mathsf{T}}Mp>0, </math> define :<math> T_M(p) = \frac{Mp} {\mathbf{1}^{\mathsf{T}}Mp}. </math> The diagonal case is recovered when :<math> M=D. </math> Off-diagonal entries permit components of the input probability vector to contribute to different output components before normalization. The matrix formulation therefore extends independent componentwise reweighting to coupled positive transformations. The mathematical behavior of this construction is closely related to established positive-matrix theory, normalized power iteration, and Perron–Frobenius theory. These relationships are discussed explicitly in Section 5. === 2.6 Measure-theoretic dilation === The same normalization principle extends naturally from finite probability vectors to probability measures. Let <math>(X,\mathcal{F},P)</math> be a probability space, and let :<math> D:X\rightarrow[0,\infty) </math> be measurable with :<math> 0< \int_X D(x)\,dP(x) < \infty. </math> Define a new probability measure <math>P_D</math> by :<math> P_D(A) = \frac{\displaystyle\int_A D(x)\,dP(x)} {\displaystyle\int_X D(x)\,dP(x)}, \qquad A\in\mathcal{F}. </math> Equivalently, the Radon–Nikodym derivative of <math>P_D</math> with respect to <math>P</math> is :<math> \frac{dP_D}{dP} = \frac{D} {\displaystyle\int_X D\,dP}. </math> Thus the finite-dimensional rule :<math> p_i \longmapsto \frac{d_ip_i} {\sum_jd_jp_j} </math> and the measure-theoretic rule :<math> dP \longmapsto \frac{D\,dP} {\int_XD\,dP} </math> share the same normalized positive-reweighting structure. This construction has direct connections with established change-of-measure and weighted-measure theory. The PDT terminology is used here as an organizing framework rather than as a claim that normalized change of measure is itself new. === 2.7 Iterated dilation === A normalized dilation operator can be iterated. Given an initial state :<math> p^{(0)}\in\Delta^{n-1}, </math> define :<math> p^{(k+1)} = \mathcal{T}_{\mathcal{L}}\left(p^{(k)}\right). </math> This generates an orbit :<math> p^{(0)} \longmapsto p^{(1)} \longmapsto p^{(2)} \longmapsto \cdots </math> on the probability simplex. For a fixed matrix <math>M</math>, :<math> p^{(k+1)} = \frac{Mp^{(k)}} {\mathbf{1}^{\mathsf{T}}Mp^{(k)}}. </math> When all required denominators are positive, repeated normalization gives :<math> p^{(k)} = \frac{M^k p^{(0)}} {\mathbf{1}^{\mathsf{T}}M^k p^{(0)}}. </math> The long-term behavior of this iteration is governed in important cases by established spectral and Perron–Frobenius theory. More general formulations may allow the transformation itself to depend on the iteration index or the current probability state, for example :<math> p^{(k+1)} = \frac{M_kp^{(k)}} {\mathbf{1}^{\mathsf{T}}M_kp^{(k)}} </math> or :<math> p^{(k+1)} = \frac{M(p^{(k)})p^{(k)}} {\mathbf{1}^{\mathsf{T}}M(p^{(k)})p^{(k)}}. </math> These state-dependent and iteration-dependent forms are treated as possible extensions rather than necessary components of the basic framework. === 2.8 Hierarchy of normalized dilation === The constructions above can be summarized by the following hierarchy: :'''diagonal reweighting → matrix transformation → positive operator → measure transformation''' At each level the essential operation is: :'''positive transformation + normalization''' The framework is deliberately broad. Its purpose is not to imply that all normalized positive transformations constitute a new mathematical theory, but to provide a common notation and viewpoint from which their dynamics and geometry can be compared. The following sections specialize this framework before examining its relationship to established mathematical constructions. == 3. Finite-Dimensional and Matrix Dilation == This section develops the finite-dimensional forms of normalized probability dilation in greater detail. The emphasis is on the relationship between diagonal reweighting and nonnegative matrix transformations, together with the basic structural properties required later in the paper. === 3.1 Finite probability states === Let :<math> p=(p_1,\ldots,p_n)^{\mathsf{T}} \in\Delta^{n-1}. </math> A positive weighting vector is written :<math> d=(d_1,\ldots,d_n)^{\mathsf{T}}, \qquad d_i>0. </math> The associated diagonal matrix is :<math> D= \operatorname{diag}(d_1,\ldots,d_n). </math> Applying the weighting gives :<math> Dp= (d_1p_1,\ldots,d_np_n)^{\mathsf{T}}. </math> Its total mass is :<math> Z(p,D) = \mathbf{1}^{\mathsf{T}}Dp = \sum_{i=1}^{n}d_ip_i. </math> Since <math>d_i>0</math> and <math>p</math> is a probability vector, :<math> Z(p,D)>0. </math> The normalized diagonal dilation operator is therefore :<math> T_D(p) = \frac{Dp}{Z(p,D)}. </math> Equivalently, :<math> T_D(p)_i = \frac{d_ip_i} {\sum_{j=1}^{n}d_jp_j}. </math> === 3.2 Relative probability transformation === Diagonal dilation has a simple effect on probability ratios. For any states <math>i</math> and <math>j</math> with <math>p_i>0</math> and <math>p_j>0</math>, :<math> \frac{T_D(p)_i}{T_D(p)_j} = \frac{d_i}{d_j} \frac{p_i}{p_j}. </math> Thus normalization does not alter the relative dilation introduced by the factors <math>d_i</math> and <math>d_j</math>. If :<math> d_i>d_j, </math> then the odds of state <math>i</math> relative to state <math>j</math> increase by the factor :<math> \frac{d_i}{d_j}. </math> This ratio form makes clear that diagonal dilation is fundamentally a relative reweighting operation. === 3.3 Scale invariance === Multiplying every dilation factor by the same positive constant does not change the normalized state. Let :<math> c>0. </math> Then :<math> T_{cD}(p) = \frac{cDp} {\mathbf{1}^{\mathsf{T}}cDp} = \frac{Dp} {\mathbf{1}^{\mathsf{T}}Dp} = T_D(p). </math> Therefore only the relative values of the dilation factors affect the transformed probability distribution. This scale invariance is a basic projective property of normalized positive transformations. === 3.4 Repeated diagonal dilation === Suppose the same diagonal operator <math>D</math> is applied repeatedly. Starting from <math>p^{(0)}</math>, define :<math> p^{(k+1)} = T_D(p^{(k)}). </math> Then :<math> p^{(k)} = \frac{D^k p^{(0)}} {\mathbf{1}^{\mathsf{T}}D^k p^{(0)}}. </math> Since :<math> D^k = \operatorname{diag}(d_1^k,\ldots,d_n^k), </math> the individual components are :<math> p_i^{(k)} = \frac{d_i^k p_i^{(0)}} {\sum_{j=1}^{n}d_j^k p_j^{(0)}}. </math> Consequently, for two initially positive components, :<math> \frac{p_i^{(k)}}{p_j^{(k)}} = \left(\frac{d_i}{d_j}\right)^k \frac{p_i^{(0)}}{p_j^{(0)}}. </math> This expression describes the concentration mechanism directly. If one dilation factor is strictly larger than all others and its corresponding initial probability is positive, repeated dilation concentrates probability on that state. If several states share the maximal dilation factor, probability concentrates on that maximal set while preserving the initial relative proportions within that set. This behavior is a direct consequence of normalized repeated weighting and is not specific to PDT terminology. === 3.5 General nonnegative matrix transformation === Let :<math> M=(M_{ij}) \in\mathbb{R}^{n\times n}, \qquad M_{ij}\geq0. </math> For <math>p\in\Delta^{n-1}</math>, define :<math> q=Mp. </math> Because <math>M</math> and <math>p</math> are nonnegative, :<math> q_i\geq0. </math> Whenever :<math> \mathbf{1}^{\mathsf{T}}Mp>0, </math> the normalized matrix dilation operator is :<math> T_M(p) = \frac{Mp} {\mathbf{1}^{\mathsf{T}}Mp}. </math> Its components are :<math> T_M(p)_i = \frac{\sum_{j=1}^{n}M_{ij}p_j} {\sum_{r=1}^{n}\sum_{j=1}^{n}M_{rj}p_j}. </math> By construction, :<math> \sum_{i=1}^{n}T_M(p)_i=1. </math> Hence :<math> T_M(p)\in\Delta^{n-1}. </math> === 3.6 Diagonal dilation as a special case === If :<math> M=D = \operatorname{diag}(d_1,\ldots,d_n), </math> then :<math> Mp=Dp, </math> and therefore :<math> T_M(p)=T_D(p). </math> Diagonal dilation is thus a special case of normalized matrix dilation. The distinction is structural. For a diagonal matrix, each output component depends only on the corresponding input component: :<math> (Dp)_i=d_ip_i. </math> For a general matrix, :<math> (Mp)_i = \sum_{j=1}^{n}M_{ij}p_j, </math> so multiple input states may contribute to a single output state before normalization. This permits coupled probability evolution. === 3.7 When normalization is unnecessary === There is an important special case. Suppose <math>M</math> satisfies :<math> \mathbf{1}^{\mathsf{T}}M = \mathbf{1}^{\mathsf{T}}. </math> Then for every probability vector <math>p</math>, :<math> \mathbf{1}^{\mathsf{T}}Mp = \mathbf{1}^{\mathsf{T}}p = 1. </math> Consequently, :<math> T_M(p)=Mp. </math> With the column-vector convention used in this paper, the condition :<math> \mathbf{1}^{\mathsf{T}}M = \mathbf{1}^{\mathsf{T}} </math> means that the columns of <math>M</math> sum to one. Thus an ordinary probability-preserving linear transition is contained as a special case of the normalized matrix framework. When <math>M</math> does not preserve total mass, normalization supplies the additional step required to return <math>Mp</math> to the simplex. === 3.8 Fixed points and eigenvectors === Suppose <math>p^{*}</math> is a fixed point of the normalized matrix operator: :<math> T_M(p^{*})=p^{*}. </math> Then :<math> \frac{Mp^{*}} {\mathbf{1}^{\mathsf{T}}Mp^{*}} = p^{*}. </math> Multiplying by the denominator gives :<math> Mp^{*} = \lambda p^{*}, </math> where :<math> \lambda = \mathbf{1}^{\mathsf{T}}Mp^{*}. </math> Therefore every fixed point of the normalized matrix transformation is a nonnegative eigenvector of <math>M</math>, normalized to have unit total mass. Conversely, if <math>v\geq0</math> is a nonzero eigenvector satisfying :<math> Mv=\lambda v, \qquad \lambda>0, </math> then :<math> p^{*} = \frac{v} {\mathbf{1}^{\mathsf{T}}v} </math> is a fixed point of <math>T_M</math>. Thus normalized fixed points and positive eigenvectors are directly related. === 3.9 Repeated matrix dilation === For a fixed nonnegative matrix <math>M</math>, define :<math> p^{(k+1)} = T_M(p^{(k)}). </math> Whenever the required denominators remain positive, :<math> p^{(k)} = \frac{M^k p^{(0)}} {\mathbf{1}^{\mathsf{T}}M^k p^{(0)}}. </math> This identity follows because the scalar normalization introduced at each intermediate step cancels under the next normalization. The iteration is therefore closely related to normalized power iteration. Under suitable positivity or primitivity assumptions, Perron–Frobenius theory describes the dominant eigenvalue and positive eigenvector governing the long-term behavior. Accordingly, convergence of the fixed-matrix case should be understood primarily through established positive-matrix and spectral theory rather than as a separate PDT convergence mechanism. === 3.10 Primitive positive matrices === A particularly important case occurs when <math>M</math> is primitive; that is, some positive integer power of <math>M</math> has strictly positive entries. Perron–Frobenius theory then provides a dominant real eigenvalue :<math> \rho(M)>0 </math> with a corresponding strictly positive eigenvector <math>v</math>. After normalization, :<math> p^{*} = \frac{v} {\mathbf{1}^{\mathsf{T}}v}, </math> this eigenvector gives the distinguished interior fixed point of the normalized matrix transformation. For suitable initial probability vectors, :<math> T_M^{k}(p^{(0)}) </math> converges toward <math>p^{*}</math>. This convergence is an established consequence of Perron–Frobenius theory and normalized power iteration. Its role here is to locate matrix dilation within known mathematics. === 3.11 Interpretation of off-diagonal terms === The off-diagonal entries of <math>M</math> distinguish matrix dilation from independent diagonal reweighting. For :<math> i\neq j, </math> a term :<math> M_{ij}p_j </math> represents a contribution from input state <math>j</math> to output component <math>i</math> before normalization. The matrix therefore combines two operations: * positive redistribution or coupling through <math>M</math>; * restoration of unit total probability through normalization. This interpretation is useful for organizing the framework, but the underlying linear transformation remains standard matrix mathematics. === 3.12 Scope of the matrix formulation === The matrix formulation substantially enlarges the class of transformations expressible within the normalized-dilation notation, but that enlargement should not be confused with mathematical novelty. For a fixed matrix <math>M</math>, the central objects :<math> Mp, \qquad M^kp, \qquad \rho(M), </math> and the associated eigenvectors and convergence properties belong to established linear algebra and positive-operator theory. The role of the PDT framework is to place diagonal reweighting, matrix transformation, iteration, and later measure-theoretic and geometric constructions within a common normalized-probability notation. This distinction between '''framework''' and '''new mathematical result''' will be maintained throughout the paper. == Relationship to the Probability Dilation Theory project == This manuscript is part of the broader [[Probability Dilation Theory]] research project on Wikiversity. Technical and exploratory material related to the manuscript is developed on associated PDT subpages, including: * [[Probability Dilation Theory/Measure-Theoretic Foundations|Measure-Theoretic Foundations]] * [[Probability Dilation Theory/Matrix Dilation Operators|Matrix Dilation Operators]] * [[Probability Dilation Theory/Dilation Vector Field|Dilation Vector Field]] * [[Probability Dilation Theory/Dilation Flows|Dilation Flows]] * [[Probability Dilation Theory/Convergence and Fixed Points|Convergence and Fixed Points]] * [[Probability Dilation Theory/Fisher Geometry and Dilation Flows|Fisher Geometry and Dilation Flows]] The present page is intended to develop a concise, standalone manuscript rather than reproduce the complete exploratory PDT project. == Draft status and research note == This manuscript is a work in progress. Some constructions discussed in the paper have direct counterparts in established mathematical literature. These relationships are identified explicitly wherever possible. Results developed specifically within the present formulation are being subjected to continuing literature review, proof checking, numerical verification, and independent mathematical scrutiny before any claim of novelty is made. Readers are encouraged to identify relevant prior literature, mathematical errors, counterexamples, alternative proofs, or useful extensions. == See also == * [[Probability Dilation Theory]] * [[Probability Dilation Theory/Matrix Dilation Operators]] * [[Probability Dilation Theory/Measure-Theoretic Foundations]] * [[Probability Dilation Theory/Fisher Geometry and Dilation Flows]] == Copyright and licensing == Text and original figures © Howard Richardson. Licensed under the [https://creativecommons.org/licenses/by/4.0/ Creative Commons Attribution 4.0 International License (CC BY 4.0)]. Reuse permitted with attribution. goqjl8zxhxuhy37f48ol2knlxlt28yz 2823778 2823777 2026-08-21T01:38:32Z Howie2024 2995240 /* 3.12 Scope of the matrix formulation */ to section 4. Measure - Theoretic Dilation 2823778 wikitext text/x-wiki {{Research project}} '''Research manuscript — Draft Version 1.0''' ''This page develops a standalone research manuscript arising from the [[Probability Dilation Theory]] project. It is a work in progress and should not be regarded as a peer-reviewed publication.'' = Normalized Probability Dilation: A Unified Framework and Its Fisher–Rao Geometry = '''Howard Richardson''' ''Draft Version 1.0 — August 2026'' == Abstract == This paper develops a unified framework for normalized positive transformations of probability distributions, referred to here as '''Probability Dilation Theory (PDT)'''. The central construction consists of applying a positive transformation to a probability state and subsequently renormalizing the result. In finite dimensions this includes diagonal reweighting, :<math> p_i'= \frac{d_i p_i} {\sum_j d_jp_j}, </math> and the matrix transformation :<math> T_M(p)= \frac{Mp} {\mathbf{1}^{\mathsf T}Mp}, </math> for suitable nonnegative matrices <math>M</math>. A corresponding measure-theoretic formulation is :<math> P_D(A)= \frac{\int_A D\,dP} {\int_X D\,dP}. </math> These constructions are compared explicitly with established mathematical structures including change of measure, normalized positive operators, Perron–Frobenius iteration, Markov operators, replicator-type dynamics, and normalized Feynman–Kac transformations. The purpose of the framework is therefore not to claim these established constructions as new, but to investigate their common dilation-normalization structure and the geometry of the resulting probability trajectories. Particular attention is given to the exponential dilation family :<math> p_i(\theta)= \frac{p_i^{(0)}e^{\theta\phi_i}} {\sum_j p_j^{(0)}e^{\theta\phi_j}}. </math> Using the square-root representation of the Fisher–Rao simplex, we establish that, under finite-dimensional strict-positivity assumptions, the image of this exponential-dilation trajectory is contained in a Fisher–Rao Levi-Civita geodesic, up to reparameterization, if and only if the generator <math>\phi</math> assumes at most two distinct values. An explicit Fisher–Rao arclength parameterization is then obtained for the nondegenerate two-level case. The framework provides a common language for normalized probability transformations while separating results inherited from established theory from geometric properties arising from the particular dilation formulation. == 1. Introduction == Probability distributions are frequently transformed by operations having a common mathematical structure: nonnegative weights are modified by a positive transformation and subsequently normalized so that total probability remains unity. Such constructions occur in numerous areas of probability, statistics, dynamical systems, numerical linear algebra, and mathematical physics. The simplest finite-dimensional example takes a probability vector :<math> p=(p_1,\ldots,p_n)^{\mathsf T}, \qquad p_i\geq 0, \qquad \sum_{i=1}^{n}p_i=1, </math> assigns positive weights <math>d_i</math>, and defines :<math> p_i'= \frac{d_i p_i} {\sum_{j=1}^{n}d_jp_j}. </math> The transformation changes the relative probability assigned to individual states while normalization returns the resulting vector to the probability simplex. This paper uses the term '''probability dilation''' for this general transformation-and-normalization structure and examines a hierarchy of related constructions. In finite dimensions, diagonal dilation extends naturally to the action of a nonnegative matrix, :<math> T_M(p)= \frac{Mp} {\mathbf{1}^{\mathsf T}Mp}, </math> whenever the denominator is positive. At the level of probability measures, multiplication by a positive measurable function <math>D</math> gives :<math> P_D(A)= \frac{\displaystyle\int_A D(x)\,dP(x)} {\displaystyle\int_X D(x)\,dP(x)}. </math> These expressions have substantial connections with existing mathematics. Normalized matrix iteration is closely related to the power method and Perron–Frobenius theory; positive weighting of measures belongs to established change-of-measure constructions; stochastic matrices provide the familiar Markov special case; and normalized potential-weighted measures occur in Feynman–Kac models. Accordingly, the objective of PDT as developed here is '''not''' to rename these established mathematical theories or to assert novelty for normalization itself. Instead, the objective is to examine them through the common structural sequence :<math> \text{positive transformation} \longrightarrow \text{normalization} \longrightarrow \text{iteration} \longrightarrow \text{probability dynamics} \longrightarrow \text{geometry}. </math> This viewpoint leads naturally to questions concerning fixed points, convergence, entropy, state-dependent transformations, and the geometry of trajectories on the probability simplex. === 1.1 Exponential dilation === A particularly useful example is obtained from exponential dilation. Given an initial strictly positive probability vector <math>p^{(0)}</math> and a real-valued generator <math>\phi</math>, define :<math> p_i(\theta)= \frac{p_i^{(0)}e^{\theta\phi_i}} {Z(\theta)}, </math> where :<math> Z(\theta)= \sum_j p_j^{(0)}e^{\theta\phi_j}. </math> This is an exponential-family construction and therefore belongs to well-established information geometry. The question considered here is more specific: :''When is this exponential trajectory also a Levi-Civita geodesic of the Fisher–Rao metric?'' The Fisher–Rao geometry of a finite probability simplex admits a square-root representation on a sphere. Under the mapping :<math> p\longmapsto 2(\sqrt{p_1},\ldots,\sqrt{p_n}), </math> Fisher–Rao geodesics correspond to spherical great-circle arcs. This representation permits a direct characterization of exponential dilation trajectories that are simultaneously Fisher–Rao geodesic. === 1.2 Principal geometric result === The principal geometric result developed below is that, for a strictly positive finite probability vector, an exponential dilation trajectory lies on a Fisher–Rao geodesic, up to reparameterization, precisely when its generator assumes no more than two distinct values. The proof reduces the problem to the dimension of the linear span generated by distinct exponential rates and uses a Vandermonde argument for the converse. The resulting two-level trajectory also admits an explicit Fisher–Rao arclength parameterization. At the present draft stage, this characterization is treated conservatively. Its constituent mathematical ingredients are established results from information geometry and linear algebra. The exact characterization developed here remains subject to further literature review and independent mathematical scrutiny. === 1.3 Organization of the paper === The remainder of the paper is organized as follows: * '''Section 2''' introduces the normalized-dilation framework and notation. * '''Section 3''' develops diagonal and matrix formulations. * '''Section 4''' develops the measure-theoretic formulation. * '''Section 5''' compares the framework explicitly with established mathematics. * '''Section 6''' introduces exponential dilation and its information-geometric representation. * '''Section 7''' states and proves the Fisher–Rao geodesic characterization theorem. * '''Section 8''' derives the two-level Fisher–Rao arclength corollary and illustrative examples. * '''Section 9''' discusses limitations, possible extensions, and open problems. * '''Section 10''' summarizes the principal conclusions. == 2. Normalized-Dilation Framework == This section introduces the common mathematical structure used throughout the paper. The essential operation consists of applying a positive transformation to a probability state and then normalizing the transformed object so that it again represents a probability distribution. === 2.1 Probability simplex === For a finite state space with <math>n</math> states, define the probability simplex :<math> \Delta^{n-1} = \left\{ p\in\mathbb{R}^{n}: p_i\geq 0,\; \sum_{i=1}^{n}p_i=1 \right\}. </math> A probability state is represented by a column vector :<math> p= (p_1,\ldots,p_n)^{\mathsf{T}} \in\Delta^{n-1}. </math> Its components satisfy :<math> p_i\geq 0 </math> and :<math> \mathbf{1}^{\mathsf{T}}p=1, </math> where :<math> \mathbf{1} = (1,\ldots,1)^{\mathsf{T}}. </math> The interior of the simplex is :<math> \Delta_{+}^{n-1} = \left\{ p\in\Delta^{n-1}:p_i>0 \text{ for all }i \right\}. </math> The distinction between the simplex and its interior becomes important later when Fisher–Rao geometry is considered. === 2.2 Positive transformations === Let <math>\mathcal{L}</math> denote a transformation acting on probability states such that :<math> p\geq 0 \quad\Longrightarrow\quad \mathcal{L}(p)\geq 0. </math> The transformed object <math>\mathcal{L}(p)</math> need not itself be normalized. Define its total mass by :<math> \mathcal{N}[\mathcal{L}(p)] = \mathbf{1}^{\mathsf{T}}\mathcal{L}(p). </math> Whenever :<math> 0< \mathcal{N}[\mathcal{L}(p)] < \infty, </math> the normalized transformation is defined by :<math> \mathcal{T}_{\mathcal{L}}(p) = \frac{\mathcal{L}(p)} {\mathcal{N}[\mathcal{L}(p)]}. </math> Equivalently, in the finite-dimensional setting, :<math> \mathcal{T}_{\mathcal{L}}(p) = \frac{\mathcal{L}(p)} {\mathbf{1}^{\mathsf{T}}\mathcal{L}(p)}. </math> By construction, :<math> \mathbf{1}^{\mathsf{T}} \mathcal{T}_{\mathcal{L}}(p) = 1, </math> so :<math> \mathcal{T}_{\mathcal{L}}(p) \in \Delta^{n-1}. </math> This positive-transformation-plus-normalization operation is the basic structure referred to in this paper as '''normalized probability dilation'''. === 2.3 Normalization as projectivization === An immediate property of the normalized transformation is invariance under multiplication by a positive scalar. If <math>c>0</math>, then :<math> \frac{c\mathcal{L}(p)} {\mathbf{1}^{\mathsf{T}}c\mathcal{L}(p)} = \frac{\mathcal{L}(p)} {\mathbf{1}^{\mathsf{T}}\mathcal{L}(p)}. </math> Hence :<math> \mathcal{T}_{c\mathcal{L}}(p) = \mathcal{T}_{\mathcal{L}}(p). </math> The normalized transformation therefore depends on the relative components of <math>\mathcal{L}(p)</math>, rather than on its overall positive scale. This projective feature connects normalized dilation with established theories of positive operators and projective dynamics. No claim of novelty is attached to the normalization or projectivization operation itself. === 2.4 Diagonal dilation === Let :<math> D= \operatorname{diag}(d_1,\ldots,d_n), \qquad d_i>0. </math> Applying <math>D</math> to <math>p</math> gives :<math> Dp= (d_1p_1,\ldots,d_np_n)^{\mathsf{T}}. </math> Normalization produces :<math> T_D(p) = \frac{Dp} {\mathbf{1}^{\mathsf{T}}Dp}. </math> Componentwise, :<math> T_D(p)_i = \frac{d_ip_i} {\sum_{j=1}^{n}d_jp_j}. </math> This is the basic finite-dimensional dilation operation from which the broader PDT formulation developed. The factors <math>d_i</math> alter the relative weights of the probability states, while the denominator restores unit total probability. === 2.5 Matrix dilation === The diagonal transformation can be generalized to a nonnegative matrix :<math> M\in\mathbb{R}^{n\times n}, \qquad M_{ij}\geq 0. </math> For any probability vector <math>p</math> satisfying :<math> \mathbf{1}^{\mathsf{T}}Mp>0, </math> define :<math> T_M(p) = \frac{Mp} {\mathbf{1}^{\mathsf{T}}Mp}. </math> The diagonal case is recovered when :<math> M=D. </math> Off-diagonal entries permit components of the input probability vector to contribute to different output components before normalization. The matrix formulation therefore extends independent componentwise reweighting to coupled positive transformations. The mathematical behavior of this construction is closely related to established positive-matrix theory, normalized power iteration, and Perron–Frobenius theory. These relationships are discussed explicitly in Section 5. === 2.6 Measure-theoretic dilation === The same normalization principle extends naturally from finite probability vectors to probability measures. Let <math>(X,\mathcal{F},P)</math> be a probability space, and let :<math> D:X\rightarrow[0,\infty) </math> be measurable with :<math> 0< \int_X D(x)\,dP(x) < \infty. </math> Define a new probability measure <math>P_D</math> by :<math> P_D(A) = \frac{\displaystyle\int_A D(x)\,dP(x)} {\displaystyle\int_X D(x)\,dP(x)}, \qquad A\in\mathcal{F}. </math> Equivalently, the Radon–Nikodym derivative of <math>P_D</math> with respect to <math>P</math> is :<math> \frac{dP_D}{dP} = \frac{D} {\displaystyle\int_X D\,dP}. </math> Thus the finite-dimensional rule :<math> p_i \longmapsto \frac{d_ip_i} {\sum_jd_jp_j} </math> and the measure-theoretic rule :<math> dP \longmapsto \frac{D\,dP} {\int_XD\,dP} </math> share the same normalized positive-reweighting structure. This construction has direct connections with established change-of-measure and weighted-measure theory. The PDT terminology is used here as an organizing framework rather than as a claim that normalized change of measure is itself new. === 2.7 Iterated dilation === A normalized dilation operator can be iterated. Given an initial state :<math> p^{(0)}\in\Delta^{n-1}, </math> define :<math> p^{(k+1)} = \mathcal{T}_{\mathcal{L}}\left(p^{(k)}\right). </math> This generates an orbit :<math> p^{(0)} \longmapsto p^{(1)} \longmapsto p^{(2)} \longmapsto \cdots </math> on the probability simplex. For a fixed matrix <math>M</math>, :<math> p^{(k+1)} = \frac{Mp^{(k)}} {\mathbf{1}^{\mathsf{T}}Mp^{(k)}}. </math> When all required denominators are positive, repeated normalization gives :<math> p^{(k)} = \frac{M^k p^{(0)}} {\mathbf{1}^{\mathsf{T}}M^k p^{(0)}}. </math> The long-term behavior of this iteration is governed in important cases by established spectral and Perron–Frobenius theory. More general formulations may allow the transformation itself to depend on the iteration index or the current probability state, for example :<math> p^{(k+1)} = \frac{M_kp^{(k)}} {\mathbf{1}^{\mathsf{T}}M_kp^{(k)}} </math> or :<math> p^{(k+1)} = \frac{M(p^{(k)})p^{(k)}} {\mathbf{1}^{\mathsf{T}}M(p^{(k)})p^{(k)}}. </math> These state-dependent and iteration-dependent forms are treated as possible extensions rather than necessary components of the basic framework. === 2.8 Hierarchy of normalized dilation === The constructions above can be summarized by the following hierarchy: :'''diagonal reweighting → matrix transformation → positive operator → measure transformation''' At each level the essential operation is: :'''positive transformation + normalization''' The framework is deliberately broad. Its purpose is not to imply that all normalized positive transformations constitute a new mathematical theory, but to provide a common notation and viewpoint from which their dynamics and geometry can be compared. The following sections specialize this framework before examining its relationship to established mathematical constructions. == 3. Finite-Dimensional and Matrix Dilation == This section develops the finite-dimensional forms of normalized probability dilation in greater detail. The emphasis is on the relationship between diagonal reweighting and nonnegative matrix transformations, together with the basic structural properties required later in the paper. === 3.1 Finite probability states === Let :<math> p=(p_1,\ldots,p_n)^{\mathsf{T}} \in\Delta^{n-1}. </math> A positive weighting vector is written :<math> d=(d_1,\ldots,d_n)^{\mathsf{T}}, \qquad d_i>0. </math> The associated diagonal matrix is :<math> D= \operatorname{diag}(d_1,\ldots,d_n). </math> Applying the weighting gives :<math> Dp= (d_1p_1,\ldots,d_np_n)^{\mathsf{T}}. </math> Its total mass is :<math> Z(p,D) = \mathbf{1}^{\mathsf{T}}Dp = \sum_{i=1}^{n}d_ip_i. </math> Since <math>d_i>0</math> and <math>p</math> is a probability vector, :<math> Z(p,D)>0. </math> The normalized diagonal dilation operator is therefore :<math> T_D(p) = \frac{Dp}{Z(p,D)}. </math> Equivalently, :<math> T_D(p)_i = \frac{d_ip_i} {\sum_{j=1}^{n}d_jp_j}. </math> === 3.2 Relative probability transformation === Diagonal dilation has a simple effect on probability ratios. For any states <math>i</math> and <math>j</math> with <math>p_i>0</math> and <math>p_j>0</math>, :<math> \frac{T_D(p)_i}{T_D(p)_j} = \frac{d_i}{d_j} \frac{p_i}{p_j}. </math> Thus normalization does not alter the relative dilation introduced by the factors <math>d_i</math> and <math>d_j</math>. If :<math> d_i>d_j, </math> then the odds of state <math>i</math> relative to state <math>j</math> increase by the factor :<math> \frac{d_i}{d_j}. </math> This ratio form makes clear that diagonal dilation is fundamentally a relative reweighting operation. === 3.3 Scale invariance === Multiplying every dilation factor by the same positive constant does not change the normalized state. Let :<math> c>0. </math> Then :<math> T_{cD}(p) = \frac{cDp} {\mathbf{1}^{\mathsf{T}}cDp} = \frac{Dp} {\mathbf{1}^{\mathsf{T}}Dp} = T_D(p). </math> Therefore only the relative values of the dilation factors affect the transformed probability distribution. This scale invariance is a basic projective property of normalized positive transformations. === 3.4 Repeated diagonal dilation === Suppose the same diagonal operator <math>D</math> is applied repeatedly. Starting from <math>p^{(0)}</math>, define :<math> p^{(k+1)} = T_D(p^{(k)}). </math> Then :<math> p^{(k)} = \frac{D^k p^{(0)}} {\mathbf{1}^{\mathsf{T}}D^k p^{(0)}}. </math> Since :<math> D^k = \operatorname{diag}(d_1^k,\ldots,d_n^k), </math> the individual components are :<math> p_i^{(k)} = \frac{d_i^k p_i^{(0)}} {\sum_{j=1}^{n}d_j^k p_j^{(0)}}. </math> Consequently, for two initially positive components, :<math> \frac{p_i^{(k)}}{p_j^{(k)}} = \left(\frac{d_i}{d_j}\right)^k \frac{p_i^{(0)}}{p_j^{(0)}}. </math> This expression describes the concentration mechanism directly. If one dilation factor is strictly larger than all others and its corresponding initial probability is positive, repeated dilation concentrates probability on that state. If several states share the maximal dilation factor, probability concentrates on that maximal set while preserving the initial relative proportions within that set. This behavior is a direct consequence of normalized repeated weighting and is not specific to PDT terminology. === 3.5 General nonnegative matrix transformation === Let :<math> M=(M_{ij}) \in\mathbb{R}^{n\times n}, \qquad M_{ij}\geq0. </math> For <math>p\in\Delta^{n-1}</math>, define :<math> q=Mp. </math> Because <math>M</math> and <math>p</math> are nonnegative, :<math> q_i\geq0. </math> Whenever :<math> \mathbf{1}^{\mathsf{T}}Mp>0, </math> the normalized matrix dilation operator is :<math> T_M(p) = \frac{Mp} {\mathbf{1}^{\mathsf{T}}Mp}. </math> Its components are :<math> T_M(p)_i = \frac{\sum_{j=1}^{n}M_{ij}p_j} {\sum_{r=1}^{n}\sum_{j=1}^{n}M_{rj}p_j}. </math> By construction, :<math> \sum_{i=1}^{n}T_M(p)_i=1. </math> Hence :<math> T_M(p)\in\Delta^{n-1}. </math> === 3.6 Diagonal dilation as a special case === If :<math> M=D = \operatorname{diag}(d_1,\ldots,d_n), </math> then :<math> Mp=Dp, </math> and therefore :<math> T_M(p)=T_D(p). </math> Diagonal dilation is thus a special case of normalized matrix dilation. The distinction is structural. For a diagonal matrix, each output component depends only on the corresponding input component: :<math> (Dp)_i=d_ip_i. </math> For a general matrix, :<math> (Mp)_i = \sum_{j=1}^{n}M_{ij}p_j, </math> so multiple input states may contribute to a single output state before normalization. This permits coupled probability evolution. === 3.7 When normalization is unnecessary === There is an important special case. Suppose <math>M</math> satisfies :<math> \mathbf{1}^{\mathsf{T}}M = \mathbf{1}^{\mathsf{T}}. </math> Then for every probability vector <math>p</math>, :<math> \mathbf{1}^{\mathsf{T}}Mp = \mathbf{1}^{\mathsf{T}}p = 1. </math> Consequently, :<math> T_M(p)=Mp. </math> With the column-vector convention used in this paper, the condition :<math> \mathbf{1}^{\mathsf{T}}M = \mathbf{1}^{\mathsf{T}} </math> means that the columns of <math>M</math> sum to one. Thus an ordinary probability-preserving linear transition is contained as a special case of the normalized matrix framework. When <math>M</math> does not preserve total mass, normalization supplies the additional step required to return <math>Mp</math> to the simplex. === 3.8 Fixed points and eigenvectors === Suppose <math>p^{*}</math> is a fixed point of the normalized matrix operator: :<math> T_M(p^{*})=p^{*}. </math> Then :<math> \frac{Mp^{*}} {\mathbf{1}^{\mathsf{T}}Mp^{*}} = p^{*}. </math> Multiplying by the denominator gives :<math> Mp^{*} = \lambda p^{*}, </math> where :<math> \lambda = \mathbf{1}^{\mathsf{T}}Mp^{*}. </math> Therefore every fixed point of the normalized matrix transformation is a nonnegative eigenvector of <math>M</math>, normalized to have unit total mass. Conversely, if <math>v\geq0</math> is a nonzero eigenvector satisfying :<math> Mv=\lambda v, \qquad \lambda>0, </math> then :<math> p^{*} = \frac{v} {\mathbf{1}^{\mathsf{T}}v} </math> is a fixed point of <math>T_M</math>. Thus normalized fixed points and positive eigenvectors are directly related. === 3.9 Repeated matrix dilation === For a fixed nonnegative matrix <math>M</math>, define :<math> p^{(k+1)} = T_M(p^{(k)}). </math> Whenever the required denominators remain positive, :<math> p^{(k)} = \frac{M^k p^{(0)}} {\mathbf{1}^{\mathsf{T}}M^k p^{(0)}}. </math> This identity follows because the scalar normalization introduced at each intermediate step cancels under the next normalization. The iteration is therefore closely related to normalized power iteration. Under suitable positivity or primitivity assumptions, Perron–Frobenius theory describes the dominant eigenvalue and positive eigenvector governing the long-term behavior. Accordingly, convergence of the fixed-matrix case should be understood primarily through established positive-matrix and spectral theory rather than as a separate PDT convergence mechanism. === 3.10 Primitive positive matrices === A particularly important case occurs when <math>M</math> is primitive; that is, some positive integer power of <math>M</math> has strictly positive entries. Perron–Frobenius theory then provides a dominant real eigenvalue :<math> \rho(M)>0 </math> with a corresponding strictly positive eigenvector <math>v</math>. After normalization, :<math> p^{*} = \frac{v} {\mathbf{1}^{\mathsf{T}}v}, </math> this eigenvector gives the distinguished interior fixed point of the normalized matrix transformation. For suitable initial probability vectors, :<math> T_M^{k}(p^{(0)}) </math> converges toward <math>p^{*}</math>. This convergence is an established consequence of Perron–Frobenius theory and normalized power iteration. Its role here is to locate matrix dilation within known mathematics. === 3.11 Interpretation of off-diagonal terms === The off-diagonal entries of <math>M</math> distinguish matrix dilation from independent diagonal reweighting. For :<math> i\neq j, </math> a term :<math> M_{ij}p_j </math> represents a contribution from input state <math>j</math> to output component <math>i</math> before normalization. The matrix therefore combines two operations: * positive redistribution or coupling through <math>M</math>; * restoration of unit total probability through normalization. This interpretation is useful for organizing the framework, but the underlying linear transformation remains standard matrix mathematics. === 3.12 Scope of the matrix formulation === The matrix formulation substantially enlarges the class of transformations expressible within the normalized-dilation notation, but that enlargement should not be confused with mathematical novelty. For a fixed matrix <math>M</math>, the central objects :<math> Mp, \qquad M^kp, \qquad \rho(M), </math> and the associated eigenvectors and convergence properties belong to established linear algebra and positive-operator theory. The role of the PDT framework is to place diagonal reweighting, matrix transformation, iteration, and later measure-theoretic and geometric constructions within a common normalized-probability notation. This distinction between '''framework''' and '''new mathematical result''' will be maintained throughout the paper. == 4. Measure-Theoretic Dilation == The finite-dimensional dilation rule extends naturally to probability measures. In this setting, componentwise multiplication by positive weights is replaced by multiplication of a probability measure by a nonnegative measurable function followed by normalization. This formulation places finite probability dilation within the standard language of measure theory and makes its relationship to change of measure explicit. === 4.1 Probability-space formulation === Let :<math> (X,\mathcal{F},P) </math> be a probability space. Let :<math> D:X\rightarrow[0,\infty) </math> be a measurable function satisfying :<math> 0< \int_X D(x)\,dP(x) < \infty. </math> Define the normalization factor :<math> Z(P,D) = \int_X D(x)\,dP(x). </math> For every measurable set :<math> A\in\mathcal{F}, </math> define :<math> P_D(A) = \frac{\displaystyle\int_A D(x)\,dP(x)} {Z(P,D)}. </math> Equivalently, :<math> P_D(A) = \frac{\displaystyle\int_A D(x)\,dP(x)} {\displaystyle\int_X D(x)\,dP(x)}. </math> The function <math>D</math> acts as a nonnegative weighting or dilation field over the probability space. === 4.2 Normalization === The transformed measure has total mass one because :<math> P_D(X) = \frac{\displaystyle\int_X D(x)\,dP(x)} {\displaystyle\int_X D(x)\,dP(x)} = 1. </math> Also, because <math>D</math> is nonnegative, :<math> P_D(A)\geq0 </math> for every <math>A\in\mathcal{F}</math>. Countable additivity follows from the countable additivity of integration with respect to <math>P</math>. Therefore <math>P_D</math> is a probability measure. === 4.3 Radon–Nikodym representation === The transformed measure <math>P_D</math> is absolutely continuous with respect to <math>P</math>. Its Radon–Nikodym derivative is :<math> \frac{dP_D}{dP}(x) = \frac{D(x)} {\displaystyle\int_X D(y)\,dP(y)}. </math> Thus normalized measure dilation can be written formally as :<math> dP_D(x) = \frac{D(x)\,dP(x)} {\displaystyle\int_X D(y)\,dP(y)}. </math> This expression makes clear that the construction is a normalized change of measure. The Radon–Nikodym framework is established measure theory. The terminology of dilation is used here to emphasize the common transformation-and-normalization structure shared with the finite-dimensional formulation. === 4.4 Scale invariance === As in the finite-dimensional case, multiplication of the dilation field by a positive constant does not change the normalized measure. Let :<math> c>0. </math> Then :<math> P_{cD}(A) = \frac{\displaystyle\int_A cD\,dP} {\displaystyle\int_X cD\,dP}. </math> The common factor cancels, giving :<math> P_{cD}(A)=P_D(A). </math> Hence the transformed probability measure depends only on the relative values of the dilation field <math>D</math>, not on its overall positive scale. === 4.5 Finite probability spaces as a special case === Consider a finite state space :<math> X=\{1,\ldots,n\}. </math> Let :<math> P(\{i\})=p_i </math> and define :<math> D(i)=d_i. </math> Then :<math> \int_X D\,dP = \sum_{j=1}^{n}d_jp_j. </math> For the singleton event <math>\{i\}</math>, :<math> P_D(\{i\}) = \frac{d_ip_i} {\sum_{j=1}^{n}d_jp_j}. </math> Thus the finite diagonal dilation rule :<math> p_i' = \frac{d_ip_i} {\sum_jd_jp_j} </math> is recovered exactly from the measure-theoretic construction. The discrete and measure-theoretic formulations are therefore instances of the same normalized positive-reweighting operation. === 4.6 Expectations under dilation === Let :<math> f:X\rightarrow\mathbb{R} </math> be measurable and integrable with respect to the transformed measure. Then :<math> \mathbb{E}_{P_D}[f] = \int_X f(x)\,dP_D(x). </math> Using the Radon–Nikodym representation, :<math> \mathbb{E}_{P_D}[f] = \frac{\displaystyle\int_X f(x)D(x)\,dP(x)} {\displaystyle\int_X D(x)\,dP(x)}. </math> Equivalently, :<math> \mathbb{E}_{P_D}[f] = \frac{\mathbb{E}_{P}[fD]} {\mathbb{E}_{P}[D]}, </math> provided the required expectations exist. This identity is a standard weighted-expectation formula and will later be useful for exponential dilation. === 4.7 Composition of dilation fields === Suppose a first dilation field <math>D_1</math> transforms <math>P</math> into <math>P_{D_1}</math>, and a second field <math>D_2</math> is then applied. The first transformation gives :<math> dP_{D_1} = \frac{D_1\,dP} {\int_XD_1\,dP}. </math> Applying <math>D_2</math> gives :<math> d(P_{D_1})_{D_2} = \frac{D_2\,dP_{D_1}} {\int_XD_2\,dP_{D_1}}. </math> Substituting the first transformation and simplifying yields :<math> d(P_{D_1})_{D_2} = \frac{D_1D_2\,dP} {\int_XD_1D_2\,dP}, </math> whenever the required integrals are finite and positive. Therefore :<math> (P_{D_1})_{D_2} = P_{D_1D_2}. </math> Sequential scalar dilation fields thus combine multiplicatively before normalization. This composition property is the measure-theoretic analogue of repeated diagonal reweighting. === 4.8 Iterated fixed dilation === If the same dilation field <math>D</math> is applied repeatedly, then after <math>k</math> iterations, :<math> dP^{(k)} = \frac{D^k\,dP^{(0)}} {\displaystyle\int_XD^k\,dP^{(0)}}. </math> Equivalently, for any measurable event <math>A</math>, :<math> P^{(k)}(A) = \frac{\displaystyle\int_A D(x)^k\,dP^{(0)}(x)} {\displaystyle\int_X D(x)^k\,dP^{(0)}(x)}. </math> This is the direct measure-theoretic counterpart of :<math> p_i^{(k)} = \frac{d_i^kp_i^{(0)}} {\sum_jd_j^kp_j^{(0)}}. </math> Regions where <math>D</math> is relatively large receive increasing relative weight under repeated application. The precise limiting behavior depends on the structure of <math>D</math> and the initial measure. === 4.9 Exponential dilation fields === A particularly important family is obtained by choosing :<math> D_{\theta}(x) = e^{\theta\phi(x)}, </math> where <math>\phi:X\rightarrow\mathbb{R}</math> is measurable and <math>\theta</math> is a real parameter for which the normalization integral is finite. Define :<math> Z(\theta) = \int_X e^{\theta\phi(x)}\,dP_0(x). </math> Then :<math> dP_{\theta}(x) = \frac{e^{\theta\phi(x)}} {Z(\theta)} dP_0(x). </math> In a finite state space this becomes :<math> p_i(\theta) = \frac{p_i^{(0)}e^{\theta\phi_i}} {\sum_jp_j^{(0)}e^{\theta\phi_j}}. </math> This is a standard exponential tilting construction and is closely related to exponential families, cumulant-generating functions, and information geometry. Its importance for the present paper is that it provides a continuous one-parameter dilation trajectory whose Fisher–Rao geometry can be studied explicitly. === 4.10 Infinitesimal evolution of exponential dilation === For the finite-dimensional exponential family, :<math> p_i(\theta) = \frac{p_i^{(0)}e^{\theta\phi_i}} {Z(\theta)}, </math> differentiate with respect to <math>\theta</math>. The logarithmic derivative is :<math> \frac{d}{d\theta}\log p_i(\theta) = \phi_i - \frac{d}{d\theta}\log Z(\theta). </math> Since :<math> \frac{d}{d\theta}\log Z(\theta) = \sum_jp_j(\theta)\phi_j, </math> define :<math> \overline{\phi}_{\theta} = \sum_jp_j(\theta)\phi_j. </math> Then :<math> \frac{dp_i}{d\theta} = p_i(\theta) \left( \phi_i-\overline{\phi}_{\theta} \right). </math> This equation has the form of a replicator-type evolution equation with a fixed state-dependent generator <math>\phi_i</math>. The relationship to established replicator dynamics is discussed in Section 5. === 4.11 Conservation of total probability === Summing the infinitesimal evolution equation gives :<math> \sum_i \frac{dp_i}{d\theta} = \sum_i p_i(\theta) \left( \phi_i-\overline{\phi}_{\theta} \right). </math> Since :<math> \sum_ip_i(\theta)\phi_i = \overline{\phi}_{\theta} </math> and :<math> \sum_ip_i(\theta)=1, </math> it follows that :<math> \sum_i \frac{dp_i}{d\theta} = 0. </math> Thus the vector field is tangent to the probability simplex. Normalization is therefore reflected infinitesimally by conservation of total probability. === 4.12 Scope of the measure-theoretic formulation === The measure-theoretic formulation shows that normalized probability dilation is not restricted to finite vectors or matrices. The same structural operation appears as :'''weight → normalize → obtain a new probability measure''' and, for exponential fields, :'''exponential weight → normalize → continuous probability trajectory'''. These constructions overlap directly with established change-of-measure theory, exponential tilting, weighted probability measures, and related probabilistic methods. Their role in the present framework is to connect the finite dilation notation to continuous probability spaces and to provide the bridge to the information-geometric analysis developed later in the paper. The next section therefore compares the normalized-dilation framework systematically with established mathematical constructions before any additional geometric results are introduced. == Relationship to the Probability Dilation Theory project == This manuscript is part of the broader [[Probability Dilation Theory]] research project on Wikiversity. Technical and exploratory material related to the manuscript is developed on associated PDT subpages, including: * [[Probability Dilation Theory/Measure-Theoretic Foundations|Measure-Theoretic Foundations]] * [[Probability Dilation Theory/Matrix Dilation Operators|Matrix Dilation Operators]] * [[Probability Dilation Theory/Dilation Vector Field|Dilation Vector Field]] * [[Probability Dilation Theory/Dilation Flows|Dilation Flows]] * [[Probability Dilation Theory/Convergence and Fixed Points|Convergence and Fixed Points]] * [[Probability Dilation Theory/Fisher Geometry and Dilation Flows|Fisher Geometry and Dilation Flows]] The present page is intended to develop a concise, standalone manuscript rather than reproduce the complete exploratory PDT project. == Draft status and research note == This manuscript is a work in progress. Some constructions discussed in the paper have direct counterparts in established mathematical literature. These relationships are identified explicitly wherever possible. Results developed specifically within the present formulation are being subjected to continuing literature review, proof checking, numerical verification, and independent mathematical scrutiny before any claim of novelty is made. Readers are encouraged to identify relevant prior literature, mathematical errors, counterexamples, alternative proofs, or useful extensions. == See also == * [[Probability Dilation Theory]] * [[Probability Dilation Theory/Matrix Dilation Operators]] * [[Probability Dilation Theory/Measure-Theoretic Foundations]] * [[Probability Dilation Theory/Fisher Geometry and Dilation Flows]] == Copyright and licensing == Text and original figures © Howard Richardson. Licensed under the [https://creativecommons.org/licenses/by/4.0/ Creative Commons Attribution 4.0 International License (CC BY 4.0)]. Reuse permitted with attribution. obw46tp3y7b0u32trg2hk3mco558za9 2823779 2823778 2026-08-21T01:40:25Z Howie2024 2995240 /* 4.12 Scope of the measure-theoretic formulation */ Insert section 5. 2823779 wikitext text/x-wiki {{Research project}} '''Research manuscript — Draft Version 1.0''' ''This page develops a standalone research manuscript arising from the [[Probability Dilation Theory]] project. It is a work in progress and should not be regarded as a peer-reviewed publication.'' = Normalized Probability Dilation: A Unified Framework and Its Fisher–Rao Geometry = '''Howard Richardson''' ''Draft Version 1.0 — August 2026'' == Abstract == This paper develops a unified framework for normalized positive transformations of probability distributions, referred to here as '''Probability Dilation Theory (PDT)'''. The central construction consists of applying a positive transformation to a probability state and subsequently renormalizing the result. In finite dimensions this includes diagonal reweighting, :<math> p_i'= \frac{d_i p_i} {\sum_j d_jp_j}, </math> and the matrix transformation :<math> T_M(p)= \frac{Mp} {\mathbf{1}^{\mathsf T}Mp}, </math> for suitable nonnegative matrices <math>M</math>. A corresponding measure-theoretic formulation is :<math> P_D(A)= \frac{\int_A D\,dP} {\int_X D\,dP}. </math> These constructions are compared explicitly with established mathematical structures including change of measure, normalized positive operators, Perron–Frobenius iteration, Markov operators, replicator-type dynamics, and normalized Feynman–Kac transformations. The purpose of the framework is therefore not to claim these established constructions as new, but to investigate their common dilation-normalization structure and the geometry of the resulting probability trajectories. Particular attention is given to the exponential dilation family :<math> p_i(\theta)= \frac{p_i^{(0)}e^{\theta\phi_i}} {\sum_j p_j^{(0)}e^{\theta\phi_j}}. </math> Using the square-root representation of the Fisher–Rao simplex, we establish that, under finite-dimensional strict-positivity assumptions, the image of this exponential-dilation trajectory is contained in a Fisher–Rao Levi-Civita geodesic, up to reparameterization, if and only if the generator <math>\phi</math> assumes at most two distinct values. An explicit Fisher–Rao arclength parameterization is then obtained for the nondegenerate two-level case. The framework provides a common language for normalized probability transformations while separating results inherited from established theory from geometric properties arising from the particular dilation formulation. == 1. Introduction == Probability distributions are frequently transformed by operations having a common mathematical structure: nonnegative weights are modified by a positive transformation and subsequently normalized so that total probability remains unity. Such constructions occur in numerous areas of probability, statistics, dynamical systems, numerical linear algebra, and mathematical physics. The simplest finite-dimensional example takes a probability vector :<math> p=(p_1,\ldots,p_n)^{\mathsf T}, \qquad p_i\geq 0, \qquad \sum_{i=1}^{n}p_i=1, </math> assigns positive weights <math>d_i</math>, and defines :<math> p_i'= \frac{d_i p_i} {\sum_{j=1}^{n}d_jp_j}. </math> The transformation changes the relative probability assigned to individual states while normalization returns the resulting vector to the probability simplex. This paper uses the term '''probability dilation''' for this general transformation-and-normalization structure and examines a hierarchy of related constructions. In finite dimensions, diagonal dilation extends naturally to the action of a nonnegative matrix, :<math> T_M(p)= \frac{Mp} {\mathbf{1}^{\mathsf T}Mp}, </math> whenever the denominator is positive. At the level of probability measures, multiplication by a positive measurable function <math>D</math> gives :<math> P_D(A)= \frac{\displaystyle\int_A D(x)\,dP(x)} {\displaystyle\int_X D(x)\,dP(x)}. </math> These expressions have substantial connections with existing mathematics. Normalized matrix iteration is closely related to the power method and Perron–Frobenius theory; positive weighting of measures belongs to established change-of-measure constructions; stochastic matrices provide the familiar Markov special case; and normalized potential-weighted measures occur in Feynman–Kac models. Accordingly, the objective of PDT as developed here is '''not''' to rename these established mathematical theories or to assert novelty for normalization itself. Instead, the objective is to examine them through the common structural sequence :<math> \text{positive transformation} \longrightarrow \text{normalization} \longrightarrow \text{iteration} \longrightarrow \text{probability dynamics} \longrightarrow \text{geometry}. </math> This viewpoint leads naturally to questions concerning fixed points, convergence, entropy, state-dependent transformations, and the geometry of trajectories on the probability simplex. === 1.1 Exponential dilation === A particularly useful example is obtained from exponential dilation. Given an initial strictly positive probability vector <math>p^{(0)}</math> and a real-valued generator <math>\phi</math>, define :<math> p_i(\theta)= \frac{p_i^{(0)}e^{\theta\phi_i}} {Z(\theta)}, </math> where :<math> Z(\theta)= \sum_j p_j^{(0)}e^{\theta\phi_j}. </math> This is an exponential-family construction and therefore belongs to well-established information geometry. The question considered here is more specific: :''When is this exponential trajectory also a Levi-Civita geodesic of the Fisher–Rao metric?'' The Fisher–Rao geometry of a finite probability simplex admits a square-root representation on a sphere. Under the mapping :<math> p\longmapsto 2(\sqrt{p_1},\ldots,\sqrt{p_n}), </math> Fisher–Rao geodesics correspond to spherical great-circle arcs. This representation permits a direct characterization of exponential dilation trajectories that are simultaneously Fisher–Rao geodesic. === 1.2 Principal geometric result === The principal geometric result developed below is that, for a strictly positive finite probability vector, an exponential dilation trajectory lies on a Fisher–Rao geodesic, up to reparameterization, precisely when its generator assumes no more than two distinct values. The proof reduces the problem to the dimension of the linear span generated by distinct exponential rates and uses a Vandermonde argument for the converse. The resulting two-level trajectory also admits an explicit Fisher–Rao arclength parameterization. At the present draft stage, this characterization is treated conservatively. Its constituent mathematical ingredients are established results from information geometry and linear algebra. The exact characterization developed here remains subject to further literature review and independent mathematical scrutiny. === 1.3 Organization of the paper === The remainder of the paper is organized as follows: * '''Section 2''' introduces the normalized-dilation framework and notation. * '''Section 3''' develops diagonal and matrix formulations. * '''Section 4''' develops the measure-theoretic formulation. * '''Section 5''' compares the framework explicitly with established mathematics. * '''Section 6''' introduces exponential dilation and its information-geometric representation. * '''Section 7''' states and proves the Fisher–Rao geodesic characterization theorem. * '''Section 8''' derives the two-level Fisher–Rao arclength corollary and illustrative examples. * '''Section 9''' discusses limitations, possible extensions, and open problems. * '''Section 10''' summarizes the principal conclusions. == 2. Normalized-Dilation Framework == This section introduces the common mathematical structure used throughout the paper. The essential operation consists of applying a positive transformation to a probability state and then normalizing the transformed object so that it again represents a probability distribution. === 2.1 Probability simplex === For a finite state space with <math>n</math> states, define the probability simplex :<math> \Delta^{n-1} = \left\{ p\in\mathbb{R}^{n}: p_i\geq 0,\; \sum_{i=1}^{n}p_i=1 \right\}. </math> A probability state is represented by a column vector :<math> p= (p_1,\ldots,p_n)^{\mathsf{T}} \in\Delta^{n-1}. </math> Its components satisfy :<math> p_i\geq 0 </math> and :<math> \mathbf{1}^{\mathsf{T}}p=1, </math> where :<math> \mathbf{1} = (1,\ldots,1)^{\mathsf{T}}. </math> The interior of the simplex is :<math> \Delta_{+}^{n-1} = \left\{ p\in\Delta^{n-1}:p_i>0 \text{ for all }i \right\}. </math> The distinction between the simplex and its interior becomes important later when Fisher–Rao geometry is considered. === 2.2 Positive transformations === Let <math>\mathcal{L}</math> denote a transformation acting on probability states such that :<math> p\geq 0 \quad\Longrightarrow\quad \mathcal{L}(p)\geq 0. </math> The transformed object <math>\mathcal{L}(p)</math> need not itself be normalized. Define its total mass by :<math> \mathcal{N}[\mathcal{L}(p)] = \mathbf{1}^{\mathsf{T}}\mathcal{L}(p). </math> Whenever :<math> 0< \mathcal{N}[\mathcal{L}(p)] < \infty, </math> the normalized transformation is defined by :<math> \mathcal{T}_{\mathcal{L}}(p) = \frac{\mathcal{L}(p)} {\mathcal{N}[\mathcal{L}(p)]}. </math> Equivalently, in the finite-dimensional setting, :<math> \mathcal{T}_{\mathcal{L}}(p) = \frac{\mathcal{L}(p)} {\mathbf{1}^{\mathsf{T}}\mathcal{L}(p)}. </math> By construction, :<math> \mathbf{1}^{\mathsf{T}} \mathcal{T}_{\mathcal{L}}(p) = 1, </math> so :<math> \mathcal{T}_{\mathcal{L}}(p) \in \Delta^{n-1}. </math> This positive-transformation-plus-normalization operation is the basic structure referred to in this paper as '''normalized probability dilation'''. === 2.3 Normalization as projectivization === An immediate property of the normalized transformation is invariance under multiplication by a positive scalar. If <math>c>0</math>, then :<math> \frac{c\mathcal{L}(p)} {\mathbf{1}^{\mathsf{T}}c\mathcal{L}(p)} = \frac{\mathcal{L}(p)} {\mathbf{1}^{\mathsf{T}}\mathcal{L}(p)}. </math> Hence :<math> \mathcal{T}_{c\mathcal{L}}(p) = \mathcal{T}_{\mathcal{L}}(p). </math> The normalized transformation therefore depends on the relative components of <math>\mathcal{L}(p)</math>, rather than on its overall positive scale. This projective feature connects normalized dilation with established theories of positive operators and projective dynamics. No claim of novelty is attached to the normalization or projectivization operation itself. === 2.4 Diagonal dilation === Let :<math> D= \operatorname{diag}(d_1,\ldots,d_n), \qquad d_i>0. </math> Applying <math>D</math> to <math>p</math> gives :<math> Dp= (d_1p_1,\ldots,d_np_n)^{\mathsf{T}}. </math> Normalization produces :<math> T_D(p) = \frac{Dp} {\mathbf{1}^{\mathsf{T}}Dp}. </math> Componentwise, :<math> T_D(p)_i = \frac{d_ip_i} {\sum_{j=1}^{n}d_jp_j}. </math> This is the basic finite-dimensional dilation operation from which the broader PDT formulation developed. The factors <math>d_i</math> alter the relative weights of the probability states, while the denominator restores unit total probability. === 2.5 Matrix dilation === The diagonal transformation can be generalized to a nonnegative matrix :<math> M\in\mathbb{R}^{n\times n}, \qquad M_{ij}\geq 0. </math> For any probability vector <math>p</math> satisfying :<math> \mathbf{1}^{\mathsf{T}}Mp>0, </math> define :<math> T_M(p) = \frac{Mp} {\mathbf{1}^{\mathsf{T}}Mp}. </math> The diagonal case is recovered when :<math> M=D. </math> Off-diagonal entries permit components of the input probability vector to contribute to different output components before normalization. The matrix formulation therefore extends independent componentwise reweighting to coupled positive transformations. The mathematical behavior of this construction is closely related to established positive-matrix theory, normalized power iteration, and Perron–Frobenius theory. These relationships are discussed explicitly in Section 5. === 2.6 Measure-theoretic dilation === The same normalization principle extends naturally from finite probability vectors to probability measures. Let <math>(X,\mathcal{F},P)</math> be a probability space, and let :<math> D:X\rightarrow[0,\infty) </math> be measurable with :<math> 0< \int_X D(x)\,dP(x) < \infty. </math> Define a new probability measure <math>P_D</math> by :<math> P_D(A) = \frac{\displaystyle\int_A D(x)\,dP(x)} {\displaystyle\int_X D(x)\,dP(x)}, \qquad A\in\mathcal{F}. </math> Equivalently, the Radon–Nikodym derivative of <math>P_D</math> with respect to <math>P</math> is :<math> \frac{dP_D}{dP} = \frac{D} {\displaystyle\int_X D\,dP}. </math> Thus the finite-dimensional rule :<math> p_i \longmapsto \frac{d_ip_i} {\sum_jd_jp_j} </math> and the measure-theoretic rule :<math> dP \longmapsto \frac{D\,dP} {\int_XD\,dP} </math> share the same normalized positive-reweighting structure. This construction has direct connections with established change-of-measure and weighted-measure theory. The PDT terminology is used here as an organizing framework rather than as a claim that normalized change of measure is itself new. === 2.7 Iterated dilation === A normalized dilation operator can be iterated. Given an initial state :<math> p^{(0)}\in\Delta^{n-1}, </math> define :<math> p^{(k+1)} = \mathcal{T}_{\mathcal{L}}\left(p^{(k)}\right). </math> This generates an orbit :<math> p^{(0)} \longmapsto p^{(1)} \longmapsto p^{(2)} \longmapsto \cdots </math> on the probability simplex. For a fixed matrix <math>M</math>, :<math> p^{(k+1)} = \frac{Mp^{(k)}} {\mathbf{1}^{\mathsf{T}}Mp^{(k)}}. </math> When all required denominators are positive, repeated normalization gives :<math> p^{(k)} = \frac{M^k p^{(0)}} {\mathbf{1}^{\mathsf{T}}M^k p^{(0)}}. </math> The long-term behavior of this iteration is governed in important cases by established spectral and Perron–Frobenius theory. More general formulations may allow the transformation itself to depend on the iteration index or the current probability state, for example :<math> p^{(k+1)} = \frac{M_kp^{(k)}} {\mathbf{1}^{\mathsf{T}}M_kp^{(k)}} </math> or :<math> p^{(k+1)} = \frac{M(p^{(k)})p^{(k)}} {\mathbf{1}^{\mathsf{T}}M(p^{(k)})p^{(k)}}. </math> These state-dependent and iteration-dependent forms are treated as possible extensions rather than necessary components of the basic framework. === 2.8 Hierarchy of normalized dilation === The constructions above can be summarized by the following hierarchy: :'''diagonal reweighting → matrix transformation → positive operator → measure transformation''' At each level the essential operation is: :'''positive transformation + normalization''' The framework is deliberately broad. Its purpose is not to imply that all normalized positive transformations constitute a new mathematical theory, but to provide a common notation and viewpoint from which their dynamics and geometry can be compared. The following sections specialize this framework before examining its relationship to established mathematical constructions. == 3. Finite-Dimensional and Matrix Dilation == This section develops the finite-dimensional forms of normalized probability dilation in greater detail. The emphasis is on the relationship between diagonal reweighting and nonnegative matrix transformations, together with the basic structural properties required later in the paper. === 3.1 Finite probability states === Let :<math> p=(p_1,\ldots,p_n)^{\mathsf{T}} \in\Delta^{n-1}. </math> A positive weighting vector is written :<math> d=(d_1,\ldots,d_n)^{\mathsf{T}}, \qquad d_i>0. </math> The associated diagonal matrix is :<math> D= \operatorname{diag}(d_1,\ldots,d_n). </math> Applying the weighting gives :<math> Dp= (d_1p_1,\ldots,d_np_n)^{\mathsf{T}}. </math> Its total mass is :<math> Z(p,D) = \mathbf{1}^{\mathsf{T}}Dp = \sum_{i=1}^{n}d_ip_i. </math> Since <math>d_i>0</math> and <math>p</math> is a probability vector, :<math> Z(p,D)>0. </math> The normalized diagonal dilation operator is therefore :<math> T_D(p) = \frac{Dp}{Z(p,D)}. </math> Equivalently, :<math> T_D(p)_i = \frac{d_ip_i} {\sum_{j=1}^{n}d_jp_j}. </math> === 3.2 Relative probability transformation === Diagonal dilation has a simple effect on probability ratios. For any states <math>i</math> and <math>j</math> with <math>p_i>0</math> and <math>p_j>0</math>, :<math> \frac{T_D(p)_i}{T_D(p)_j} = \frac{d_i}{d_j} \frac{p_i}{p_j}. </math> Thus normalization does not alter the relative dilation introduced by the factors <math>d_i</math> and <math>d_j</math>. If :<math> d_i>d_j, </math> then the odds of state <math>i</math> relative to state <math>j</math> increase by the factor :<math> \frac{d_i}{d_j}. </math> This ratio form makes clear that diagonal dilation is fundamentally a relative reweighting operation. === 3.3 Scale invariance === Multiplying every dilation factor by the same positive constant does not change the normalized state. Let :<math> c>0. </math> Then :<math> T_{cD}(p) = \frac{cDp} {\mathbf{1}^{\mathsf{T}}cDp} = \frac{Dp} {\mathbf{1}^{\mathsf{T}}Dp} = T_D(p). </math> Therefore only the relative values of the dilation factors affect the transformed probability distribution. This scale invariance is a basic projective property of normalized positive transformations. === 3.4 Repeated diagonal dilation === Suppose the same diagonal operator <math>D</math> is applied repeatedly. Starting from <math>p^{(0)}</math>, define :<math> p^{(k+1)} = T_D(p^{(k)}). </math> Then :<math> p^{(k)} = \frac{D^k p^{(0)}} {\mathbf{1}^{\mathsf{T}}D^k p^{(0)}}. </math> Since :<math> D^k = \operatorname{diag}(d_1^k,\ldots,d_n^k), </math> the individual components are :<math> p_i^{(k)} = \frac{d_i^k p_i^{(0)}} {\sum_{j=1}^{n}d_j^k p_j^{(0)}}. </math> Consequently, for two initially positive components, :<math> \frac{p_i^{(k)}}{p_j^{(k)}} = \left(\frac{d_i}{d_j}\right)^k \frac{p_i^{(0)}}{p_j^{(0)}}. </math> This expression describes the concentration mechanism directly. If one dilation factor is strictly larger than all others and its corresponding initial probability is positive, repeated dilation concentrates probability on that state. If several states share the maximal dilation factor, probability concentrates on that maximal set while preserving the initial relative proportions within that set. This behavior is a direct consequence of normalized repeated weighting and is not specific to PDT terminology. === 3.5 General nonnegative matrix transformation === Let :<math> M=(M_{ij}) \in\mathbb{R}^{n\times n}, \qquad M_{ij}\geq0. </math> For <math>p\in\Delta^{n-1}</math>, define :<math> q=Mp. </math> Because <math>M</math> and <math>p</math> are nonnegative, :<math> q_i\geq0. </math> Whenever :<math> \mathbf{1}^{\mathsf{T}}Mp>0, </math> the normalized matrix dilation operator is :<math> T_M(p) = \frac{Mp} {\mathbf{1}^{\mathsf{T}}Mp}. </math> Its components are :<math> T_M(p)_i = \frac{\sum_{j=1}^{n}M_{ij}p_j} {\sum_{r=1}^{n}\sum_{j=1}^{n}M_{rj}p_j}. </math> By construction, :<math> \sum_{i=1}^{n}T_M(p)_i=1. </math> Hence :<math> T_M(p)\in\Delta^{n-1}. </math> === 3.6 Diagonal dilation as a special case === If :<math> M=D = \operatorname{diag}(d_1,\ldots,d_n), </math> then :<math> Mp=Dp, </math> and therefore :<math> T_M(p)=T_D(p). </math> Diagonal dilation is thus a special case of normalized matrix dilation. The distinction is structural. For a diagonal matrix, each output component depends only on the corresponding input component: :<math> (Dp)_i=d_ip_i. </math> For a general matrix, :<math> (Mp)_i = \sum_{j=1}^{n}M_{ij}p_j, </math> so multiple input states may contribute to a single output state before normalization. This permits coupled probability evolution. === 3.7 When normalization is unnecessary === There is an important special case. Suppose <math>M</math> satisfies :<math> \mathbf{1}^{\mathsf{T}}M = \mathbf{1}^{\mathsf{T}}. </math> Then for every probability vector <math>p</math>, :<math> \mathbf{1}^{\mathsf{T}}Mp = \mathbf{1}^{\mathsf{T}}p = 1. </math> Consequently, :<math> T_M(p)=Mp. </math> With the column-vector convention used in this paper, the condition :<math> \mathbf{1}^{\mathsf{T}}M = \mathbf{1}^{\mathsf{T}} </math> means that the columns of <math>M</math> sum to one. Thus an ordinary probability-preserving linear transition is contained as a special case of the normalized matrix framework. When <math>M</math> does not preserve total mass, normalization supplies the additional step required to return <math>Mp</math> to the simplex. === 3.8 Fixed points and eigenvectors === Suppose <math>p^{*}</math> is a fixed point of the normalized matrix operator: :<math> T_M(p^{*})=p^{*}. </math> Then :<math> \frac{Mp^{*}} {\mathbf{1}^{\mathsf{T}}Mp^{*}} = p^{*}. </math> Multiplying by the denominator gives :<math> Mp^{*} = \lambda p^{*}, </math> where :<math> \lambda = \mathbf{1}^{\mathsf{T}}Mp^{*}. </math> Therefore every fixed point of the normalized matrix transformation is a nonnegative eigenvector of <math>M</math>, normalized to have unit total mass. Conversely, if <math>v\geq0</math> is a nonzero eigenvector satisfying :<math> Mv=\lambda v, \qquad \lambda>0, </math> then :<math> p^{*} = \frac{v} {\mathbf{1}^{\mathsf{T}}v} </math> is a fixed point of <math>T_M</math>. Thus normalized fixed points and positive eigenvectors are directly related. === 3.9 Repeated matrix dilation === For a fixed nonnegative matrix <math>M</math>, define :<math> p^{(k+1)} = T_M(p^{(k)}). </math> Whenever the required denominators remain positive, :<math> p^{(k)} = \frac{M^k p^{(0)}} {\mathbf{1}^{\mathsf{T}}M^k p^{(0)}}. </math> This identity follows because the scalar normalization introduced at each intermediate step cancels under the next normalization. The iteration is therefore closely related to normalized power iteration. Under suitable positivity or primitivity assumptions, Perron–Frobenius theory describes the dominant eigenvalue and positive eigenvector governing the long-term behavior. Accordingly, convergence of the fixed-matrix case should be understood primarily through established positive-matrix and spectral theory rather than as a separate PDT convergence mechanism. === 3.10 Primitive positive matrices === A particularly important case occurs when <math>M</math> is primitive; that is, some positive integer power of <math>M</math> has strictly positive entries. Perron–Frobenius theory then provides a dominant real eigenvalue :<math> \rho(M)>0 </math> with a corresponding strictly positive eigenvector <math>v</math>. After normalization, :<math> p^{*} = \frac{v} {\mathbf{1}^{\mathsf{T}}v}, </math> this eigenvector gives the distinguished interior fixed point of the normalized matrix transformation. For suitable initial probability vectors, :<math> T_M^{k}(p^{(0)}) </math> converges toward <math>p^{*}</math>. This convergence is an established consequence of Perron–Frobenius theory and normalized power iteration. Its role here is to locate matrix dilation within known mathematics. === 3.11 Interpretation of off-diagonal terms === The off-diagonal entries of <math>M</math> distinguish matrix dilation from independent diagonal reweighting. For :<math> i\neq j, </math> a term :<math> M_{ij}p_j </math> represents a contribution from input state <math>j</math> to output component <math>i</math> before normalization. The matrix therefore combines two operations: * positive redistribution or coupling through <math>M</math>; * restoration of unit total probability through normalization. This interpretation is useful for organizing the framework, but the underlying linear transformation remains standard matrix mathematics. === 3.12 Scope of the matrix formulation === The matrix formulation substantially enlarges the class of transformations expressible within the normalized-dilation notation, but that enlargement should not be confused with mathematical novelty. For a fixed matrix <math>M</math>, the central objects :<math> Mp, \qquad M^kp, \qquad \rho(M), </math> and the associated eigenvectors and convergence properties belong to established linear algebra and positive-operator theory. The role of the PDT framework is to place diagonal reweighting, matrix transformation, iteration, and later measure-theoretic and geometric constructions within a common normalized-probability notation. This distinction between '''framework''' and '''new mathematical result''' will be maintained throughout the paper. == 4. Measure-Theoretic Dilation == The finite-dimensional dilation rule extends naturally to probability measures. In this setting, componentwise multiplication by positive weights is replaced by multiplication of a probability measure by a nonnegative measurable function followed by normalization. This formulation places finite probability dilation within the standard language of measure theory and makes its relationship to change of measure explicit. === 4.1 Probability-space formulation === Let :<math> (X,\mathcal{F},P) </math> be a probability space. Let :<math> D:X\rightarrow[0,\infty) </math> be a measurable function satisfying :<math> 0< \int_X D(x)\,dP(x) < \infty. </math> Define the normalization factor :<math> Z(P,D) = \int_X D(x)\,dP(x). </math> For every measurable set :<math> A\in\mathcal{F}, </math> define :<math> P_D(A) = \frac{\displaystyle\int_A D(x)\,dP(x)} {Z(P,D)}. </math> Equivalently, :<math> P_D(A) = \frac{\displaystyle\int_A D(x)\,dP(x)} {\displaystyle\int_X D(x)\,dP(x)}. </math> The function <math>D</math> acts as a nonnegative weighting or dilation field over the probability space. === 4.2 Normalization === The transformed measure has total mass one because :<math> P_D(X) = \frac{\displaystyle\int_X D(x)\,dP(x)} {\displaystyle\int_X D(x)\,dP(x)} = 1. </math> Also, because <math>D</math> is nonnegative, :<math> P_D(A)\geq0 </math> for every <math>A\in\mathcal{F}</math>. Countable additivity follows from the countable additivity of integration with respect to <math>P</math>. Therefore <math>P_D</math> is a probability measure. === 4.3 Radon–Nikodym representation === The transformed measure <math>P_D</math> is absolutely continuous with respect to <math>P</math>. Its Radon–Nikodym derivative is :<math> \frac{dP_D}{dP}(x) = \frac{D(x)} {\displaystyle\int_X D(y)\,dP(y)}. </math> Thus normalized measure dilation can be written formally as :<math> dP_D(x) = \frac{D(x)\,dP(x)} {\displaystyle\int_X D(y)\,dP(y)}. </math> This expression makes clear that the construction is a normalized change of measure. The Radon–Nikodym framework is established measure theory. The terminology of dilation is used here to emphasize the common transformation-and-normalization structure shared with the finite-dimensional formulation. === 4.4 Scale invariance === As in the finite-dimensional case, multiplication of the dilation field by a positive constant does not change the normalized measure. Let :<math> c>0. </math> Then :<math> P_{cD}(A) = \frac{\displaystyle\int_A cD\,dP} {\displaystyle\int_X cD\,dP}. </math> The common factor cancels, giving :<math> P_{cD}(A)=P_D(A). </math> Hence the transformed probability measure depends only on the relative values of the dilation field <math>D</math>, not on its overall positive scale. === 4.5 Finite probability spaces as a special case === Consider a finite state space :<math> X=\{1,\ldots,n\}. </math> Let :<math> P(\{i\})=p_i </math> and define :<math> D(i)=d_i. </math> Then :<math> \int_X D\,dP = \sum_{j=1}^{n}d_jp_j. </math> For the singleton event <math>\{i\}</math>, :<math> P_D(\{i\}) = \frac{d_ip_i} {\sum_{j=1}^{n}d_jp_j}. </math> Thus the finite diagonal dilation rule :<math> p_i' = \frac{d_ip_i} {\sum_jd_jp_j} </math> is recovered exactly from the measure-theoretic construction. The discrete and measure-theoretic formulations are therefore instances of the same normalized positive-reweighting operation. === 4.6 Expectations under dilation === Let :<math> f:X\rightarrow\mathbb{R} </math> be measurable and integrable with respect to the transformed measure. Then :<math> \mathbb{E}_{P_D}[f] = \int_X f(x)\,dP_D(x). </math> Using the Radon–Nikodym representation, :<math> \mathbb{E}_{P_D}[f] = \frac{\displaystyle\int_X f(x)D(x)\,dP(x)} {\displaystyle\int_X D(x)\,dP(x)}. </math> Equivalently, :<math> \mathbb{E}_{P_D}[f] = \frac{\mathbb{E}_{P}[fD]} {\mathbb{E}_{P}[D]}, </math> provided the required expectations exist. This identity is a standard weighted-expectation formula and will later be useful for exponential dilation. === 4.7 Composition of dilation fields === Suppose a first dilation field <math>D_1</math> transforms <math>P</math> into <math>P_{D_1}</math>, and a second field <math>D_2</math> is then applied. The first transformation gives :<math> dP_{D_1} = \frac{D_1\,dP} {\int_XD_1\,dP}. </math> Applying <math>D_2</math> gives :<math> d(P_{D_1})_{D_2} = \frac{D_2\,dP_{D_1}} {\int_XD_2\,dP_{D_1}}. </math> Substituting the first transformation and simplifying yields :<math> d(P_{D_1})_{D_2} = \frac{D_1D_2\,dP} {\int_XD_1D_2\,dP}, </math> whenever the required integrals are finite and positive. Therefore :<math> (P_{D_1})_{D_2} = P_{D_1D_2}. </math> Sequential scalar dilation fields thus combine multiplicatively before normalization. This composition property is the measure-theoretic analogue of repeated diagonal reweighting. === 4.8 Iterated fixed dilation === If the same dilation field <math>D</math> is applied repeatedly, then after <math>k</math> iterations, :<math> dP^{(k)} = \frac{D^k\,dP^{(0)}} {\displaystyle\int_XD^k\,dP^{(0)}}. </math> Equivalently, for any measurable event <math>A</math>, :<math> P^{(k)}(A) = \frac{\displaystyle\int_A D(x)^k\,dP^{(0)}(x)} {\displaystyle\int_X D(x)^k\,dP^{(0)}(x)}. </math> This is the direct measure-theoretic counterpart of :<math> p_i^{(k)} = \frac{d_i^kp_i^{(0)}} {\sum_jd_j^kp_j^{(0)}}. </math> Regions where <math>D</math> is relatively large receive increasing relative weight under repeated application. The precise limiting behavior depends on the structure of <math>D</math> and the initial measure. === 4.9 Exponential dilation fields === A particularly important family is obtained by choosing :<math> D_{\theta}(x) = e^{\theta\phi(x)}, </math> where <math>\phi:X\rightarrow\mathbb{R}</math> is measurable and <math>\theta</math> is a real parameter for which the normalization integral is finite. Define :<math> Z(\theta) = \int_X e^{\theta\phi(x)}\,dP_0(x). </math> Then :<math> dP_{\theta}(x) = \frac{e^{\theta\phi(x)}} {Z(\theta)} dP_0(x). </math> In a finite state space this becomes :<math> p_i(\theta) = \frac{p_i^{(0)}e^{\theta\phi_i}} {\sum_jp_j^{(0)}e^{\theta\phi_j}}. </math> This is a standard exponential tilting construction and is closely related to exponential families, cumulant-generating functions, and information geometry. Its importance for the present paper is that it provides a continuous one-parameter dilation trajectory whose Fisher–Rao geometry can be studied explicitly. === 4.10 Infinitesimal evolution of exponential dilation === For the finite-dimensional exponential family, :<math> p_i(\theta) = \frac{p_i^{(0)}e^{\theta\phi_i}} {Z(\theta)}, </math> differentiate with respect to <math>\theta</math>. The logarithmic derivative is :<math> \frac{d}{d\theta}\log p_i(\theta) = \phi_i - \frac{d}{d\theta}\log Z(\theta). </math> Since :<math> \frac{d}{d\theta}\log Z(\theta) = \sum_jp_j(\theta)\phi_j, </math> define :<math> \overline{\phi}_{\theta} = \sum_jp_j(\theta)\phi_j. </math> Then :<math> \frac{dp_i}{d\theta} = p_i(\theta) \left( \phi_i-\overline{\phi}_{\theta} \right). </math> This equation has the form of a replicator-type evolution equation with a fixed state-dependent generator <math>\phi_i</math>. The relationship to established replicator dynamics is discussed in Section 5. === 4.11 Conservation of total probability === Summing the infinitesimal evolution equation gives :<math> \sum_i \frac{dp_i}{d\theta} = \sum_i p_i(\theta) \left( \phi_i-\overline{\phi}_{\theta} \right). </math> Since :<math> \sum_ip_i(\theta)\phi_i = \overline{\phi}_{\theta} </math> and :<math> \sum_ip_i(\theta)=1, </math> it follows that :<math> \sum_i \frac{dp_i}{d\theta} = 0. </math> Thus the vector field is tangent to the probability simplex. Normalization is therefore reflected infinitesimally by conservation of total probability. === 4.12 Scope of the measure-theoretic formulation === The measure-theoretic formulation shows that normalized probability dilation is not restricted to finite vectors or matrices. The same structural operation appears as :'''weight → normalize → obtain a new probability measure''' and, for exponential fields, :'''exponential weight → normalize → continuous probability trajectory'''. These constructions overlap directly with established change-of-measure theory, exponential tilting, weighted probability measures, and related probabilistic methods. Their role in the present framework is to connect the finite dilation notation to continuous probability spaces and to provide the bridge to the information-geometric analysis developed later in the paper. The next section therefore compares the normalized-dilation framework systematically with established mathematical constructions before any additional geometric results are introduced. == 5. Relation to Established Mathematics == The normalized-dilation framework overlaps with several established areas of mathematics. This section identifies those relationships explicitly. The purpose is twofold: first, to place the notation used in this paper within its appropriate mathematical context; and second, to distinguish established constructions from the particular synthesis and geometric questions developed later in the paper. The term '''probability dilation''' is therefore used as an organizing description of a transformation-and-normalization structure, not as a claim that the underlying operations of reweighting, normalization, positive matrix iteration, or change of measure are themselves new. === 5.1 Weighted probability and change of measure === The measure-theoretic transformation :<math> dP_D = \frac{D\,dP} {\int_XD\,dP} </math> is a standard normalized change of measure. Its Radon–Nikodym derivative with respect to <math>P</math> is :<math> \frac{dP_D}{dP} = \frac{D} {\int_XD\,dP}. </math> Consequently, for an integrable observable <math>f</math>, :<math> \mathbb{E}_{P_D}[f] = \frac{\mathbb{E}_{P}[fD]} {\mathbb{E}_{P}[D]}. </math> These expressions belong to established measure-theoretic probability. Within the present framework, their role is to show that finite diagonal dilation and continuous weighted change of measure share the same normalized reweighting structure. === 5.2 Bayesian reweighting === A closely related normalization structure occurs in Bayesian inference. If <math>\pi(x)</math> is a prior density and <math>L(y\mid x)</math> is a likelihood for observed data <math>y</math>, Bayes' rule gives :<math> \pi(x\mid y) = \frac{L(y\mid x)\pi(x)} {\int L(y\mid z)\pi(z)\,dz}, </math> when the denominator is finite and nonzero. Structurally, this has the same form as :<math> dP_D = \frac{D\,dP} {\int D\,dP}, </math> with the likelihood acting as a positive weighting function. The statistical interpretation is different: Bayesian updating has a specific inferential meaning associated with conditioning on data. The comparison here concerns only the common mathematical normalization structure. === 5.3 Importance weighting and exponential tilting === Weighted probability measures also arise in importance sampling, exponential tilting, large-deviation methods, and related statistical constructions. For a generator <math>\phi</math>, exponential tilting takes the form :<math> dP_{\theta}(x) = \frac{e^{\theta\phi(x)}} {Z(\theta)} dP_0(x), </math> where :<math> Z(\theta) = \int_Xe^{\theta\phi(x)}\,dP_0(x). </math> This is an established exponential-family construction. The corresponding finite-dimensional expression, :<math> p_i(\theta) = \frac{p_i^{(0)}e^{\theta\phi_i}} {\sum_jp_j^{(0)}e^{\theta\phi_j}}, </math> will be the principal object of the Fisher–Rao analysis in Sections 6 through 8. The geometric analysis developed later concerns this established exponential-tilt family under a particular question about coincidence of information-geometric and Fisher–Rao geodesics. === 5.4 Positive matrices and Perron–Frobenius theory === For a fixed nonnegative matrix <math>M</math>, the normalized transformation :<math> T_M(p) = \frac{Mp} {\mathbf{1}^{\mathsf{T}}Mp} </math> is closely related to classical positive-matrix theory. If <math>M</math> is primitive, Perron–Frobenius theory provides a dominant positive eigenvalue :<math> \rho(M)>0 </math> and a corresponding strictly positive eigenvector. Repeated normalized iteration, :<math> p^{(k)} = \frac{M^kp^{(0)}} {\mathbf{1}^{\mathsf{T}}M^kp^{(0)}}, </math> is therefore closely related to normalized power iteration. Under appropriate hypotheses, its asymptotic direction is governed by the Perron eigenvector. These spectral and convergence results are established mathematics and are not presented here as new consequences of PDT. === 5.5 Markov operators === Suppose <math>M</math> is nonnegative and satisfies :<math> \mathbf{1}^{\mathsf{T}}M = \mathbf{1}^{\mathsf{T}}. </math> With the column-vector convention used in this paper, :<math> \mathbf{1}^{\mathsf{T}}Mp = 1 </math> for every probability vector <math>p</math>. Thus :<math> T_M(p)=Mp. </math> In this mass-preserving case, the normalization step is unnecessary. Accordingly, ordinary finite-state Markov evolution is contained as a special mass-preserving case of the broader positive-transformation framework. This observation is structural. It does not imply that normalized dilation provides a replacement for Markov-chain theory. === 5.6 Replicator-type dynamics === The exponential dilation family satisfies :<math> \frac{dp_i}{d\theta} = p_i \left( \phi_i-\overline{\phi}_{\theta} \right), </math> where :<math> \overline{\phi}_{\theta} = \sum_jp_j(\theta)\phi_j. </math> The standard replicator equation has the form :<math> \frac{dp_i}{dt} = p_i \left( f_i(p)-\overline{f}(p) \right). </math> Thus exponential dilation with fixed generator values <math>\phi_i</math> has the same algebraic structure as a replicator equation with state-independent fitness values. The mean-subtraction term guarantees :<math> \sum_i\frac{dp_i}{d\theta}=0, </math> so the flow remains tangent to the probability simplex. Replicator dynamics and their geometric interpretations are established subjects. The present paper uses this connection to relate normalized dilation to known simplex dynamics. === 5.7 Fisher–Rao and Shahshahani geometry === The interior of the probability simplex carries the Fisher–Rao metric. For tangent vectors <math>u</math> and <math>v</math> satisfying :<math> \sum_i u_i = \sum_i v_i = 0, </math> the finite-dimensional Fisher–Rao metric can be written as :<math> g_p(u,v) = \sum_{i=1}^{n} \frac{u_iv_i}{p_i}. </math> Closely related forms of this metric appear in evolutionary dynamics under the name Shahshahani metric. The square-root mapping :<math> \Psi(p) = 2(\sqrt{p_1},\ldots,\sqrt{p_n}) </math> satisfies :<math> \sum_i\Psi_i(p)^2=4. </math> Thus the simplex interior is represented in the positive orthant of a sphere of radius <math>2</math>. Under this representation, the Fisher–Rao metric becomes the metric induced by the ambient Euclidean space, and Levi-Civita Fisher–Rao geodesics correspond locally to great-circle arcs. This established spherical representation will be the principal geometric tool used in Section 7. === 5.8 Exponential families and the e-connection === The exponential dilation path :<math> p_i(\theta) = \frac{p_i^{(0)}e^{\theta\phi_i}} {Z(\theta)} </math> is a one-parameter exponential family. Taking logarithms gives :<math> \log p_i(\theta) = \log p_i^{(0)} + \theta\phi_i - \log Z(\theta). </math> The natural parameter varies linearly with <math>\theta</math>. In information geometry, exponential families are naturally associated with the exponential, or '''e''', connection. A path linear in natural parameters is an e-geodesic. This notion of geodesic is distinct from a Levi-Civita geodesic of the Fisher–Rao metric. Consequently, an exponential dilation trajectory may be straight with respect to the e-connection while being curved with respect to the Fisher–Rao Levi-Civita connection. This distinction is central to the geometric question investigated later in the paper. === 5.9 Fisher information and variance === For the exponential dilation family, :<math> \frac{d}{d\theta} \log p_i(\theta) = \phi_i-\overline{\phi}_{\theta}. </math> The Fisher information associated with the parameter <math>\theta</math> is therefore :<math> I(\theta) = \sum_i p_i(\theta) \left( \phi_i-\overline{\phi}_{\theta} \right)^2. </math> Hence :<math> I(\theta) = \operatorname{Var}_{p(\theta)}(\phi). </math> The Fisher–Rao speed of the trajectory is :<math> v_{\mathrm{FR}}(\theta) = \sqrt{I(\theta)} = \sqrt{\operatorname{Var}_{p(\theta)}(\phi)}. </math> This variance identity is a standard property of one-parameter exponential families. It will be used later when deriving the arclength parameterization of the two-level case. === 5.10 Normalized Feynman–Kac transformations === Another closely related structure occurs in Feynman–Kac models. At an abstract level, a positive measure may first be weighted by a nonnegative potential and then propagated through a positive or Markov operator, followed by normalization. Schematically, such an evolution has the form :'''weight → propagate → normalize'''. The matrix expression :<math> T_M(p) = \frac{Mp} {\mathbf{1}^{\mathsf{T}}Mp} </math> and the measure expression :<math> dP_D = \frac{D\,dP} {\int D\,dP} </math> therefore have structural analogues within normalized Feynman–Kac theory. The exact interpretation and assumptions differ among applications. The comparison made here is structural rather than an assertion of equivalence between PDT and Feynman–Kac theory. === 5.11 Projective dynamics === Because normalized dilation is invariant under multiplication of the unnormalized transformed state by a positive scalar, it naturally has a projective character. For example, :<math> T_{cM}(p) = T_M(p) </math> for every <math>c>0</math> for which the transformation is defined. Thus the normalized state depends on the ray determined by <math>Mp</math>, rather than its magnitude. Positive projective geometry and projective metrics, including Hilbert-type metrics, are established tools in the study of positive operators and their contraction properties. These methods provide natural mathematical machinery for analyzing normalized positive transformations, particularly in convergence problems. === 5.12 What the PDT framework contributes === The preceding comparisons show that the principal operations used in normalized probability dilation have substantial established precedents. The proposed contribution of the framework is therefore not the isolated operation :'''multiply or transform, then normalize'''. Rather, the framework provides a common notation and organizational viewpoint connecting: * finite diagonal reweighting; * nonnegative matrix transformations; * normalized positive iteration; * weighted change of measure; * exponential probability trajectories; * simplex dynamics; * information geometry. This synthesis is useful only insofar as it clarifies relationships, generates mathematically precise questions, or produces results that are not merely restatements of known theory. For that reason, the remainder of this paper concentrates on a narrower geometric problem. === 5.13 Transition to the geometric question === Every exponential dilation trajectory of the form :<math> p_i(\theta) = \frac{p_i^{(0)}e^{\theta\phi_i}} {Z(\theta)} </math> is an exponential-family trajectory and hence is naturally straight with respect to the e-connection. It does not follow that the same trajectory is a Levi-Civita geodesic of the Fisher–Rao metric. This leads to the central question considered in the remainder of the paper: :''Under what conditions is an exponential dilation trajectory simultaneously an e-geodesic and, up to reparameterization, a Fisher–Rao Levi-Civita geodesic?'' The next section develops the geometric representation required to answer this question. == Relationship to the Probability Dilation Theory project == This manuscript is part of the broader [[Probability Dilation Theory]] research project on Wikiversity. Technical and exploratory material related to the manuscript is developed on associated PDT subpages, including: * [[Probability Dilation Theory/Measure-Theoretic Foundations|Measure-Theoretic Foundations]] * [[Probability Dilation Theory/Matrix Dilation Operators|Matrix Dilation Operators]] * [[Probability Dilation Theory/Dilation Vector Field|Dilation Vector Field]] * [[Probability Dilation Theory/Dilation Flows|Dilation Flows]] * [[Probability Dilation Theory/Convergence and Fixed Points|Convergence and Fixed Points]] * [[Probability Dilation Theory/Fisher Geometry and Dilation Flows|Fisher Geometry and Dilation Flows]] The present page is intended to develop a concise, standalone manuscript rather than reproduce the complete exploratory PDT project. == Draft status and research note == This manuscript is a work in progress. Some constructions discussed in the paper have direct counterparts in established mathematical literature. These relationships are identified explicitly wherever possible. Results developed specifically within the present formulation are being subjected to continuing literature review, proof checking, numerical verification, and independent mathematical scrutiny before any claim of novelty is made. Readers are encouraged to identify relevant prior literature, mathematical errors, counterexamples, alternative proofs, or useful extensions. == See also == * [[Probability Dilation Theory]] * [[Probability Dilation Theory/Matrix Dilation Operators]] * [[Probability Dilation Theory/Measure-Theoretic Foundations]] * [[Probability Dilation Theory/Fisher Geometry and Dilation Flows]] == Copyright and licensing == Text and original figures © Howard Richardson. Licensed under the [https://creativecommons.org/licenses/by/4.0/ Creative Commons Attribution 4.0 International License (CC BY 4.0)]. Reuse permitted with attribution. 26hpgbhr1v5zblj35b7t0vvl6ftp9ll 2823780 2823779 2026-08-21T01:42:13Z Howie2024 2995240 /* 5.13 Transition to the geometric question */ Insert section 6. 2823780 wikitext text/x-wiki {{Research project}} '''Research manuscript — Draft Version 1.0''' ''This page develops a standalone research manuscript arising from the [[Probability Dilation Theory]] project. It is a work in progress and should not be regarded as a peer-reviewed publication.'' = Normalized Probability Dilation: A Unified Framework and Its Fisher–Rao Geometry = '''Howard Richardson''' ''Draft Version 1.0 — August 2026'' == Abstract == This paper develops a unified framework for normalized positive transformations of probability distributions, referred to here as '''Probability Dilation Theory (PDT)'''. The central construction consists of applying a positive transformation to a probability state and subsequently renormalizing the result. In finite dimensions this includes diagonal reweighting, :<math> p_i'= \frac{d_i p_i} {\sum_j d_jp_j}, </math> and the matrix transformation :<math> T_M(p)= \frac{Mp} {\mathbf{1}^{\mathsf T}Mp}, </math> for suitable nonnegative matrices <math>M</math>. A corresponding measure-theoretic formulation is :<math> P_D(A)= \frac{\int_A D\,dP} {\int_X D\,dP}. </math> These constructions are compared explicitly with established mathematical structures including change of measure, normalized positive operators, Perron–Frobenius iteration, Markov operators, replicator-type dynamics, and normalized Feynman–Kac transformations. The purpose of the framework is therefore not to claim these established constructions as new, but to investigate their common dilation-normalization structure and the geometry of the resulting probability trajectories. Particular attention is given to the exponential dilation family :<math> p_i(\theta)= \frac{p_i^{(0)}e^{\theta\phi_i}} {\sum_j p_j^{(0)}e^{\theta\phi_j}}. </math> Using the square-root representation of the Fisher–Rao simplex, we establish that, under finite-dimensional strict-positivity assumptions, the image of this exponential-dilation trajectory is contained in a Fisher–Rao Levi-Civita geodesic, up to reparameterization, if and only if the generator <math>\phi</math> assumes at most two distinct values. An explicit Fisher–Rao arclength parameterization is then obtained for the nondegenerate two-level case. The framework provides a common language for normalized probability transformations while separating results inherited from established theory from geometric properties arising from the particular dilation formulation. == 1. Introduction == Probability distributions are frequently transformed by operations having a common mathematical structure: nonnegative weights are modified by a positive transformation and subsequently normalized so that total probability remains unity. Such constructions occur in numerous areas of probability, statistics, dynamical systems, numerical linear algebra, and mathematical physics. The simplest finite-dimensional example takes a probability vector :<math> p=(p_1,\ldots,p_n)^{\mathsf T}, \qquad p_i\geq 0, \qquad \sum_{i=1}^{n}p_i=1, </math> assigns positive weights <math>d_i</math>, and defines :<math> p_i'= \frac{d_i p_i} {\sum_{j=1}^{n}d_jp_j}. </math> The transformation changes the relative probability assigned to individual states while normalization returns the resulting vector to the probability simplex. This paper uses the term '''probability dilation''' for this general transformation-and-normalization structure and examines a hierarchy of related constructions. In finite dimensions, diagonal dilation extends naturally to the action of a nonnegative matrix, :<math> T_M(p)= \frac{Mp} {\mathbf{1}^{\mathsf T}Mp}, </math> whenever the denominator is positive. At the level of probability measures, multiplication by a positive measurable function <math>D</math> gives :<math> P_D(A)= \frac{\displaystyle\int_A D(x)\,dP(x)} {\displaystyle\int_X D(x)\,dP(x)}. </math> These expressions have substantial connections with existing mathematics. Normalized matrix iteration is closely related to the power method and Perron–Frobenius theory; positive weighting of measures belongs to established change-of-measure constructions; stochastic matrices provide the familiar Markov special case; and normalized potential-weighted measures occur in Feynman–Kac models. Accordingly, the objective of PDT as developed here is '''not''' to rename these established mathematical theories or to assert novelty for normalization itself. Instead, the objective is to examine them through the common structural sequence :<math> \text{positive transformation} \longrightarrow \text{normalization} \longrightarrow \text{iteration} \longrightarrow \text{probability dynamics} \longrightarrow \text{geometry}. </math> This viewpoint leads naturally to questions concerning fixed points, convergence, entropy, state-dependent transformations, and the geometry of trajectories on the probability simplex. === 1.1 Exponential dilation === A particularly useful example is obtained from exponential dilation. Given an initial strictly positive probability vector <math>p^{(0)}</math> and a real-valued generator <math>\phi</math>, define :<math> p_i(\theta)= \frac{p_i^{(0)}e^{\theta\phi_i}} {Z(\theta)}, </math> where :<math> Z(\theta)= \sum_j p_j^{(0)}e^{\theta\phi_j}. </math> This is an exponential-family construction and therefore belongs to well-established information geometry. The question considered here is more specific: :''When is this exponential trajectory also a Levi-Civita geodesic of the Fisher–Rao metric?'' The Fisher–Rao geometry of a finite probability simplex admits a square-root representation on a sphere. Under the mapping :<math> p\longmapsto 2(\sqrt{p_1},\ldots,\sqrt{p_n}), </math> Fisher–Rao geodesics correspond to spherical great-circle arcs. This representation permits a direct characterization of exponential dilation trajectories that are simultaneously Fisher–Rao geodesic. === 1.2 Principal geometric result === The principal geometric result developed below is that, for a strictly positive finite probability vector, an exponential dilation trajectory lies on a Fisher–Rao geodesic, up to reparameterization, precisely when its generator assumes no more than two distinct values. The proof reduces the problem to the dimension of the linear span generated by distinct exponential rates and uses a Vandermonde argument for the converse. The resulting two-level trajectory also admits an explicit Fisher–Rao arclength parameterization. At the present draft stage, this characterization is treated conservatively. Its constituent mathematical ingredients are established results from information geometry and linear algebra. The exact characterization developed here remains subject to further literature review and independent mathematical scrutiny. === 1.3 Organization of the paper === The remainder of the paper is organized as follows: * '''Section 2''' introduces the normalized-dilation framework and notation. * '''Section 3''' develops diagonal and matrix formulations. * '''Section 4''' develops the measure-theoretic formulation. * '''Section 5''' compares the framework explicitly with established mathematics. * '''Section 6''' introduces exponential dilation and its information-geometric representation. * '''Section 7''' states and proves the Fisher–Rao geodesic characterization theorem. * '''Section 8''' derives the two-level Fisher–Rao arclength corollary and illustrative examples. * '''Section 9''' discusses limitations, possible extensions, and open problems. * '''Section 10''' summarizes the principal conclusions. == 2. Normalized-Dilation Framework == This section introduces the common mathematical structure used throughout the paper. The essential operation consists of applying a positive transformation to a probability state and then normalizing the transformed object so that it again represents a probability distribution. === 2.1 Probability simplex === For a finite state space with <math>n</math> states, define the probability simplex :<math> \Delta^{n-1} = \left\{ p\in\mathbb{R}^{n}: p_i\geq 0,\; \sum_{i=1}^{n}p_i=1 \right\}. </math> A probability state is represented by a column vector :<math> p= (p_1,\ldots,p_n)^{\mathsf{T}} \in\Delta^{n-1}. </math> Its components satisfy :<math> p_i\geq 0 </math> and :<math> \mathbf{1}^{\mathsf{T}}p=1, </math> where :<math> \mathbf{1} = (1,\ldots,1)^{\mathsf{T}}. </math> The interior of the simplex is :<math> \Delta_{+}^{n-1} = \left\{ p\in\Delta^{n-1}:p_i>0 \text{ for all }i \right\}. </math> The distinction between the simplex and its interior becomes important later when Fisher–Rao geometry is considered. === 2.2 Positive transformations === Let <math>\mathcal{L}</math> denote a transformation acting on probability states such that :<math> p\geq 0 \quad\Longrightarrow\quad \mathcal{L}(p)\geq 0. </math> The transformed object <math>\mathcal{L}(p)</math> need not itself be normalized. Define its total mass by :<math> \mathcal{N}[\mathcal{L}(p)] = \mathbf{1}^{\mathsf{T}}\mathcal{L}(p). </math> Whenever :<math> 0< \mathcal{N}[\mathcal{L}(p)] < \infty, </math> the normalized transformation is defined by :<math> \mathcal{T}_{\mathcal{L}}(p) = \frac{\mathcal{L}(p)} {\mathcal{N}[\mathcal{L}(p)]}. </math> Equivalently, in the finite-dimensional setting, :<math> \mathcal{T}_{\mathcal{L}}(p) = \frac{\mathcal{L}(p)} {\mathbf{1}^{\mathsf{T}}\mathcal{L}(p)}. </math> By construction, :<math> \mathbf{1}^{\mathsf{T}} \mathcal{T}_{\mathcal{L}}(p) = 1, </math> so :<math> \mathcal{T}_{\mathcal{L}}(p) \in \Delta^{n-1}. </math> This positive-transformation-plus-normalization operation is the basic structure referred to in this paper as '''normalized probability dilation'''. === 2.3 Normalization as projectivization === An immediate property of the normalized transformation is invariance under multiplication by a positive scalar. If <math>c>0</math>, then :<math> \frac{c\mathcal{L}(p)} {\mathbf{1}^{\mathsf{T}}c\mathcal{L}(p)} = \frac{\mathcal{L}(p)} {\mathbf{1}^{\mathsf{T}}\mathcal{L}(p)}. </math> Hence :<math> \mathcal{T}_{c\mathcal{L}}(p) = \mathcal{T}_{\mathcal{L}}(p). </math> The normalized transformation therefore depends on the relative components of <math>\mathcal{L}(p)</math>, rather than on its overall positive scale. This projective feature connects normalized dilation with established theories of positive operators and projective dynamics. No claim of novelty is attached to the normalization or projectivization operation itself. === 2.4 Diagonal dilation === Let :<math> D= \operatorname{diag}(d_1,\ldots,d_n), \qquad d_i>0. </math> Applying <math>D</math> to <math>p</math> gives :<math> Dp= (d_1p_1,\ldots,d_np_n)^{\mathsf{T}}. </math> Normalization produces :<math> T_D(p) = \frac{Dp} {\mathbf{1}^{\mathsf{T}}Dp}. </math> Componentwise, :<math> T_D(p)_i = \frac{d_ip_i} {\sum_{j=1}^{n}d_jp_j}. </math> This is the basic finite-dimensional dilation operation from which the broader PDT formulation developed. The factors <math>d_i</math> alter the relative weights of the probability states, while the denominator restores unit total probability. === 2.5 Matrix dilation === The diagonal transformation can be generalized to a nonnegative matrix :<math> M\in\mathbb{R}^{n\times n}, \qquad M_{ij}\geq 0. </math> For any probability vector <math>p</math> satisfying :<math> \mathbf{1}^{\mathsf{T}}Mp>0, </math> define :<math> T_M(p) = \frac{Mp} {\mathbf{1}^{\mathsf{T}}Mp}. </math> The diagonal case is recovered when :<math> M=D. </math> Off-diagonal entries permit components of the input probability vector to contribute to different output components before normalization. The matrix formulation therefore extends independent componentwise reweighting to coupled positive transformations. The mathematical behavior of this construction is closely related to established positive-matrix theory, normalized power iteration, and Perron–Frobenius theory. These relationships are discussed explicitly in Section 5. === 2.6 Measure-theoretic dilation === The same normalization principle extends naturally from finite probability vectors to probability measures. Let <math>(X,\mathcal{F},P)</math> be a probability space, and let :<math> D:X\rightarrow[0,\infty) </math> be measurable with :<math> 0< \int_X D(x)\,dP(x) < \infty. </math> Define a new probability measure <math>P_D</math> by :<math> P_D(A) = \frac{\displaystyle\int_A D(x)\,dP(x)} {\displaystyle\int_X D(x)\,dP(x)}, \qquad A\in\mathcal{F}. </math> Equivalently, the Radon–Nikodym derivative of <math>P_D</math> with respect to <math>P</math> is :<math> \frac{dP_D}{dP} = \frac{D} {\displaystyle\int_X D\,dP}. </math> Thus the finite-dimensional rule :<math> p_i \longmapsto \frac{d_ip_i} {\sum_jd_jp_j} </math> and the measure-theoretic rule :<math> dP \longmapsto \frac{D\,dP} {\int_XD\,dP} </math> share the same normalized positive-reweighting structure. This construction has direct connections with established change-of-measure and weighted-measure theory. The PDT terminology is used here as an organizing framework rather than as a claim that normalized change of measure is itself new. === 2.7 Iterated dilation === A normalized dilation operator can be iterated. Given an initial state :<math> p^{(0)}\in\Delta^{n-1}, </math> define :<math> p^{(k+1)} = \mathcal{T}_{\mathcal{L}}\left(p^{(k)}\right). </math> This generates an orbit :<math> p^{(0)} \longmapsto p^{(1)} \longmapsto p^{(2)} \longmapsto \cdots </math> on the probability simplex. For a fixed matrix <math>M</math>, :<math> p^{(k+1)} = \frac{Mp^{(k)}} {\mathbf{1}^{\mathsf{T}}Mp^{(k)}}. </math> When all required denominators are positive, repeated normalization gives :<math> p^{(k)} = \frac{M^k p^{(0)}} {\mathbf{1}^{\mathsf{T}}M^k p^{(0)}}. </math> The long-term behavior of this iteration is governed in important cases by established spectral and Perron–Frobenius theory. More general formulations may allow the transformation itself to depend on the iteration index or the current probability state, for example :<math> p^{(k+1)} = \frac{M_kp^{(k)}} {\mathbf{1}^{\mathsf{T}}M_kp^{(k)}} </math> or :<math> p^{(k+1)} = \frac{M(p^{(k)})p^{(k)}} {\mathbf{1}^{\mathsf{T}}M(p^{(k)})p^{(k)}}. </math> These state-dependent and iteration-dependent forms are treated as possible extensions rather than necessary components of the basic framework. === 2.8 Hierarchy of normalized dilation === The constructions above can be summarized by the following hierarchy: :'''diagonal reweighting → matrix transformation → positive operator → measure transformation''' At each level the essential operation is: :'''positive transformation + normalization''' The framework is deliberately broad. Its purpose is not to imply that all normalized positive transformations constitute a new mathematical theory, but to provide a common notation and viewpoint from which their dynamics and geometry can be compared. The following sections specialize this framework before examining its relationship to established mathematical constructions. == 3. Finite-Dimensional and Matrix Dilation == This section develops the finite-dimensional forms of normalized probability dilation in greater detail. The emphasis is on the relationship between diagonal reweighting and nonnegative matrix transformations, together with the basic structural properties required later in the paper. === 3.1 Finite probability states === Let :<math> p=(p_1,\ldots,p_n)^{\mathsf{T}} \in\Delta^{n-1}. </math> A positive weighting vector is written :<math> d=(d_1,\ldots,d_n)^{\mathsf{T}}, \qquad d_i>0. </math> The associated diagonal matrix is :<math> D= \operatorname{diag}(d_1,\ldots,d_n). </math> Applying the weighting gives :<math> Dp= (d_1p_1,\ldots,d_np_n)^{\mathsf{T}}. </math> Its total mass is :<math> Z(p,D) = \mathbf{1}^{\mathsf{T}}Dp = \sum_{i=1}^{n}d_ip_i. </math> Since <math>d_i>0</math> and <math>p</math> is a probability vector, :<math> Z(p,D)>0. </math> The normalized diagonal dilation operator is therefore :<math> T_D(p) = \frac{Dp}{Z(p,D)}. </math> Equivalently, :<math> T_D(p)_i = \frac{d_ip_i} {\sum_{j=1}^{n}d_jp_j}. </math> === 3.2 Relative probability transformation === Diagonal dilation has a simple effect on probability ratios. For any states <math>i</math> and <math>j</math> with <math>p_i>0</math> and <math>p_j>0</math>, :<math> \frac{T_D(p)_i}{T_D(p)_j} = \frac{d_i}{d_j} \frac{p_i}{p_j}. </math> Thus normalization does not alter the relative dilation introduced by the factors <math>d_i</math> and <math>d_j</math>. If :<math> d_i>d_j, </math> then the odds of state <math>i</math> relative to state <math>j</math> increase by the factor :<math> \frac{d_i}{d_j}. </math> This ratio form makes clear that diagonal dilation is fundamentally a relative reweighting operation. === 3.3 Scale invariance === Multiplying every dilation factor by the same positive constant does not change the normalized state. Let :<math> c>0. </math> Then :<math> T_{cD}(p) = \frac{cDp} {\mathbf{1}^{\mathsf{T}}cDp} = \frac{Dp} {\mathbf{1}^{\mathsf{T}}Dp} = T_D(p). </math> Therefore only the relative values of the dilation factors affect the transformed probability distribution. This scale invariance is a basic projective property of normalized positive transformations. === 3.4 Repeated diagonal dilation === Suppose the same diagonal operator <math>D</math> is applied repeatedly. Starting from <math>p^{(0)}</math>, define :<math> p^{(k+1)} = T_D(p^{(k)}). </math> Then :<math> p^{(k)} = \frac{D^k p^{(0)}} {\mathbf{1}^{\mathsf{T}}D^k p^{(0)}}. </math> Since :<math> D^k = \operatorname{diag}(d_1^k,\ldots,d_n^k), </math> the individual components are :<math> p_i^{(k)} = \frac{d_i^k p_i^{(0)}} {\sum_{j=1}^{n}d_j^k p_j^{(0)}}. </math> Consequently, for two initially positive components, :<math> \frac{p_i^{(k)}}{p_j^{(k)}} = \left(\frac{d_i}{d_j}\right)^k \frac{p_i^{(0)}}{p_j^{(0)}}. </math> This expression describes the concentration mechanism directly. If one dilation factor is strictly larger than all others and its corresponding initial probability is positive, repeated dilation concentrates probability on that state. If several states share the maximal dilation factor, probability concentrates on that maximal set while preserving the initial relative proportions within that set. This behavior is a direct consequence of normalized repeated weighting and is not specific to PDT terminology. === 3.5 General nonnegative matrix transformation === Let :<math> M=(M_{ij}) \in\mathbb{R}^{n\times n}, \qquad M_{ij}\geq0. </math> For <math>p\in\Delta^{n-1}</math>, define :<math> q=Mp. </math> Because <math>M</math> and <math>p</math> are nonnegative, :<math> q_i\geq0. </math> Whenever :<math> \mathbf{1}^{\mathsf{T}}Mp>0, </math> the normalized matrix dilation operator is :<math> T_M(p) = \frac{Mp} {\mathbf{1}^{\mathsf{T}}Mp}. </math> Its components are :<math> T_M(p)_i = \frac{\sum_{j=1}^{n}M_{ij}p_j} {\sum_{r=1}^{n}\sum_{j=1}^{n}M_{rj}p_j}. </math> By construction, :<math> \sum_{i=1}^{n}T_M(p)_i=1. </math> Hence :<math> T_M(p)\in\Delta^{n-1}. </math> === 3.6 Diagonal dilation as a special case === If :<math> M=D = \operatorname{diag}(d_1,\ldots,d_n), </math> then :<math> Mp=Dp, </math> and therefore :<math> T_M(p)=T_D(p). </math> Diagonal dilation is thus a special case of normalized matrix dilation. The distinction is structural. For a diagonal matrix, each output component depends only on the corresponding input component: :<math> (Dp)_i=d_ip_i. </math> For a general matrix, :<math> (Mp)_i = \sum_{j=1}^{n}M_{ij}p_j, </math> so multiple input states may contribute to a single output state before normalization. This permits coupled probability evolution. === 3.7 When normalization is unnecessary === There is an important special case. Suppose <math>M</math> satisfies :<math> \mathbf{1}^{\mathsf{T}}M = \mathbf{1}^{\mathsf{T}}. </math> Then for every probability vector <math>p</math>, :<math> \mathbf{1}^{\mathsf{T}}Mp = \mathbf{1}^{\mathsf{T}}p = 1. </math> Consequently, :<math> T_M(p)=Mp. </math> With the column-vector convention used in this paper, the condition :<math> \mathbf{1}^{\mathsf{T}}M = \mathbf{1}^{\mathsf{T}} </math> means that the columns of <math>M</math> sum to one. Thus an ordinary probability-preserving linear transition is contained as a special case of the normalized matrix framework. When <math>M</math> does not preserve total mass, normalization supplies the additional step required to return <math>Mp</math> to the simplex. === 3.8 Fixed points and eigenvectors === Suppose <math>p^{*}</math> is a fixed point of the normalized matrix operator: :<math> T_M(p^{*})=p^{*}. </math> Then :<math> \frac{Mp^{*}} {\mathbf{1}^{\mathsf{T}}Mp^{*}} = p^{*}. </math> Multiplying by the denominator gives :<math> Mp^{*} = \lambda p^{*}, </math> where :<math> \lambda = \mathbf{1}^{\mathsf{T}}Mp^{*}. </math> Therefore every fixed point of the normalized matrix transformation is a nonnegative eigenvector of <math>M</math>, normalized to have unit total mass. Conversely, if <math>v\geq0</math> is a nonzero eigenvector satisfying :<math> Mv=\lambda v, \qquad \lambda>0, </math> then :<math> p^{*} = \frac{v} {\mathbf{1}^{\mathsf{T}}v} </math> is a fixed point of <math>T_M</math>. Thus normalized fixed points and positive eigenvectors are directly related. === 3.9 Repeated matrix dilation === For a fixed nonnegative matrix <math>M</math>, define :<math> p^{(k+1)} = T_M(p^{(k)}). </math> Whenever the required denominators remain positive, :<math> p^{(k)} = \frac{M^k p^{(0)}} {\mathbf{1}^{\mathsf{T}}M^k p^{(0)}}. </math> This identity follows because the scalar normalization introduced at each intermediate step cancels under the next normalization. The iteration is therefore closely related to normalized power iteration. Under suitable positivity or primitivity assumptions, Perron–Frobenius theory describes the dominant eigenvalue and positive eigenvector governing the long-term behavior. Accordingly, convergence of the fixed-matrix case should be understood primarily through established positive-matrix and spectral theory rather than as a separate PDT convergence mechanism. === 3.10 Primitive positive matrices === A particularly important case occurs when <math>M</math> is primitive; that is, some positive integer power of <math>M</math> has strictly positive entries. Perron–Frobenius theory then provides a dominant real eigenvalue :<math> \rho(M)>0 </math> with a corresponding strictly positive eigenvector <math>v</math>. After normalization, :<math> p^{*} = \frac{v} {\mathbf{1}^{\mathsf{T}}v}, </math> this eigenvector gives the distinguished interior fixed point of the normalized matrix transformation. For suitable initial probability vectors, :<math> T_M^{k}(p^{(0)}) </math> converges toward <math>p^{*}</math>. This convergence is an established consequence of Perron–Frobenius theory and normalized power iteration. Its role here is to locate matrix dilation within known mathematics. === 3.11 Interpretation of off-diagonal terms === The off-diagonal entries of <math>M</math> distinguish matrix dilation from independent diagonal reweighting. For :<math> i\neq j, </math> a term :<math> M_{ij}p_j </math> represents a contribution from input state <math>j</math> to output component <math>i</math> before normalization. The matrix therefore combines two operations: * positive redistribution or coupling through <math>M</math>; * restoration of unit total probability through normalization. This interpretation is useful for organizing the framework, but the underlying linear transformation remains standard matrix mathematics. === 3.12 Scope of the matrix formulation === The matrix formulation substantially enlarges the class of transformations expressible within the normalized-dilation notation, but that enlargement should not be confused with mathematical novelty. For a fixed matrix <math>M</math>, the central objects :<math> Mp, \qquad M^kp, \qquad \rho(M), </math> and the associated eigenvectors and convergence properties belong to established linear algebra and positive-operator theory. The role of the PDT framework is to place diagonal reweighting, matrix transformation, iteration, and later measure-theoretic and geometric constructions within a common normalized-probability notation. This distinction between '''framework''' and '''new mathematical result''' will be maintained throughout the paper. == 4. Measure-Theoretic Dilation == The finite-dimensional dilation rule extends naturally to probability measures. In this setting, componentwise multiplication by positive weights is replaced by multiplication of a probability measure by a nonnegative measurable function followed by normalization. This formulation places finite probability dilation within the standard language of measure theory and makes its relationship to change of measure explicit. === 4.1 Probability-space formulation === Let :<math> (X,\mathcal{F},P) </math> be a probability space. Let :<math> D:X\rightarrow[0,\infty) </math> be a measurable function satisfying :<math> 0< \int_X D(x)\,dP(x) < \infty. </math> Define the normalization factor :<math> Z(P,D) = \int_X D(x)\,dP(x). </math> For every measurable set :<math> A\in\mathcal{F}, </math> define :<math> P_D(A) = \frac{\displaystyle\int_A D(x)\,dP(x)} {Z(P,D)}. </math> Equivalently, :<math> P_D(A) = \frac{\displaystyle\int_A D(x)\,dP(x)} {\displaystyle\int_X D(x)\,dP(x)}. </math> The function <math>D</math> acts as a nonnegative weighting or dilation field over the probability space. === 4.2 Normalization === The transformed measure has total mass one because :<math> P_D(X) = \frac{\displaystyle\int_X D(x)\,dP(x)} {\displaystyle\int_X D(x)\,dP(x)} = 1. </math> Also, because <math>D</math> is nonnegative, :<math> P_D(A)\geq0 </math> for every <math>A\in\mathcal{F}</math>. Countable additivity follows from the countable additivity of integration with respect to <math>P</math>. Therefore <math>P_D</math> is a probability measure. === 4.3 Radon–Nikodym representation === The transformed measure <math>P_D</math> is absolutely continuous with respect to <math>P</math>. Its Radon–Nikodym derivative is :<math> \frac{dP_D}{dP}(x) = \frac{D(x)} {\displaystyle\int_X D(y)\,dP(y)}. </math> Thus normalized measure dilation can be written formally as :<math> dP_D(x) = \frac{D(x)\,dP(x)} {\displaystyle\int_X D(y)\,dP(y)}. </math> This expression makes clear that the construction is a normalized change of measure. The Radon–Nikodym framework is established measure theory. The terminology of dilation is used here to emphasize the common transformation-and-normalization structure shared with the finite-dimensional formulation. === 4.4 Scale invariance === As in the finite-dimensional case, multiplication of the dilation field by a positive constant does not change the normalized measure. Let :<math> c>0. </math> Then :<math> P_{cD}(A) = \frac{\displaystyle\int_A cD\,dP} {\displaystyle\int_X cD\,dP}. </math> The common factor cancels, giving :<math> P_{cD}(A)=P_D(A). </math> Hence the transformed probability measure depends only on the relative values of the dilation field <math>D</math>, not on its overall positive scale. === 4.5 Finite probability spaces as a special case === Consider a finite state space :<math> X=\{1,\ldots,n\}. </math> Let :<math> P(\{i\})=p_i </math> and define :<math> D(i)=d_i. </math> Then :<math> \int_X D\,dP = \sum_{j=1}^{n}d_jp_j. </math> For the singleton event <math>\{i\}</math>, :<math> P_D(\{i\}) = \frac{d_ip_i} {\sum_{j=1}^{n}d_jp_j}. </math> Thus the finite diagonal dilation rule :<math> p_i' = \frac{d_ip_i} {\sum_jd_jp_j} </math> is recovered exactly from the measure-theoretic construction. The discrete and measure-theoretic formulations are therefore instances of the same normalized positive-reweighting operation. === 4.6 Expectations under dilation === Let :<math> f:X\rightarrow\mathbb{R} </math> be measurable and integrable with respect to the transformed measure. Then :<math> \mathbb{E}_{P_D}[f] = \int_X f(x)\,dP_D(x). </math> Using the Radon–Nikodym representation, :<math> \mathbb{E}_{P_D}[f] = \frac{\displaystyle\int_X f(x)D(x)\,dP(x)} {\displaystyle\int_X D(x)\,dP(x)}. </math> Equivalently, :<math> \mathbb{E}_{P_D}[f] = \frac{\mathbb{E}_{P}[fD]} {\mathbb{E}_{P}[D]}, </math> provided the required expectations exist. This identity is a standard weighted-expectation formula and will later be useful for exponential dilation. === 4.7 Composition of dilation fields === Suppose a first dilation field <math>D_1</math> transforms <math>P</math> into <math>P_{D_1}</math>, and a second field <math>D_2</math> is then applied. The first transformation gives :<math> dP_{D_1} = \frac{D_1\,dP} {\int_XD_1\,dP}. </math> Applying <math>D_2</math> gives :<math> d(P_{D_1})_{D_2} = \frac{D_2\,dP_{D_1}} {\int_XD_2\,dP_{D_1}}. </math> Substituting the first transformation and simplifying yields :<math> d(P_{D_1})_{D_2} = \frac{D_1D_2\,dP} {\int_XD_1D_2\,dP}, </math> whenever the required integrals are finite and positive. Therefore :<math> (P_{D_1})_{D_2} = P_{D_1D_2}. </math> Sequential scalar dilation fields thus combine multiplicatively before normalization. This composition property is the measure-theoretic analogue of repeated diagonal reweighting. === 4.8 Iterated fixed dilation === If the same dilation field <math>D</math> is applied repeatedly, then after <math>k</math> iterations, :<math> dP^{(k)} = \frac{D^k\,dP^{(0)}} {\displaystyle\int_XD^k\,dP^{(0)}}. </math> Equivalently, for any measurable event <math>A</math>, :<math> P^{(k)}(A) = \frac{\displaystyle\int_A D(x)^k\,dP^{(0)}(x)} {\displaystyle\int_X D(x)^k\,dP^{(0)}(x)}. </math> This is the direct measure-theoretic counterpart of :<math> p_i^{(k)} = \frac{d_i^kp_i^{(0)}} {\sum_jd_j^kp_j^{(0)}}. </math> Regions where <math>D</math> is relatively large receive increasing relative weight under repeated application. The precise limiting behavior depends on the structure of <math>D</math> and the initial measure. === 4.9 Exponential dilation fields === A particularly important family is obtained by choosing :<math> D_{\theta}(x) = e^{\theta\phi(x)}, </math> where <math>\phi:X\rightarrow\mathbb{R}</math> is measurable and <math>\theta</math> is a real parameter for which the normalization integral is finite. Define :<math> Z(\theta) = \int_X e^{\theta\phi(x)}\,dP_0(x). </math> Then :<math> dP_{\theta}(x) = \frac{e^{\theta\phi(x)}} {Z(\theta)} dP_0(x). </math> In a finite state space this becomes :<math> p_i(\theta) = \frac{p_i^{(0)}e^{\theta\phi_i}} {\sum_jp_j^{(0)}e^{\theta\phi_j}}. </math> This is a standard exponential tilting construction and is closely related to exponential families, cumulant-generating functions, and information geometry. Its importance for the present paper is that it provides a continuous one-parameter dilation trajectory whose Fisher–Rao geometry can be studied explicitly. === 4.10 Infinitesimal evolution of exponential dilation === For the finite-dimensional exponential family, :<math> p_i(\theta) = \frac{p_i^{(0)}e^{\theta\phi_i}} {Z(\theta)}, </math> differentiate with respect to <math>\theta</math>. The logarithmic derivative is :<math> \frac{d}{d\theta}\log p_i(\theta) = \phi_i - \frac{d}{d\theta}\log Z(\theta). </math> Since :<math> \frac{d}{d\theta}\log Z(\theta) = \sum_jp_j(\theta)\phi_j, </math> define :<math> \overline{\phi}_{\theta} = \sum_jp_j(\theta)\phi_j. </math> Then :<math> \frac{dp_i}{d\theta} = p_i(\theta) \left( \phi_i-\overline{\phi}_{\theta} \right). </math> This equation has the form of a replicator-type evolution equation with a fixed state-dependent generator <math>\phi_i</math>. The relationship to established replicator dynamics is discussed in Section 5. === 4.11 Conservation of total probability === Summing the infinitesimal evolution equation gives :<math> \sum_i \frac{dp_i}{d\theta} = \sum_i p_i(\theta) \left( \phi_i-\overline{\phi}_{\theta} \right). </math> Since :<math> \sum_ip_i(\theta)\phi_i = \overline{\phi}_{\theta} </math> and :<math> \sum_ip_i(\theta)=1, </math> it follows that :<math> \sum_i \frac{dp_i}{d\theta} = 0. </math> Thus the vector field is tangent to the probability simplex. Normalization is therefore reflected infinitesimally by conservation of total probability. === 4.12 Scope of the measure-theoretic formulation === The measure-theoretic formulation shows that normalized probability dilation is not restricted to finite vectors or matrices. The same structural operation appears as :'''weight → normalize → obtain a new probability measure''' and, for exponential fields, :'''exponential weight → normalize → continuous probability trajectory'''. These constructions overlap directly with established change-of-measure theory, exponential tilting, weighted probability measures, and related probabilistic methods. Their role in the present framework is to connect the finite dilation notation to continuous probability spaces and to provide the bridge to the information-geometric analysis developed later in the paper. The next section therefore compares the normalized-dilation framework systematically with established mathematical constructions before any additional geometric results are introduced. == 5. Relation to Established Mathematics == The normalized-dilation framework overlaps with several established areas of mathematics. This section identifies those relationships explicitly. The purpose is twofold: first, to place the notation used in this paper within its appropriate mathematical context; and second, to distinguish established constructions from the particular synthesis and geometric questions developed later in the paper. The term '''probability dilation''' is therefore used as an organizing description of a transformation-and-normalization structure, not as a claim that the underlying operations of reweighting, normalization, positive matrix iteration, or change of measure are themselves new. === 5.1 Weighted probability and change of measure === The measure-theoretic transformation :<math> dP_D = \frac{D\,dP} {\int_XD\,dP} </math> is a standard normalized change of measure. Its Radon–Nikodym derivative with respect to <math>P</math> is :<math> \frac{dP_D}{dP} = \frac{D} {\int_XD\,dP}. </math> Consequently, for an integrable observable <math>f</math>, :<math> \mathbb{E}_{P_D}[f] = \frac{\mathbb{E}_{P}[fD]} {\mathbb{E}_{P}[D]}. </math> These expressions belong to established measure-theoretic probability. Within the present framework, their role is to show that finite diagonal dilation and continuous weighted change of measure share the same normalized reweighting structure. === 5.2 Bayesian reweighting === A closely related normalization structure occurs in Bayesian inference. If <math>\pi(x)</math> is a prior density and <math>L(y\mid x)</math> is a likelihood for observed data <math>y</math>, Bayes' rule gives :<math> \pi(x\mid y) = \frac{L(y\mid x)\pi(x)} {\int L(y\mid z)\pi(z)\,dz}, </math> when the denominator is finite and nonzero. Structurally, this has the same form as :<math> dP_D = \frac{D\,dP} {\int D\,dP}, </math> with the likelihood acting as a positive weighting function. The statistical interpretation is different: Bayesian updating has a specific inferential meaning associated with conditioning on data. The comparison here concerns only the common mathematical normalization structure. === 5.3 Importance weighting and exponential tilting === Weighted probability measures also arise in importance sampling, exponential tilting, large-deviation methods, and related statistical constructions. For a generator <math>\phi</math>, exponential tilting takes the form :<math> dP_{\theta}(x) = \frac{e^{\theta\phi(x)}} {Z(\theta)} dP_0(x), </math> where :<math> Z(\theta) = \int_Xe^{\theta\phi(x)}\,dP_0(x). </math> This is an established exponential-family construction. The corresponding finite-dimensional expression, :<math> p_i(\theta) = \frac{p_i^{(0)}e^{\theta\phi_i}} {\sum_jp_j^{(0)}e^{\theta\phi_j}}, </math> will be the principal object of the Fisher–Rao analysis in Sections 6 through 8. The geometric analysis developed later concerns this established exponential-tilt family under a particular question about coincidence of information-geometric and Fisher–Rao geodesics. === 5.4 Positive matrices and Perron–Frobenius theory === For a fixed nonnegative matrix <math>M</math>, the normalized transformation :<math> T_M(p) = \frac{Mp} {\mathbf{1}^{\mathsf{T}}Mp} </math> is closely related to classical positive-matrix theory. If <math>M</math> is primitive, Perron–Frobenius theory provides a dominant positive eigenvalue :<math> \rho(M)>0 </math> and a corresponding strictly positive eigenvector. Repeated normalized iteration, :<math> p^{(k)} = \frac{M^kp^{(0)}} {\mathbf{1}^{\mathsf{T}}M^kp^{(0)}}, </math> is therefore closely related to normalized power iteration. Under appropriate hypotheses, its asymptotic direction is governed by the Perron eigenvector. These spectral and convergence results are established mathematics and are not presented here as new consequences of PDT. === 5.5 Markov operators === Suppose <math>M</math> is nonnegative and satisfies :<math> \mathbf{1}^{\mathsf{T}}M = \mathbf{1}^{\mathsf{T}}. </math> With the column-vector convention used in this paper, :<math> \mathbf{1}^{\mathsf{T}}Mp = 1 </math> for every probability vector <math>p</math>. Thus :<math> T_M(p)=Mp. </math> In this mass-preserving case, the normalization step is unnecessary. Accordingly, ordinary finite-state Markov evolution is contained as a special mass-preserving case of the broader positive-transformation framework. This observation is structural. It does not imply that normalized dilation provides a replacement for Markov-chain theory. === 5.6 Replicator-type dynamics === The exponential dilation family satisfies :<math> \frac{dp_i}{d\theta} = p_i \left( \phi_i-\overline{\phi}_{\theta} \right), </math> where :<math> \overline{\phi}_{\theta} = \sum_jp_j(\theta)\phi_j. </math> The standard replicator equation has the form :<math> \frac{dp_i}{dt} = p_i \left( f_i(p)-\overline{f}(p) \right). </math> Thus exponential dilation with fixed generator values <math>\phi_i</math> has the same algebraic structure as a replicator equation with state-independent fitness values. The mean-subtraction term guarantees :<math> \sum_i\frac{dp_i}{d\theta}=0, </math> so the flow remains tangent to the probability simplex. Replicator dynamics and their geometric interpretations are established subjects. The present paper uses this connection to relate normalized dilation to known simplex dynamics. === 5.7 Fisher–Rao and Shahshahani geometry === The interior of the probability simplex carries the Fisher–Rao metric. For tangent vectors <math>u</math> and <math>v</math> satisfying :<math> \sum_i u_i = \sum_i v_i = 0, </math> the finite-dimensional Fisher–Rao metric can be written as :<math> g_p(u,v) = \sum_{i=1}^{n} \frac{u_iv_i}{p_i}. </math> Closely related forms of this metric appear in evolutionary dynamics under the name Shahshahani metric. The square-root mapping :<math> \Psi(p) = 2(\sqrt{p_1},\ldots,\sqrt{p_n}) </math> satisfies :<math> \sum_i\Psi_i(p)^2=4. </math> Thus the simplex interior is represented in the positive orthant of a sphere of radius <math>2</math>. Under this representation, the Fisher–Rao metric becomes the metric induced by the ambient Euclidean space, and Levi-Civita Fisher–Rao geodesics correspond locally to great-circle arcs. This established spherical representation will be the principal geometric tool used in Section 7. === 5.8 Exponential families and the e-connection === The exponential dilation path :<math> p_i(\theta) = \frac{p_i^{(0)}e^{\theta\phi_i}} {Z(\theta)} </math> is a one-parameter exponential family. Taking logarithms gives :<math> \log p_i(\theta) = \log p_i^{(0)} + \theta\phi_i - \log Z(\theta). </math> The natural parameter varies linearly with <math>\theta</math>. In information geometry, exponential families are naturally associated with the exponential, or '''e''', connection. A path linear in natural parameters is an e-geodesic. This notion of geodesic is distinct from a Levi-Civita geodesic of the Fisher–Rao metric. Consequently, an exponential dilation trajectory may be straight with respect to the e-connection while being curved with respect to the Fisher–Rao Levi-Civita connection. This distinction is central to the geometric question investigated later in the paper. === 5.9 Fisher information and variance === For the exponential dilation family, :<math> \frac{d}{d\theta} \log p_i(\theta) = \phi_i-\overline{\phi}_{\theta}. </math> The Fisher information associated with the parameter <math>\theta</math> is therefore :<math> I(\theta) = \sum_i p_i(\theta) \left( \phi_i-\overline{\phi}_{\theta} \right)^2. </math> Hence :<math> I(\theta) = \operatorname{Var}_{p(\theta)}(\phi). </math> The Fisher–Rao speed of the trajectory is :<math> v_{\mathrm{FR}}(\theta) = \sqrt{I(\theta)} = \sqrt{\operatorname{Var}_{p(\theta)}(\phi)}. </math> This variance identity is a standard property of one-parameter exponential families. It will be used later when deriving the arclength parameterization of the two-level case. === 5.10 Normalized Feynman–Kac transformations === Another closely related structure occurs in Feynman–Kac models. At an abstract level, a positive measure may first be weighted by a nonnegative potential and then propagated through a positive or Markov operator, followed by normalization. Schematically, such an evolution has the form :'''weight → propagate → normalize'''. The matrix expression :<math> T_M(p) = \frac{Mp} {\mathbf{1}^{\mathsf{T}}Mp} </math> and the measure expression :<math> dP_D = \frac{D\,dP} {\int D\,dP} </math> therefore have structural analogues within normalized Feynman–Kac theory. The exact interpretation and assumptions differ among applications. The comparison made here is structural rather than an assertion of equivalence between PDT and Feynman–Kac theory. === 5.11 Projective dynamics === Because normalized dilation is invariant under multiplication of the unnormalized transformed state by a positive scalar, it naturally has a projective character. For example, :<math> T_{cM}(p) = T_M(p) </math> for every <math>c>0</math> for which the transformation is defined. Thus the normalized state depends on the ray determined by <math>Mp</math>, rather than its magnitude. Positive projective geometry and projective metrics, including Hilbert-type metrics, are established tools in the study of positive operators and their contraction properties. These methods provide natural mathematical machinery for analyzing normalized positive transformations, particularly in convergence problems. === 5.12 What the PDT framework contributes === The preceding comparisons show that the principal operations used in normalized probability dilation have substantial established precedents. The proposed contribution of the framework is therefore not the isolated operation :'''multiply or transform, then normalize'''. Rather, the framework provides a common notation and organizational viewpoint connecting: * finite diagonal reweighting; * nonnegative matrix transformations; * normalized positive iteration; * weighted change of measure; * exponential probability trajectories; * simplex dynamics; * information geometry. This synthesis is useful only insofar as it clarifies relationships, generates mathematically precise questions, or produces results that are not merely restatements of known theory. For that reason, the remainder of this paper concentrates on a narrower geometric problem. === 5.13 Transition to the geometric question === Every exponential dilation trajectory of the form :<math> p_i(\theta) = \frac{p_i^{(0)}e^{\theta\phi_i}} {Z(\theta)} </math> is an exponential-family trajectory and hence is naturally straight with respect to the e-connection. It does not follow that the same trajectory is a Levi-Civita geodesic of the Fisher–Rao metric. This leads to the central question considered in the remainder of the paper: :''Under what conditions is an exponential dilation trajectory simultaneously an e-geodesic and, up to reparameterization, a Fisher–Rao Levi-Civita geodesic?'' The next section develops the geometric representation required to answer this question. == 6. Exponential Dilation and Fisher–Rao Geometry == This section develops the geometric representation of exponential dilation required for the main characterization theorem. The central object is the one-parameter exponential family :<math> p_i(\theta) = \frac{p_i^{(0)}e^{\theta\phi_i}} {Z(\theta)}, </math> where :<math> Z(\theta) = \sum_{j=1}^{n}p_j^{(0)}e^{\theta\phi_j}. </math> Throughout this section, assume :<math> p_i^{(0)}>0 </math> for all <math>i</math>, and let :<math> \phi=(\phi_1,\ldots,\phi_n) </math> be a real-valued generator. === 6.1 Exponential dilation trajectory === Let :<math> p^{(0)} \in \Delta_{+}^{n-1}. </math> For a real parameter <math>\theta</math>, define :<math> p_i(\theta) = \frac{p_i^{(0)}e^{\theta\phi_i}} {\sum_{j=1}^{n}p_j^{(0)}e^{\theta\phi_j}}. </math> Since every initial component is strictly positive and the exponential function is positive, :<math> p_i(\theta)>0 </math> for every finite <math>\theta</math>. Therefore the trajectory remains in the interior of the probability simplex. The normalization factor satisfies :<math> Z(\theta)>0. </math> Hence the trajectory is well defined for every finite <math>\theta</math> in the finite-dimensional setting. === 6.2 Logarithmic form === Taking logarithms gives :<math> \log p_i(\theta) = \log p_i^{(0)} + \theta\phi_i - \log Z(\theta). </math> Differentiating with respect to <math>\theta</math> gives :<math> \frac{d}{d\theta}\log p_i(\theta) = \phi_i - \frac{d}{d\theta}\log Z(\theta). </math> Now :<math> \frac{dZ}{d\theta} = \sum_j p_j^{(0)} \phi_j e^{\theta\phi_j}. </math> Therefore :<math> \frac{d}{d\theta}\log Z(\theta) = \sum_jp_j(\theta)\phi_j. </math> Define the expectation of the generator by :<math> \mu(\theta) = \mathbb{E}_{p(\theta)}[\phi] = \sum_jp_j(\theta)\phi_j. </math> Then :<math> \frac{d}{d\theta}\log p_i(\theta) = \phi_i-\mu(\theta). </math> === 6.3 Tangent vector === Multiplying the logarithmic derivative by <math>p_i(\theta)</math> gives :<math> \frac{dp_i}{d\theta} = p_i(\theta) \left( \phi_i-\mu(\theta) \right). </math> Define the centered generator :<math> h_i(\theta) = \phi_i-\mu(\theta). </math> Then :<math> \frac{dp_i}{d\theta} = p_i(\theta)h_i(\theta). </math> Because :<math> \sum_i p_i(\theta)h_i(\theta) = 0, </math> we obtain :<math> \sum_i \frac{dp_i}{d\theta} = 0. </math> Thus the velocity vector is tangent to the probability simplex. === 6.4 Fisher information and speed === The Fisher–Rao metric on the simplex interior is :<math> g_p(u,v) = \sum_i \frac{u_iv_i}{p_i}, </math> for tangent vectors <math>u</math> and <math>v</math>. For the exponential dilation trajectory, :<math> \frac{dp_i}{d\theta} = p_i h_i. </math> Its squared Fisher–Rao speed is therefore :<math> v_{\mathrm{FR}}(\theta)^2 = \sum_i \frac{1}{p_i} \left( \frac{dp_i}{d\theta} \right)^2. </math> Substitution gives :<math> v_{\mathrm{FR}}(\theta)^2 = \sum_i p_i(\theta)h_i(\theta)^2. </math> Hence :<math> v_{\mathrm{FR}}(\theta)^2 = \operatorname{Var}_{p(\theta)}(\phi). </math> Therefore :<math> v_{\mathrm{FR}}(\theta) = \sqrt{ \operatorname{Var}_{p(\theta)}(\phi) }. </math> This is the standard Fisher-information identity for a one-parameter exponential family. === 6.5 Square-root representation === Define the square-root map :<math> \Psi: \Delta_{+}^{n-1} \rightarrow \mathbb{R}^{n} </math> by :<math> \Psi(p) = 2(\sqrt{p_1},\ldots,\sqrt{p_n}). </math> Write :<math> q(\theta) = \Psi(p(\theta)). </math> Then :<math> q_i(\theta) = 2\sqrt{p_i(\theta)}. </math> Because :<math> \sum_i p_i(\theta)=1, </math> we have :<math> \sum_iq_i(\theta)^2 = 4. </math> Thus :<math> q(\theta) </math> lies on the positive orthant of the sphere of radius <math>2</math> in <math>\mathbb{R}^{n}</math>. === 6.6 Isometry of the square-root representation === Let <math>u</math> be a tangent vector to the simplex. Differentiating :<math> q_i=2\sqrt{p_i} </math> gives :<math> dq_i = \frac{dp_i}{\sqrt{p_i}}. </math> Therefore the Euclidean squared length of the corresponding tangent displacement on the sphere is :<math> \sum_i(dq_i)^2 = \sum_i \frac{(dp_i)^2}{p_i}. </math> This is precisely the Fisher–Rao line element. Thus the square-root map identifies the Fisher–Rao metric on the simplex interior with the Euclidean metric induced on the positive orthant of the radius-<math>2</math> sphere. Consequently, Fisher–Rao Levi-Civita geodesics correspond locally to great-circle arcs on this sphere. === 6.7 Square-root form of exponential dilation === Substituting the exponential dilation family into the square-root representation gives :<math> q_i(\theta) = \frac{ 2\sqrt{p_i^{(0)}}e^{\theta\phi_i/2} } {\sqrt{Z(\theta)}}. </math> Define the unnormalized square-root vector :<math> r_i(\theta) = \sqrt{p_i^{(0)}}e^{\theta\phi_i/2}. </math> Then :<math> q(\theta) = \frac{2r(\theta)} {\sqrt{Z(\theta)}}. </math> Also, :<math> \|r(\theta)\|^2 = Z(\theta). </math> Hence :<math> q(\theta) = \frac{2r(\theta)} {\|r(\theta)\|}. </math> The normalized square-root trajectory and the unnormalized vector <math>r(\theta)</math> therefore determine the same ray through the origin. This observation allows the Fisher–Rao geodesic question to be reduced to a linear-subspace question in <math>\mathbb{R}^{n}</math>. === 6.8 Distinct generator levels === Suppose the generator <math>\phi</math> assumes exactly <math>m</math> distinct values :<math> a_1,\ldots,a_m. </math> Define the level sets :<math> A_{\ell} = \{i:\phi_i=a_{\ell}\}, </math> for :<math> \ell=1,\ldots,m. </math> For each level, define a vector <math>u_{\ell}</math> by :<math> (u_{\ell})_i = \begin{cases} \sqrt{p_i^{(0)}} & \text{if } i\in A_{\ell},\\ 0 & \text{otherwise}. \end{cases} </math> Because the level sets are disjoint, the vectors :<math> u_1,\ldots,u_m </math> have disjoint supports and are therefore mutually orthogonal. In particular, they are linearly independent. The unnormalized square-root trajectory can now be written as :<math> r(\theta) = \sum_{\ell=1}^{m} e^{a_{\ell}\theta/2} u_{\ell}. </math> This decomposition is central to the geometric characterization developed in the next section. === 6.9 The one-level case === If <math>m=1</math>, then every component of <math>\phi</math> has the same value <math>a</math>. Thus :<math> r(\theta) = e^{a\theta/2}u_1. </math> After normalization, the scalar exponential factor cancels. Therefore :<math> p(\theta)=p^{(0)} </math> for all <math>\theta</math>. The trajectory is constant. This is the degenerate case of exponential dilation. === 6.10 The two-level case === Suppose <math>\phi</math> assumes exactly two distinct values :<math> a </math> and :<math> b, </math> with <math>a\neq b</math>. Then :<math> r(\theta) = e^{a\theta/2}u + e^{b\theta/2}v, </math> where <math>u</math> and <math>v</math> are nonzero orthogonal vectors associated with the two generator levels. Consequently, :<math> r(\theta) \in \operatorname{span}\{u,v\} </math> for every <math>\theta</math>. Since <math>q(\theta)</math> is obtained from <math>r(\theta)</math> by positive scalar normalization, :<math> q(\theta) \in \operatorname{span}\{u,v\} </math> as well. The intersection of a two-dimensional linear subspace through the origin with the radius-<math>2</math> sphere is a great circle. Thus the two-level case naturally produces a Fisher–Rao great-circle trajectory. The formal statement and converse are given in Section 7. === 6.11 Three or more generator levels === If the generator assumes three or more distinct values, then :<math> r(\theta) = \sum_{\ell=1}^{m} e^{a_{\ell}\theta/2}u_{\ell}, </math> with :<math> m\geq3. </math> The vectors <math>u_{\ell}</math> are linearly independent, but this fact alone is not sufficient to conclude that the trajectory spans all <math>m</math> directions. The required result follows from the linear independence of the distinct exponential rates. In Section 7, derivatives of <math>r(\theta)</math> are evaluated at a fixed parameter value. The resulting coefficient matrix is of Vandermonde type and is invertible when the generator levels <math>a_{\ell}</math> are distinct. This shows that a trajectory with <math>m</math> distinct active generator levels spans an <math>m</math>-dimensional linear subspace. Consequently, when <math>m\geq3</math>, the square-root trajectory cannot lie in a two-dimensional great-circle plane. === 6.12 e-geodesic versus Fisher–Rao geodesic === The exponential dilation trajectory is an exponential-family path. In natural coordinates, the parameter <math>\theta</math> enters linearly through :<math> \theta\phi_i. </math> Accordingly, the trajectory is naturally an e-geodesic in the exponential connection of information geometry. The Fisher–Rao Levi-Civita geodesic condition is different. Under the square-root representation, it requires the image of the trajectory to lie on a great-circle arc. Thus the central geometric distinction is: :'''e-geodesic: linearity in exponential-family natural coordinates''' versus :'''Fisher–Rao Levi-Civita geodesic: great-circle geometry under the square-root representation''' The two notions coincide only under additional conditions. === 6.13 Geometric question in linear form === The original probability-geometric question can now be reformulated. Given :<math> r(\theta) = \sum_{\ell=1}^{m} e^{a_{\ell}\theta/2}u_{\ell}, </math> when does the normalized curve :<math> q(\theta) = \frac{2r(\theta)} {\|r(\theta)\|} </math> remain in a fixed two-dimensional linear subspace? If it does, its image lies on a great circle and is therefore a Fisher–Rao Levi-Civita geodesic up to reparameterization. If it does not, the exponential trajectory remains an e-geodesic but is not a Fisher–Rao Levi-Civita geodesic. The next section gives an exact finite-dimensional characterization. == Relationship to the Probability Dilation Theory project == This manuscript is part of the broader [[Probability Dilation Theory]] research project on Wikiversity. Technical and exploratory material related to the manuscript is developed on associated PDT subpages, including: * [[Probability Dilation Theory/Measure-Theoretic Foundations|Measure-Theoretic Foundations]] * [[Probability Dilation Theory/Matrix Dilation Operators|Matrix Dilation Operators]] * [[Probability Dilation Theory/Dilation Vector Field|Dilation Vector Field]] * [[Probability Dilation Theory/Dilation Flows|Dilation Flows]] * [[Probability Dilation Theory/Convergence and Fixed Points|Convergence and Fixed Points]] * [[Probability Dilation Theory/Fisher Geometry and Dilation Flows|Fisher Geometry and Dilation Flows]] The present page is intended to develop a concise, standalone manuscript rather than reproduce the complete exploratory PDT project. == Draft status and research note == This manuscript is a work in progress. Some constructions discussed in the paper have direct counterparts in established mathematical literature. These relationships are identified explicitly wherever possible. Results developed specifically within the present formulation are being subjected to continuing literature review, proof checking, numerical verification, and independent mathematical scrutiny before any claim of novelty is made. Readers are encouraged to identify relevant prior literature, mathematical errors, counterexamples, alternative proofs, or useful extensions. == See also == * [[Probability Dilation Theory]] * [[Probability Dilation Theory/Matrix Dilation Operators]] * [[Probability Dilation Theory/Measure-Theoretic Foundations]] * [[Probability Dilation Theory/Fisher Geometry and Dilation Flows]] == Copyright and licensing == Text and original figures © Howard Richardson. Licensed under the [https://creativecommons.org/licenses/by/4.0/ Creative Commons Attribution 4.0 International License (CC BY 4.0)]. Reuse permitted with attribution. 86pr71zbsz9mto10al9ntnnqr3zi9df 2823783 2823780 2026-08-21T01:43:45Z Howie2024 2995240 /* 6.13 Geometric question in linear form */ Insert section 7. 2823783 wikitext text/x-wiki {{Research project}} '''Research manuscript — Draft Version 1.0''' ''This page develops a standalone research manuscript arising from the [[Probability Dilation Theory]] project. It is a work in progress and should not be regarded as a peer-reviewed publication.'' = Normalized Probability Dilation: A Unified Framework and Its Fisher–Rao Geometry = '''Howard Richardson''' ''Draft Version 1.0 — August 2026'' == Abstract == This paper develops a unified framework for normalized positive transformations of probability distributions, referred to here as '''Probability Dilation Theory (PDT)'''. The central construction consists of applying a positive transformation to a probability state and subsequently renormalizing the result. In finite dimensions this includes diagonal reweighting, :<math> p_i'= \frac{d_i p_i} {\sum_j d_jp_j}, </math> and the matrix transformation :<math> T_M(p)= \frac{Mp} {\mathbf{1}^{\mathsf T}Mp}, </math> for suitable nonnegative matrices <math>M</math>. A corresponding measure-theoretic formulation is :<math> P_D(A)= \frac{\int_A D\,dP} {\int_X D\,dP}. </math> These constructions are compared explicitly with established mathematical structures including change of measure, normalized positive operators, Perron–Frobenius iteration, Markov operators, replicator-type dynamics, and normalized Feynman–Kac transformations. The purpose of the framework is therefore not to claim these established constructions as new, but to investigate their common dilation-normalization structure and the geometry of the resulting probability trajectories. Particular attention is given to the exponential dilation family :<math> p_i(\theta)= \frac{p_i^{(0)}e^{\theta\phi_i}} {\sum_j p_j^{(0)}e^{\theta\phi_j}}. </math> Using the square-root representation of the Fisher–Rao simplex, we establish that, under finite-dimensional strict-positivity assumptions, the image of this exponential-dilation trajectory is contained in a Fisher–Rao Levi-Civita geodesic, up to reparameterization, if and only if the generator <math>\phi</math> assumes at most two distinct values. An explicit Fisher–Rao arclength parameterization is then obtained for the nondegenerate two-level case. The framework provides a common language for normalized probability transformations while separating results inherited from established theory from geometric properties arising from the particular dilation formulation. == 1. Introduction == Probability distributions are frequently transformed by operations having a common mathematical structure: nonnegative weights are modified by a positive transformation and subsequently normalized so that total probability remains unity. Such constructions occur in numerous areas of probability, statistics, dynamical systems, numerical linear algebra, and mathematical physics. The simplest finite-dimensional example takes a probability vector :<math> p=(p_1,\ldots,p_n)^{\mathsf T}, \qquad p_i\geq 0, \qquad \sum_{i=1}^{n}p_i=1, </math> assigns positive weights <math>d_i</math>, and defines :<math> p_i'= \frac{d_i p_i} {\sum_{j=1}^{n}d_jp_j}. </math> The transformation changes the relative probability assigned to individual states while normalization returns the resulting vector to the probability simplex. This paper uses the term '''probability dilation''' for this general transformation-and-normalization structure and examines a hierarchy of related constructions. In finite dimensions, diagonal dilation extends naturally to the action of a nonnegative matrix, :<math> T_M(p)= \frac{Mp} {\mathbf{1}^{\mathsf T}Mp}, </math> whenever the denominator is positive. At the level of probability measures, multiplication by a positive measurable function <math>D</math> gives :<math> P_D(A)= \frac{\displaystyle\int_A D(x)\,dP(x)} {\displaystyle\int_X D(x)\,dP(x)}. </math> These expressions have substantial connections with existing mathematics. Normalized matrix iteration is closely related to the power method and Perron–Frobenius theory; positive weighting of measures belongs to established change-of-measure constructions; stochastic matrices provide the familiar Markov special case; and normalized potential-weighted measures occur in Feynman–Kac models. Accordingly, the objective of PDT as developed here is '''not''' to rename these established mathematical theories or to assert novelty for normalization itself. Instead, the objective is to examine them through the common structural sequence :<math> \text{positive transformation} \longrightarrow \text{normalization} \longrightarrow \text{iteration} \longrightarrow \text{probability dynamics} \longrightarrow \text{geometry}. </math> This viewpoint leads naturally to questions concerning fixed points, convergence, entropy, state-dependent transformations, and the geometry of trajectories on the probability simplex. === 1.1 Exponential dilation === A particularly useful example is obtained from exponential dilation. Given an initial strictly positive probability vector <math>p^{(0)}</math> and a real-valued generator <math>\phi</math>, define :<math> p_i(\theta)= \frac{p_i^{(0)}e^{\theta\phi_i}} {Z(\theta)}, </math> where :<math> Z(\theta)= \sum_j p_j^{(0)}e^{\theta\phi_j}. </math> This is an exponential-family construction and therefore belongs to well-established information geometry. The question considered here is more specific: :''When is this exponential trajectory also a Levi-Civita geodesic of the Fisher–Rao metric?'' The Fisher–Rao geometry of a finite probability simplex admits a square-root representation on a sphere. Under the mapping :<math> p\longmapsto 2(\sqrt{p_1},\ldots,\sqrt{p_n}), </math> Fisher–Rao geodesics correspond to spherical great-circle arcs. This representation permits a direct characterization of exponential dilation trajectories that are simultaneously Fisher–Rao geodesic. === 1.2 Principal geometric result === The principal geometric result developed below is that, for a strictly positive finite probability vector, an exponential dilation trajectory lies on a Fisher–Rao geodesic, up to reparameterization, precisely when its generator assumes no more than two distinct values. The proof reduces the problem to the dimension of the linear span generated by distinct exponential rates and uses a Vandermonde argument for the converse. The resulting two-level trajectory also admits an explicit Fisher–Rao arclength parameterization. At the present draft stage, this characterization is treated conservatively. Its constituent mathematical ingredients are established results from information geometry and linear algebra. The exact characterization developed here remains subject to further literature review and independent mathematical scrutiny. === 1.3 Organization of the paper === The remainder of the paper is organized as follows: * '''Section 2''' introduces the normalized-dilation framework and notation. * '''Section 3''' develops diagonal and matrix formulations. * '''Section 4''' develops the measure-theoretic formulation. * '''Section 5''' compares the framework explicitly with established mathematics. * '''Section 6''' introduces exponential dilation and its information-geometric representation. * '''Section 7''' states and proves the Fisher–Rao geodesic characterization theorem. * '''Section 8''' derives the two-level Fisher–Rao arclength corollary and illustrative examples. * '''Section 9''' discusses limitations, possible extensions, and open problems. * '''Section 10''' summarizes the principal conclusions. == 2. Normalized-Dilation Framework == This section introduces the common mathematical structure used throughout the paper. The essential operation consists of applying a positive transformation to a probability state and then normalizing the transformed object so that it again represents a probability distribution. === 2.1 Probability simplex === For a finite state space with <math>n</math> states, define the probability simplex :<math> \Delta^{n-1} = \left\{ p\in\mathbb{R}^{n}: p_i\geq 0,\; \sum_{i=1}^{n}p_i=1 \right\}. </math> A probability state is represented by a column vector :<math> p= (p_1,\ldots,p_n)^{\mathsf{T}} \in\Delta^{n-1}. </math> Its components satisfy :<math> p_i\geq 0 </math> and :<math> \mathbf{1}^{\mathsf{T}}p=1, </math> where :<math> \mathbf{1} = (1,\ldots,1)^{\mathsf{T}}. </math> The interior of the simplex is :<math> \Delta_{+}^{n-1} = \left\{ p\in\Delta^{n-1}:p_i>0 \text{ for all }i \right\}. </math> The distinction between the simplex and its interior becomes important later when Fisher–Rao geometry is considered. === 2.2 Positive transformations === Let <math>\mathcal{L}</math> denote a transformation acting on probability states such that :<math> p\geq 0 \quad\Longrightarrow\quad \mathcal{L}(p)\geq 0. </math> The transformed object <math>\mathcal{L}(p)</math> need not itself be normalized. Define its total mass by :<math> \mathcal{N}[\mathcal{L}(p)] = \mathbf{1}^{\mathsf{T}}\mathcal{L}(p). </math> Whenever :<math> 0< \mathcal{N}[\mathcal{L}(p)] < \infty, </math> the normalized transformation is defined by :<math> \mathcal{T}_{\mathcal{L}}(p) = \frac{\mathcal{L}(p)} {\mathcal{N}[\mathcal{L}(p)]}. </math> Equivalently, in the finite-dimensional setting, :<math> \mathcal{T}_{\mathcal{L}}(p) = \frac{\mathcal{L}(p)} {\mathbf{1}^{\mathsf{T}}\mathcal{L}(p)}. </math> By construction, :<math> \mathbf{1}^{\mathsf{T}} \mathcal{T}_{\mathcal{L}}(p) = 1, </math> so :<math> \mathcal{T}_{\mathcal{L}}(p) \in \Delta^{n-1}. </math> This positive-transformation-plus-normalization operation is the basic structure referred to in this paper as '''normalized probability dilation'''. === 2.3 Normalization as projectivization === An immediate property of the normalized transformation is invariance under multiplication by a positive scalar. If <math>c>0</math>, then :<math> \frac{c\mathcal{L}(p)} {\mathbf{1}^{\mathsf{T}}c\mathcal{L}(p)} = \frac{\mathcal{L}(p)} {\mathbf{1}^{\mathsf{T}}\mathcal{L}(p)}. </math> Hence :<math> \mathcal{T}_{c\mathcal{L}}(p) = \mathcal{T}_{\mathcal{L}}(p). </math> The normalized transformation therefore depends on the relative components of <math>\mathcal{L}(p)</math>, rather than on its overall positive scale. This projective feature connects normalized dilation with established theories of positive operators and projective dynamics. No claim of novelty is attached to the normalization or projectivization operation itself. === 2.4 Diagonal dilation === Let :<math> D= \operatorname{diag}(d_1,\ldots,d_n), \qquad d_i>0. </math> Applying <math>D</math> to <math>p</math> gives :<math> Dp= (d_1p_1,\ldots,d_np_n)^{\mathsf{T}}. </math> Normalization produces :<math> T_D(p) = \frac{Dp} {\mathbf{1}^{\mathsf{T}}Dp}. </math> Componentwise, :<math> T_D(p)_i = \frac{d_ip_i} {\sum_{j=1}^{n}d_jp_j}. </math> This is the basic finite-dimensional dilation operation from which the broader PDT formulation developed. The factors <math>d_i</math> alter the relative weights of the probability states, while the denominator restores unit total probability. === 2.5 Matrix dilation === The diagonal transformation can be generalized to a nonnegative matrix :<math> M\in\mathbb{R}^{n\times n}, \qquad M_{ij}\geq 0. </math> For any probability vector <math>p</math> satisfying :<math> \mathbf{1}^{\mathsf{T}}Mp>0, </math> define :<math> T_M(p) = \frac{Mp} {\mathbf{1}^{\mathsf{T}}Mp}. </math> The diagonal case is recovered when :<math> M=D. </math> Off-diagonal entries permit components of the input probability vector to contribute to different output components before normalization. The matrix formulation therefore extends independent componentwise reweighting to coupled positive transformations. The mathematical behavior of this construction is closely related to established positive-matrix theory, normalized power iteration, and Perron–Frobenius theory. These relationships are discussed explicitly in Section 5. === 2.6 Measure-theoretic dilation === The same normalization principle extends naturally from finite probability vectors to probability measures. Let <math>(X,\mathcal{F},P)</math> be a probability space, and let :<math> D:X\rightarrow[0,\infty) </math> be measurable with :<math> 0< \int_X D(x)\,dP(x) < \infty. </math> Define a new probability measure <math>P_D</math> by :<math> P_D(A) = \frac{\displaystyle\int_A D(x)\,dP(x)} {\displaystyle\int_X D(x)\,dP(x)}, \qquad A\in\mathcal{F}. </math> Equivalently, the Radon–Nikodym derivative of <math>P_D</math> with respect to <math>P</math> is :<math> \frac{dP_D}{dP} = \frac{D} {\displaystyle\int_X D\,dP}. </math> Thus the finite-dimensional rule :<math> p_i \longmapsto \frac{d_ip_i} {\sum_jd_jp_j} </math> and the measure-theoretic rule :<math> dP \longmapsto \frac{D\,dP} {\int_XD\,dP} </math> share the same normalized positive-reweighting structure. This construction has direct connections with established change-of-measure and weighted-measure theory. The PDT terminology is used here as an organizing framework rather than as a claim that normalized change of measure is itself new. === 2.7 Iterated dilation === A normalized dilation operator can be iterated. Given an initial state :<math> p^{(0)}\in\Delta^{n-1}, </math> define :<math> p^{(k+1)} = \mathcal{T}_{\mathcal{L}}\left(p^{(k)}\right). </math> This generates an orbit :<math> p^{(0)} \longmapsto p^{(1)} \longmapsto p^{(2)} \longmapsto \cdots </math> on the probability simplex. For a fixed matrix <math>M</math>, :<math> p^{(k+1)} = \frac{Mp^{(k)}} {\mathbf{1}^{\mathsf{T}}Mp^{(k)}}. </math> When all required denominators are positive, repeated normalization gives :<math> p^{(k)} = \frac{M^k p^{(0)}} {\mathbf{1}^{\mathsf{T}}M^k p^{(0)}}. </math> The long-term behavior of this iteration is governed in important cases by established spectral and Perron–Frobenius theory. More general formulations may allow the transformation itself to depend on the iteration index or the current probability state, for example :<math> p^{(k+1)} = \frac{M_kp^{(k)}} {\mathbf{1}^{\mathsf{T}}M_kp^{(k)}} </math> or :<math> p^{(k+1)} = \frac{M(p^{(k)})p^{(k)}} {\mathbf{1}^{\mathsf{T}}M(p^{(k)})p^{(k)}}. </math> These state-dependent and iteration-dependent forms are treated as possible extensions rather than necessary components of the basic framework. === 2.8 Hierarchy of normalized dilation === The constructions above can be summarized by the following hierarchy: :'''diagonal reweighting → matrix transformation → positive operator → measure transformation''' At each level the essential operation is: :'''positive transformation + normalization''' The framework is deliberately broad. Its purpose is not to imply that all normalized positive transformations constitute a new mathematical theory, but to provide a common notation and viewpoint from which their dynamics and geometry can be compared. The following sections specialize this framework before examining its relationship to established mathematical constructions. == 3. Finite-Dimensional and Matrix Dilation == This section develops the finite-dimensional forms of normalized probability dilation in greater detail. The emphasis is on the relationship between diagonal reweighting and nonnegative matrix transformations, together with the basic structural properties required later in the paper. === 3.1 Finite probability states === Let :<math> p=(p_1,\ldots,p_n)^{\mathsf{T}} \in\Delta^{n-1}. </math> A positive weighting vector is written :<math> d=(d_1,\ldots,d_n)^{\mathsf{T}}, \qquad d_i>0. </math> The associated diagonal matrix is :<math> D= \operatorname{diag}(d_1,\ldots,d_n). </math> Applying the weighting gives :<math> Dp= (d_1p_1,\ldots,d_np_n)^{\mathsf{T}}. </math> Its total mass is :<math> Z(p,D) = \mathbf{1}^{\mathsf{T}}Dp = \sum_{i=1}^{n}d_ip_i. </math> Since <math>d_i>0</math> and <math>p</math> is a probability vector, :<math> Z(p,D)>0. </math> The normalized diagonal dilation operator is therefore :<math> T_D(p) = \frac{Dp}{Z(p,D)}. </math> Equivalently, :<math> T_D(p)_i = \frac{d_ip_i} {\sum_{j=1}^{n}d_jp_j}. </math> === 3.2 Relative probability transformation === Diagonal dilation has a simple effect on probability ratios. For any states <math>i</math> and <math>j</math> with <math>p_i>0</math> and <math>p_j>0</math>, :<math> \frac{T_D(p)_i}{T_D(p)_j} = \frac{d_i}{d_j} \frac{p_i}{p_j}. </math> Thus normalization does not alter the relative dilation introduced by the factors <math>d_i</math> and <math>d_j</math>. If :<math> d_i>d_j, </math> then the odds of state <math>i</math> relative to state <math>j</math> increase by the factor :<math> \frac{d_i}{d_j}. </math> This ratio form makes clear that diagonal dilation is fundamentally a relative reweighting operation. === 3.3 Scale invariance === Multiplying every dilation factor by the same positive constant does not change the normalized state. Let :<math> c>0. </math> Then :<math> T_{cD}(p) = \frac{cDp} {\mathbf{1}^{\mathsf{T}}cDp} = \frac{Dp} {\mathbf{1}^{\mathsf{T}}Dp} = T_D(p). </math> Therefore only the relative values of the dilation factors affect the transformed probability distribution. This scale invariance is a basic projective property of normalized positive transformations. === 3.4 Repeated diagonal dilation === Suppose the same diagonal operator <math>D</math> is applied repeatedly. Starting from <math>p^{(0)}</math>, define :<math> p^{(k+1)} = T_D(p^{(k)}). </math> Then :<math> p^{(k)} = \frac{D^k p^{(0)}} {\mathbf{1}^{\mathsf{T}}D^k p^{(0)}}. </math> Since :<math> D^k = \operatorname{diag}(d_1^k,\ldots,d_n^k), </math> the individual components are :<math> p_i^{(k)} = \frac{d_i^k p_i^{(0)}} {\sum_{j=1}^{n}d_j^k p_j^{(0)}}. </math> Consequently, for two initially positive components, :<math> \frac{p_i^{(k)}}{p_j^{(k)}} = \left(\frac{d_i}{d_j}\right)^k \frac{p_i^{(0)}}{p_j^{(0)}}. </math> This expression describes the concentration mechanism directly. If one dilation factor is strictly larger than all others and its corresponding initial probability is positive, repeated dilation concentrates probability on that state. If several states share the maximal dilation factor, probability concentrates on that maximal set while preserving the initial relative proportions within that set. This behavior is a direct consequence of normalized repeated weighting and is not specific to PDT terminology. === 3.5 General nonnegative matrix transformation === Let :<math> M=(M_{ij}) \in\mathbb{R}^{n\times n}, \qquad M_{ij}\geq0. </math> For <math>p\in\Delta^{n-1}</math>, define :<math> q=Mp. </math> Because <math>M</math> and <math>p</math> are nonnegative, :<math> q_i\geq0. </math> Whenever :<math> \mathbf{1}^{\mathsf{T}}Mp>0, </math> the normalized matrix dilation operator is :<math> T_M(p) = \frac{Mp} {\mathbf{1}^{\mathsf{T}}Mp}. </math> Its components are :<math> T_M(p)_i = \frac{\sum_{j=1}^{n}M_{ij}p_j} {\sum_{r=1}^{n}\sum_{j=1}^{n}M_{rj}p_j}. </math> By construction, :<math> \sum_{i=1}^{n}T_M(p)_i=1. </math> Hence :<math> T_M(p)\in\Delta^{n-1}. </math> === 3.6 Diagonal dilation as a special case === If :<math> M=D = \operatorname{diag}(d_1,\ldots,d_n), </math> then :<math> Mp=Dp, </math> and therefore :<math> T_M(p)=T_D(p). </math> Diagonal dilation is thus a special case of normalized matrix dilation. The distinction is structural. For a diagonal matrix, each output component depends only on the corresponding input component: :<math> (Dp)_i=d_ip_i. </math> For a general matrix, :<math> (Mp)_i = \sum_{j=1}^{n}M_{ij}p_j, </math> so multiple input states may contribute to a single output state before normalization. This permits coupled probability evolution. === 3.7 When normalization is unnecessary === There is an important special case. Suppose <math>M</math> satisfies :<math> \mathbf{1}^{\mathsf{T}}M = \mathbf{1}^{\mathsf{T}}. </math> Then for every probability vector <math>p</math>, :<math> \mathbf{1}^{\mathsf{T}}Mp = \mathbf{1}^{\mathsf{T}}p = 1. </math> Consequently, :<math> T_M(p)=Mp. </math> With the column-vector convention used in this paper, the condition :<math> \mathbf{1}^{\mathsf{T}}M = \mathbf{1}^{\mathsf{T}} </math> means that the columns of <math>M</math> sum to one. Thus an ordinary probability-preserving linear transition is contained as a special case of the normalized matrix framework. When <math>M</math> does not preserve total mass, normalization supplies the additional step required to return <math>Mp</math> to the simplex. === 3.8 Fixed points and eigenvectors === Suppose <math>p^{*}</math> is a fixed point of the normalized matrix operator: :<math> T_M(p^{*})=p^{*}. </math> Then :<math> \frac{Mp^{*}} {\mathbf{1}^{\mathsf{T}}Mp^{*}} = p^{*}. </math> Multiplying by the denominator gives :<math> Mp^{*} = \lambda p^{*}, </math> where :<math> \lambda = \mathbf{1}^{\mathsf{T}}Mp^{*}. </math> Therefore every fixed point of the normalized matrix transformation is a nonnegative eigenvector of <math>M</math>, normalized to have unit total mass. Conversely, if <math>v\geq0</math> is a nonzero eigenvector satisfying :<math> Mv=\lambda v, \qquad \lambda>0, </math> then :<math> p^{*} = \frac{v} {\mathbf{1}^{\mathsf{T}}v} </math> is a fixed point of <math>T_M</math>. Thus normalized fixed points and positive eigenvectors are directly related. === 3.9 Repeated matrix dilation === For a fixed nonnegative matrix <math>M</math>, define :<math> p^{(k+1)} = T_M(p^{(k)}). </math> Whenever the required denominators remain positive, :<math> p^{(k)} = \frac{M^k p^{(0)}} {\mathbf{1}^{\mathsf{T}}M^k p^{(0)}}. </math> This identity follows because the scalar normalization introduced at each intermediate step cancels under the next normalization. The iteration is therefore closely related to normalized power iteration. Under suitable positivity or primitivity assumptions, Perron–Frobenius theory describes the dominant eigenvalue and positive eigenvector governing the long-term behavior. Accordingly, convergence of the fixed-matrix case should be understood primarily through established positive-matrix and spectral theory rather than as a separate PDT convergence mechanism. === 3.10 Primitive positive matrices === A particularly important case occurs when <math>M</math> is primitive; that is, some positive integer power of <math>M</math> has strictly positive entries. Perron–Frobenius theory then provides a dominant real eigenvalue :<math> \rho(M)>0 </math> with a corresponding strictly positive eigenvector <math>v</math>. After normalization, :<math> p^{*} = \frac{v} {\mathbf{1}^{\mathsf{T}}v}, </math> this eigenvector gives the distinguished interior fixed point of the normalized matrix transformation. For suitable initial probability vectors, :<math> T_M^{k}(p^{(0)}) </math> converges toward <math>p^{*}</math>. This convergence is an established consequence of Perron–Frobenius theory and normalized power iteration. Its role here is to locate matrix dilation within known mathematics. === 3.11 Interpretation of off-diagonal terms === The off-diagonal entries of <math>M</math> distinguish matrix dilation from independent diagonal reweighting. For :<math> i\neq j, </math> a term :<math> M_{ij}p_j </math> represents a contribution from input state <math>j</math> to output component <math>i</math> before normalization. The matrix therefore combines two operations: * positive redistribution or coupling through <math>M</math>; * restoration of unit total probability through normalization. This interpretation is useful for organizing the framework, but the underlying linear transformation remains standard matrix mathematics. === 3.12 Scope of the matrix formulation === The matrix formulation substantially enlarges the class of transformations expressible within the normalized-dilation notation, but that enlargement should not be confused with mathematical novelty. For a fixed matrix <math>M</math>, the central objects :<math> Mp, \qquad M^kp, \qquad \rho(M), </math> and the associated eigenvectors and convergence properties belong to established linear algebra and positive-operator theory. The role of the PDT framework is to place diagonal reweighting, matrix transformation, iteration, and later measure-theoretic and geometric constructions within a common normalized-probability notation. This distinction between '''framework''' and '''new mathematical result''' will be maintained throughout the paper. == 4. Measure-Theoretic Dilation == The finite-dimensional dilation rule extends naturally to probability measures. In this setting, componentwise multiplication by positive weights is replaced by multiplication of a probability measure by a nonnegative measurable function followed by normalization. This formulation places finite probability dilation within the standard language of measure theory and makes its relationship to change of measure explicit. === 4.1 Probability-space formulation === Let :<math> (X,\mathcal{F},P) </math> be a probability space. Let :<math> D:X\rightarrow[0,\infty) </math> be a measurable function satisfying :<math> 0< \int_X D(x)\,dP(x) < \infty. </math> Define the normalization factor :<math> Z(P,D) = \int_X D(x)\,dP(x). </math> For every measurable set :<math> A\in\mathcal{F}, </math> define :<math> P_D(A) = \frac{\displaystyle\int_A D(x)\,dP(x)} {Z(P,D)}. </math> Equivalently, :<math> P_D(A) = \frac{\displaystyle\int_A D(x)\,dP(x)} {\displaystyle\int_X D(x)\,dP(x)}. </math> The function <math>D</math> acts as a nonnegative weighting or dilation field over the probability space. === 4.2 Normalization === The transformed measure has total mass one because :<math> P_D(X) = \frac{\displaystyle\int_X D(x)\,dP(x)} {\displaystyle\int_X D(x)\,dP(x)} = 1. </math> Also, because <math>D</math> is nonnegative, :<math> P_D(A)\geq0 </math> for every <math>A\in\mathcal{F}</math>. Countable additivity follows from the countable additivity of integration with respect to <math>P</math>. Therefore <math>P_D</math> is a probability measure. === 4.3 Radon–Nikodym representation === The transformed measure <math>P_D</math> is absolutely continuous with respect to <math>P</math>. Its Radon–Nikodym derivative is :<math> \frac{dP_D}{dP}(x) = \frac{D(x)} {\displaystyle\int_X D(y)\,dP(y)}. </math> Thus normalized measure dilation can be written formally as :<math> dP_D(x) = \frac{D(x)\,dP(x)} {\displaystyle\int_X D(y)\,dP(y)}. </math> This expression makes clear that the construction is a normalized change of measure. The Radon–Nikodym framework is established measure theory. The terminology of dilation is used here to emphasize the common transformation-and-normalization structure shared with the finite-dimensional formulation. === 4.4 Scale invariance === As in the finite-dimensional case, multiplication of the dilation field by a positive constant does not change the normalized measure. Let :<math> c>0. </math> Then :<math> P_{cD}(A) = \frac{\displaystyle\int_A cD\,dP} {\displaystyle\int_X cD\,dP}. </math> The common factor cancels, giving :<math> P_{cD}(A)=P_D(A). </math> Hence the transformed probability measure depends only on the relative values of the dilation field <math>D</math>, not on its overall positive scale. === 4.5 Finite probability spaces as a special case === Consider a finite state space :<math> X=\{1,\ldots,n\}. </math> Let :<math> P(\{i\})=p_i </math> and define :<math> D(i)=d_i. </math> Then :<math> \int_X D\,dP = \sum_{j=1}^{n}d_jp_j. </math> For the singleton event <math>\{i\}</math>, :<math> P_D(\{i\}) = \frac{d_ip_i} {\sum_{j=1}^{n}d_jp_j}. </math> Thus the finite diagonal dilation rule :<math> p_i' = \frac{d_ip_i} {\sum_jd_jp_j} </math> is recovered exactly from the measure-theoretic construction. The discrete and measure-theoretic formulations are therefore instances of the same normalized positive-reweighting operation. === 4.6 Expectations under dilation === Let :<math> f:X\rightarrow\mathbb{R} </math> be measurable and integrable with respect to the transformed measure. Then :<math> \mathbb{E}_{P_D}[f] = \int_X f(x)\,dP_D(x). </math> Using the Radon–Nikodym representation, :<math> \mathbb{E}_{P_D}[f] = \frac{\displaystyle\int_X f(x)D(x)\,dP(x)} {\displaystyle\int_X D(x)\,dP(x)}. </math> Equivalently, :<math> \mathbb{E}_{P_D}[f] = \frac{\mathbb{E}_{P}[fD]} {\mathbb{E}_{P}[D]}, </math> provided the required expectations exist. This identity is a standard weighted-expectation formula and will later be useful for exponential dilation. === 4.7 Composition of dilation fields === Suppose a first dilation field <math>D_1</math> transforms <math>P</math> into <math>P_{D_1}</math>, and a second field <math>D_2</math> is then applied. The first transformation gives :<math> dP_{D_1} = \frac{D_1\,dP} {\int_XD_1\,dP}. </math> Applying <math>D_2</math> gives :<math> d(P_{D_1})_{D_2} = \frac{D_2\,dP_{D_1}} {\int_XD_2\,dP_{D_1}}. </math> Substituting the first transformation and simplifying yields :<math> d(P_{D_1})_{D_2} = \frac{D_1D_2\,dP} {\int_XD_1D_2\,dP}, </math> whenever the required integrals are finite and positive. Therefore :<math> (P_{D_1})_{D_2} = P_{D_1D_2}. </math> Sequential scalar dilation fields thus combine multiplicatively before normalization. This composition property is the measure-theoretic analogue of repeated diagonal reweighting. === 4.8 Iterated fixed dilation === If the same dilation field <math>D</math> is applied repeatedly, then after <math>k</math> iterations, :<math> dP^{(k)} = \frac{D^k\,dP^{(0)}} {\displaystyle\int_XD^k\,dP^{(0)}}. </math> Equivalently, for any measurable event <math>A</math>, :<math> P^{(k)}(A) = \frac{\displaystyle\int_A D(x)^k\,dP^{(0)}(x)} {\displaystyle\int_X D(x)^k\,dP^{(0)}(x)}. </math> This is the direct measure-theoretic counterpart of :<math> p_i^{(k)} = \frac{d_i^kp_i^{(0)}} {\sum_jd_j^kp_j^{(0)}}. </math> Regions where <math>D</math> is relatively large receive increasing relative weight under repeated application. The precise limiting behavior depends on the structure of <math>D</math> and the initial measure. === 4.9 Exponential dilation fields === A particularly important family is obtained by choosing :<math> D_{\theta}(x) = e^{\theta\phi(x)}, </math> where <math>\phi:X\rightarrow\mathbb{R}</math> is measurable and <math>\theta</math> is a real parameter for which the normalization integral is finite. Define :<math> Z(\theta) = \int_X e^{\theta\phi(x)}\,dP_0(x). </math> Then :<math> dP_{\theta}(x) = \frac{e^{\theta\phi(x)}} {Z(\theta)} dP_0(x). </math> In a finite state space this becomes :<math> p_i(\theta) = \frac{p_i^{(0)}e^{\theta\phi_i}} {\sum_jp_j^{(0)}e^{\theta\phi_j}}. </math> This is a standard exponential tilting construction and is closely related to exponential families, cumulant-generating functions, and information geometry. Its importance for the present paper is that it provides a continuous one-parameter dilation trajectory whose Fisher–Rao geometry can be studied explicitly. === 4.10 Infinitesimal evolution of exponential dilation === For the finite-dimensional exponential family, :<math> p_i(\theta) = \frac{p_i^{(0)}e^{\theta\phi_i}} {Z(\theta)}, </math> differentiate with respect to <math>\theta</math>. The logarithmic derivative is :<math> \frac{d}{d\theta}\log p_i(\theta) = \phi_i - \frac{d}{d\theta}\log Z(\theta). </math> Since :<math> \frac{d}{d\theta}\log Z(\theta) = \sum_jp_j(\theta)\phi_j, </math> define :<math> \overline{\phi}_{\theta} = \sum_jp_j(\theta)\phi_j. </math> Then :<math> \frac{dp_i}{d\theta} = p_i(\theta) \left( \phi_i-\overline{\phi}_{\theta} \right). </math> This equation has the form of a replicator-type evolution equation with a fixed state-dependent generator <math>\phi_i</math>. The relationship to established replicator dynamics is discussed in Section 5. === 4.11 Conservation of total probability === Summing the infinitesimal evolution equation gives :<math> \sum_i \frac{dp_i}{d\theta} = \sum_i p_i(\theta) \left( \phi_i-\overline{\phi}_{\theta} \right). </math> Since :<math> \sum_ip_i(\theta)\phi_i = \overline{\phi}_{\theta} </math> and :<math> \sum_ip_i(\theta)=1, </math> it follows that :<math> \sum_i \frac{dp_i}{d\theta} = 0. </math> Thus the vector field is tangent to the probability simplex. Normalization is therefore reflected infinitesimally by conservation of total probability. === 4.12 Scope of the measure-theoretic formulation === The measure-theoretic formulation shows that normalized probability dilation is not restricted to finite vectors or matrices. The same structural operation appears as :'''weight → normalize → obtain a new probability measure''' and, for exponential fields, :'''exponential weight → normalize → continuous probability trajectory'''. These constructions overlap directly with established change-of-measure theory, exponential tilting, weighted probability measures, and related probabilistic methods. Their role in the present framework is to connect the finite dilation notation to continuous probability spaces and to provide the bridge to the information-geometric analysis developed later in the paper. The next section therefore compares the normalized-dilation framework systematically with established mathematical constructions before any additional geometric results are introduced. == 5. Relation to Established Mathematics == The normalized-dilation framework overlaps with several established areas of mathematics. This section identifies those relationships explicitly. The purpose is twofold: first, to place the notation used in this paper within its appropriate mathematical context; and second, to distinguish established constructions from the particular synthesis and geometric questions developed later in the paper. The term '''probability dilation''' is therefore used as an organizing description of a transformation-and-normalization structure, not as a claim that the underlying operations of reweighting, normalization, positive matrix iteration, or change of measure are themselves new. === 5.1 Weighted probability and change of measure === The measure-theoretic transformation :<math> dP_D = \frac{D\,dP} {\int_XD\,dP} </math> is a standard normalized change of measure. Its Radon–Nikodym derivative with respect to <math>P</math> is :<math> \frac{dP_D}{dP} = \frac{D} {\int_XD\,dP}. </math> Consequently, for an integrable observable <math>f</math>, :<math> \mathbb{E}_{P_D}[f] = \frac{\mathbb{E}_{P}[fD]} {\mathbb{E}_{P}[D]}. </math> These expressions belong to established measure-theoretic probability. Within the present framework, their role is to show that finite diagonal dilation and continuous weighted change of measure share the same normalized reweighting structure. === 5.2 Bayesian reweighting === A closely related normalization structure occurs in Bayesian inference. If <math>\pi(x)</math> is a prior density and <math>L(y\mid x)</math> is a likelihood for observed data <math>y</math>, Bayes' rule gives :<math> \pi(x\mid y) = \frac{L(y\mid x)\pi(x)} {\int L(y\mid z)\pi(z)\,dz}, </math> when the denominator is finite and nonzero. Structurally, this has the same form as :<math> dP_D = \frac{D\,dP} {\int D\,dP}, </math> with the likelihood acting as a positive weighting function. The statistical interpretation is different: Bayesian updating has a specific inferential meaning associated with conditioning on data. The comparison here concerns only the common mathematical normalization structure. === 5.3 Importance weighting and exponential tilting === Weighted probability measures also arise in importance sampling, exponential tilting, large-deviation methods, and related statistical constructions. For a generator <math>\phi</math>, exponential tilting takes the form :<math> dP_{\theta}(x) = \frac{e^{\theta\phi(x)}} {Z(\theta)} dP_0(x), </math> where :<math> Z(\theta) = \int_Xe^{\theta\phi(x)}\,dP_0(x). </math> This is an established exponential-family construction. The corresponding finite-dimensional expression, :<math> p_i(\theta) = \frac{p_i^{(0)}e^{\theta\phi_i}} {\sum_jp_j^{(0)}e^{\theta\phi_j}}, </math> will be the principal object of the Fisher–Rao analysis in Sections 6 through 8. The geometric analysis developed later concerns this established exponential-tilt family under a particular question about coincidence of information-geometric and Fisher–Rao geodesics. === 5.4 Positive matrices and Perron–Frobenius theory === For a fixed nonnegative matrix <math>M</math>, the normalized transformation :<math> T_M(p) = \frac{Mp} {\mathbf{1}^{\mathsf{T}}Mp} </math> is closely related to classical positive-matrix theory. If <math>M</math> is primitive, Perron–Frobenius theory provides a dominant positive eigenvalue :<math> \rho(M)>0 </math> and a corresponding strictly positive eigenvector. Repeated normalized iteration, :<math> p^{(k)} = \frac{M^kp^{(0)}} {\mathbf{1}^{\mathsf{T}}M^kp^{(0)}}, </math> is therefore closely related to normalized power iteration. Under appropriate hypotheses, its asymptotic direction is governed by the Perron eigenvector. These spectral and convergence results are established mathematics and are not presented here as new consequences of PDT. === 5.5 Markov operators === Suppose <math>M</math> is nonnegative and satisfies :<math> \mathbf{1}^{\mathsf{T}}M = \mathbf{1}^{\mathsf{T}}. </math> With the column-vector convention used in this paper, :<math> \mathbf{1}^{\mathsf{T}}Mp = 1 </math> for every probability vector <math>p</math>. Thus :<math> T_M(p)=Mp. </math> In this mass-preserving case, the normalization step is unnecessary. Accordingly, ordinary finite-state Markov evolution is contained as a special mass-preserving case of the broader positive-transformation framework. This observation is structural. It does not imply that normalized dilation provides a replacement for Markov-chain theory. === 5.6 Replicator-type dynamics === The exponential dilation family satisfies :<math> \frac{dp_i}{d\theta} = p_i \left( \phi_i-\overline{\phi}_{\theta} \right), </math> where :<math> \overline{\phi}_{\theta} = \sum_jp_j(\theta)\phi_j. </math> The standard replicator equation has the form :<math> \frac{dp_i}{dt} = p_i \left( f_i(p)-\overline{f}(p) \right). </math> Thus exponential dilation with fixed generator values <math>\phi_i</math> has the same algebraic structure as a replicator equation with state-independent fitness values. The mean-subtraction term guarantees :<math> \sum_i\frac{dp_i}{d\theta}=0, </math> so the flow remains tangent to the probability simplex. Replicator dynamics and their geometric interpretations are established subjects. The present paper uses this connection to relate normalized dilation to known simplex dynamics. === 5.7 Fisher–Rao and Shahshahani geometry === The interior of the probability simplex carries the Fisher–Rao metric. For tangent vectors <math>u</math> and <math>v</math> satisfying :<math> \sum_i u_i = \sum_i v_i = 0, </math> the finite-dimensional Fisher–Rao metric can be written as :<math> g_p(u,v) = \sum_{i=1}^{n} \frac{u_iv_i}{p_i}. </math> Closely related forms of this metric appear in evolutionary dynamics under the name Shahshahani metric. The square-root mapping :<math> \Psi(p) = 2(\sqrt{p_1},\ldots,\sqrt{p_n}) </math> satisfies :<math> \sum_i\Psi_i(p)^2=4. </math> Thus the simplex interior is represented in the positive orthant of a sphere of radius <math>2</math>. Under this representation, the Fisher–Rao metric becomes the metric induced by the ambient Euclidean space, and Levi-Civita Fisher–Rao geodesics correspond locally to great-circle arcs. This established spherical representation will be the principal geometric tool used in Section 7. === 5.8 Exponential families and the e-connection === The exponential dilation path :<math> p_i(\theta) = \frac{p_i^{(0)}e^{\theta\phi_i}} {Z(\theta)} </math> is a one-parameter exponential family. Taking logarithms gives :<math> \log p_i(\theta) = \log p_i^{(0)} + \theta\phi_i - \log Z(\theta). </math> The natural parameter varies linearly with <math>\theta</math>. In information geometry, exponential families are naturally associated with the exponential, or '''e''', connection. A path linear in natural parameters is an e-geodesic. This notion of geodesic is distinct from a Levi-Civita geodesic of the Fisher–Rao metric. Consequently, an exponential dilation trajectory may be straight with respect to the e-connection while being curved with respect to the Fisher–Rao Levi-Civita connection. This distinction is central to the geometric question investigated later in the paper. === 5.9 Fisher information and variance === For the exponential dilation family, :<math> \frac{d}{d\theta} \log p_i(\theta) = \phi_i-\overline{\phi}_{\theta}. </math> The Fisher information associated with the parameter <math>\theta</math> is therefore :<math> I(\theta) = \sum_i p_i(\theta) \left( \phi_i-\overline{\phi}_{\theta} \right)^2. </math> Hence :<math> I(\theta) = \operatorname{Var}_{p(\theta)}(\phi). </math> The Fisher–Rao speed of the trajectory is :<math> v_{\mathrm{FR}}(\theta) = \sqrt{I(\theta)} = \sqrt{\operatorname{Var}_{p(\theta)}(\phi)}. </math> This variance identity is a standard property of one-parameter exponential families. It will be used later when deriving the arclength parameterization of the two-level case. === 5.10 Normalized Feynman–Kac transformations === Another closely related structure occurs in Feynman–Kac models. At an abstract level, a positive measure may first be weighted by a nonnegative potential and then propagated through a positive or Markov operator, followed by normalization. Schematically, such an evolution has the form :'''weight → propagate → normalize'''. The matrix expression :<math> T_M(p) = \frac{Mp} {\mathbf{1}^{\mathsf{T}}Mp} </math> and the measure expression :<math> dP_D = \frac{D\,dP} {\int D\,dP} </math> therefore have structural analogues within normalized Feynman–Kac theory. The exact interpretation and assumptions differ among applications. The comparison made here is structural rather than an assertion of equivalence between PDT and Feynman–Kac theory. === 5.11 Projective dynamics === Because normalized dilation is invariant under multiplication of the unnormalized transformed state by a positive scalar, it naturally has a projective character. For example, :<math> T_{cM}(p) = T_M(p) </math> for every <math>c>0</math> for which the transformation is defined. Thus the normalized state depends on the ray determined by <math>Mp</math>, rather than its magnitude. Positive projective geometry and projective metrics, including Hilbert-type metrics, are established tools in the study of positive operators and their contraction properties. These methods provide natural mathematical machinery for analyzing normalized positive transformations, particularly in convergence problems. === 5.12 What the PDT framework contributes === The preceding comparisons show that the principal operations used in normalized probability dilation have substantial established precedents. The proposed contribution of the framework is therefore not the isolated operation :'''multiply or transform, then normalize'''. Rather, the framework provides a common notation and organizational viewpoint connecting: * finite diagonal reweighting; * nonnegative matrix transformations; * normalized positive iteration; * weighted change of measure; * exponential probability trajectories; * simplex dynamics; * information geometry. This synthesis is useful only insofar as it clarifies relationships, generates mathematically precise questions, or produces results that are not merely restatements of known theory. For that reason, the remainder of this paper concentrates on a narrower geometric problem. === 5.13 Transition to the geometric question === Every exponential dilation trajectory of the form :<math> p_i(\theta) = \frac{p_i^{(0)}e^{\theta\phi_i}} {Z(\theta)} </math> is an exponential-family trajectory and hence is naturally straight with respect to the e-connection. It does not follow that the same trajectory is a Levi-Civita geodesic of the Fisher–Rao metric. This leads to the central question considered in the remainder of the paper: :''Under what conditions is an exponential dilation trajectory simultaneously an e-geodesic and, up to reparameterization, a Fisher–Rao Levi-Civita geodesic?'' The next section develops the geometric representation required to answer this question. == 6. Exponential Dilation and Fisher–Rao Geometry == This section develops the geometric representation of exponential dilation required for the main characterization theorem. The central object is the one-parameter exponential family :<math> p_i(\theta) = \frac{p_i^{(0)}e^{\theta\phi_i}} {Z(\theta)}, </math> where :<math> Z(\theta) = \sum_{j=1}^{n}p_j^{(0)}e^{\theta\phi_j}. </math> Throughout this section, assume :<math> p_i^{(0)}>0 </math> for all <math>i</math>, and let :<math> \phi=(\phi_1,\ldots,\phi_n) </math> be a real-valued generator. === 6.1 Exponential dilation trajectory === Let :<math> p^{(0)} \in \Delta_{+}^{n-1}. </math> For a real parameter <math>\theta</math>, define :<math> p_i(\theta) = \frac{p_i^{(0)}e^{\theta\phi_i}} {\sum_{j=1}^{n}p_j^{(0)}e^{\theta\phi_j}}. </math> Since every initial component is strictly positive and the exponential function is positive, :<math> p_i(\theta)>0 </math> for every finite <math>\theta</math>. Therefore the trajectory remains in the interior of the probability simplex. The normalization factor satisfies :<math> Z(\theta)>0. </math> Hence the trajectory is well defined for every finite <math>\theta</math> in the finite-dimensional setting. === 6.2 Logarithmic form === Taking logarithms gives :<math> \log p_i(\theta) = \log p_i^{(0)} + \theta\phi_i - \log Z(\theta). </math> Differentiating with respect to <math>\theta</math> gives :<math> \frac{d}{d\theta}\log p_i(\theta) = \phi_i - \frac{d}{d\theta}\log Z(\theta). </math> Now :<math> \frac{dZ}{d\theta} = \sum_j p_j^{(0)} \phi_j e^{\theta\phi_j}. </math> Therefore :<math> \frac{d}{d\theta}\log Z(\theta) = \sum_jp_j(\theta)\phi_j. </math> Define the expectation of the generator by :<math> \mu(\theta) = \mathbb{E}_{p(\theta)}[\phi] = \sum_jp_j(\theta)\phi_j. </math> Then :<math> \frac{d}{d\theta}\log p_i(\theta) = \phi_i-\mu(\theta). </math> === 6.3 Tangent vector === Multiplying the logarithmic derivative by <math>p_i(\theta)</math> gives :<math> \frac{dp_i}{d\theta} = p_i(\theta) \left( \phi_i-\mu(\theta) \right). </math> Define the centered generator :<math> h_i(\theta) = \phi_i-\mu(\theta). </math> Then :<math> \frac{dp_i}{d\theta} = p_i(\theta)h_i(\theta). </math> Because :<math> \sum_i p_i(\theta)h_i(\theta) = 0, </math> we obtain :<math> \sum_i \frac{dp_i}{d\theta} = 0. </math> Thus the velocity vector is tangent to the probability simplex. === 6.4 Fisher information and speed === The Fisher–Rao metric on the simplex interior is :<math> g_p(u,v) = \sum_i \frac{u_iv_i}{p_i}, </math> for tangent vectors <math>u</math> and <math>v</math>. For the exponential dilation trajectory, :<math> \frac{dp_i}{d\theta} = p_i h_i. </math> Its squared Fisher–Rao speed is therefore :<math> v_{\mathrm{FR}}(\theta)^2 = \sum_i \frac{1}{p_i} \left( \frac{dp_i}{d\theta} \right)^2. </math> Substitution gives :<math> v_{\mathrm{FR}}(\theta)^2 = \sum_i p_i(\theta)h_i(\theta)^2. </math> Hence :<math> v_{\mathrm{FR}}(\theta)^2 = \operatorname{Var}_{p(\theta)}(\phi). </math> Therefore :<math> v_{\mathrm{FR}}(\theta) = \sqrt{ \operatorname{Var}_{p(\theta)}(\phi) }. </math> This is the standard Fisher-information identity for a one-parameter exponential family. === 6.5 Square-root representation === Define the square-root map :<math> \Psi: \Delta_{+}^{n-1} \rightarrow \mathbb{R}^{n} </math> by :<math> \Psi(p) = 2(\sqrt{p_1},\ldots,\sqrt{p_n}). </math> Write :<math> q(\theta) = \Psi(p(\theta)). </math> Then :<math> q_i(\theta) = 2\sqrt{p_i(\theta)}. </math> Because :<math> \sum_i p_i(\theta)=1, </math> we have :<math> \sum_iq_i(\theta)^2 = 4. </math> Thus :<math> q(\theta) </math> lies on the positive orthant of the sphere of radius <math>2</math> in <math>\mathbb{R}^{n}</math>. === 6.6 Isometry of the square-root representation === Let <math>u</math> be a tangent vector to the simplex. Differentiating :<math> q_i=2\sqrt{p_i} </math> gives :<math> dq_i = \frac{dp_i}{\sqrt{p_i}}. </math> Therefore the Euclidean squared length of the corresponding tangent displacement on the sphere is :<math> \sum_i(dq_i)^2 = \sum_i \frac{(dp_i)^2}{p_i}. </math> This is precisely the Fisher–Rao line element. Thus the square-root map identifies the Fisher–Rao metric on the simplex interior with the Euclidean metric induced on the positive orthant of the radius-<math>2</math> sphere. Consequently, Fisher–Rao Levi-Civita geodesics correspond locally to great-circle arcs on this sphere. === 6.7 Square-root form of exponential dilation === Substituting the exponential dilation family into the square-root representation gives :<math> q_i(\theta) = \frac{ 2\sqrt{p_i^{(0)}}e^{\theta\phi_i/2} } {\sqrt{Z(\theta)}}. </math> Define the unnormalized square-root vector :<math> r_i(\theta) = \sqrt{p_i^{(0)}}e^{\theta\phi_i/2}. </math> Then :<math> q(\theta) = \frac{2r(\theta)} {\sqrt{Z(\theta)}}. </math> Also, :<math> \|r(\theta)\|^2 = Z(\theta). </math> Hence :<math> q(\theta) = \frac{2r(\theta)} {\|r(\theta)\|}. </math> The normalized square-root trajectory and the unnormalized vector <math>r(\theta)</math> therefore determine the same ray through the origin. This observation allows the Fisher–Rao geodesic question to be reduced to a linear-subspace question in <math>\mathbb{R}^{n}</math>. === 6.8 Distinct generator levels === Suppose the generator <math>\phi</math> assumes exactly <math>m</math> distinct values :<math> a_1,\ldots,a_m. </math> Define the level sets :<math> A_{\ell} = \{i:\phi_i=a_{\ell}\}, </math> for :<math> \ell=1,\ldots,m. </math> For each level, define a vector <math>u_{\ell}</math> by :<math> (u_{\ell})_i = \begin{cases} \sqrt{p_i^{(0)}} & \text{if } i\in A_{\ell},\\ 0 & \text{otherwise}. \end{cases} </math> Because the level sets are disjoint, the vectors :<math> u_1,\ldots,u_m </math> have disjoint supports and are therefore mutually orthogonal. In particular, they are linearly independent. The unnormalized square-root trajectory can now be written as :<math> r(\theta) = \sum_{\ell=1}^{m} e^{a_{\ell}\theta/2} u_{\ell}. </math> This decomposition is central to the geometric characterization developed in the next section. === 6.9 The one-level case === If <math>m=1</math>, then every component of <math>\phi</math> has the same value <math>a</math>. Thus :<math> r(\theta) = e^{a\theta/2}u_1. </math> After normalization, the scalar exponential factor cancels. Therefore :<math> p(\theta)=p^{(0)} </math> for all <math>\theta</math>. The trajectory is constant. This is the degenerate case of exponential dilation. === 6.10 The two-level case === Suppose <math>\phi</math> assumes exactly two distinct values :<math> a </math> and :<math> b, </math> with <math>a\neq b</math>. Then :<math> r(\theta) = e^{a\theta/2}u + e^{b\theta/2}v, </math> where <math>u</math> and <math>v</math> are nonzero orthogonal vectors associated with the two generator levels. Consequently, :<math> r(\theta) \in \operatorname{span}\{u,v\} </math> for every <math>\theta</math>. Since <math>q(\theta)</math> is obtained from <math>r(\theta)</math> by positive scalar normalization, :<math> q(\theta) \in \operatorname{span}\{u,v\} </math> as well. The intersection of a two-dimensional linear subspace through the origin with the radius-<math>2</math> sphere is a great circle. Thus the two-level case naturally produces a Fisher–Rao great-circle trajectory. The formal statement and converse are given in Section 7. === 6.11 Three or more generator levels === If the generator assumes three or more distinct values, then :<math> r(\theta) = \sum_{\ell=1}^{m} e^{a_{\ell}\theta/2}u_{\ell}, </math> with :<math> m\geq3. </math> The vectors <math>u_{\ell}</math> are linearly independent, but this fact alone is not sufficient to conclude that the trajectory spans all <math>m</math> directions. The required result follows from the linear independence of the distinct exponential rates. In Section 7, derivatives of <math>r(\theta)</math> are evaluated at a fixed parameter value. The resulting coefficient matrix is of Vandermonde type and is invertible when the generator levels <math>a_{\ell}</math> are distinct. This shows that a trajectory with <math>m</math> distinct active generator levels spans an <math>m</math>-dimensional linear subspace. Consequently, when <math>m\geq3</math>, the square-root trajectory cannot lie in a two-dimensional great-circle plane. === 6.12 e-geodesic versus Fisher–Rao geodesic === The exponential dilation trajectory is an exponential-family path. In natural coordinates, the parameter <math>\theta</math> enters linearly through :<math> \theta\phi_i. </math> Accordingly, the trajectory is naturally an e-geodesic in the exponential connection of information geometry. The Fisher–Rao Levi-Civita geodesic condition is different. Under the square-root representation, it requires the image of the trajectory to lie on a great-circle arc. Thus the central geometric distinction is: :'''e-geodesic: linearity in exponential-family natural coordinates''' versus :'''Fisher–Rao Levi-Civita geodesic: great-circle geometry under the square-root representation''' The two notions coincide only under additional conditions. === 6.13 Geometric question in linear form === The original probability-geometric question can now be reformulated. Given :<math> r(\theta) = \sum_{\ell=1}^{m} e^{a_{\ell}\theta/2}u_{\ell}, </math> when does the normalized curve :<math> q(\theta) = \frac{2r(\theta)} {\|r(\theta)\|} </math> remain in a fixed two-dimensional linear subspace? If it does, its image lies on a great circle and is therefore a Fisher–Rao Levi-Civita geodesic up to reparameterization. If it does not, the exponential trajectory remains an e-geodesic but is not a Fisher–Rao Levi-Civita geodesic. The next section gives an exact finite-dimensional characterization. == 7. Fisher–Rao Geodesic Characterization == This section gives the principal geometric result of the paper. The question is whether the image of a finite-dimensional exponential dilation trajectory is contained in a Fisher–Rao Levi-Civita geodesic. The parameter <math>\theta</math> itself is not required to be an affine or arclength parameter for that geodesic. === 7.1 Setting and assumptions === Let :<math> p^{(0)} = (p_1^{(0)},\ldots,p_n^{(0)})^{\mathsf{T}} \in \Delta_{+}^{n-1}, </math> so that :<math> p_i^{(0)}>0 </math> for every <math>i</math>. Let :<math> \phi = (\phi_1,\ldots,\phi_n) \in \mathbb{R}^{n}. </math> Define the exponential dilation trajectory :<math> p_i(\theta) = \frac{ p_i^{(0)}e^{\theta\phi_i} } { \sum_{j=1}^{n} p_j^{(0)}e^{\theta\phi_j} }, </math> for :<math> \theta\in\mathbb{R}. </math> Let <math>m</math> denote the number of distinct values assumed by the generator components :<math> \phi_1,\ldots,\phi_n. </math> === 7.2 Theorem 1: two-level Fisher–Rao characterization === '''Theorem 1.''' Under the assumptions above, the image of the exponential dilation trajectory <math>p(\theta)</math> is contained in a Fisher–Rao Levi-Civita geodesic if and only if :<math> m\leq2. </math> Equivalently, the generator <math>\phi</math> must assume at most two distinct values. When <math>m=1</math>, the trajectory is constant. When <math>m=2</math>, the trajectory is nonconstant and its square-root image lies on a great-circle arc. === 7.3 Proof: square-root representation === Define :<math> q_i(\theta) = 2\sqrt{p_i(\theta)}. </math> As shown in Section 6, :<math> q(\theta) </math> lies on the sphere :<math> \sum_iq_i^2=4. </math> The square-root representation is an isometric representation of the Fisher–Rao simplex interior. Therefore the image of <math>p(\theta)</math> is contained in a Fisher–Rao Levi-Civita geodesic if and only if the image of <math>q(\theta)</math> is contained in a great circle of the radius-<math>2</math> sphere. A great circle is the intersection of the sphere with a two-dimensional linear subspace through the origin. === 7.4 Grouping equal generator values === Let the distinct values of <math>\phi</math> be :<math> a_1,\ldots,a_m. </math> For each <math>\ell</math>, define :<math> A_{\ell} = \{i:\phi_i=a_{\ell}\}. </math> Define <math>u_{\ell}\in\mathbb{R}^{n}</math> by :<math> (u_{\ell})_i = \begin{cases} \sqrt{p_i^{(0)}} & \text{if }i\in A_{\ell},\\ 0 & \text{otherwise}. \end{cases} </math> Because the sets <math>A_{\ell}</math> are disjoint and every initial component is strictly positive, the vectors :<math> u_1,\ldots,u_m </math> are nonzero and mutually orthogonal. Hence they are linearly independent. Define the unnormalized square-root trajectory :<math> r(\theta) = \sum_{\ell=1}^{m} e^{a_{\ell}\theta/2} u_{\ell}. </math> Then :<math> q(\theta) = \frac{2r(\theta)} {\|r(\theta)\|}. </math> Since normalization multiplies <math>r(\theta)</math> only by a positive scalar, <math>q(\theta)</math> and <math>r(\theta)</math> lie on the same ray through the origin. === 7.5 Sufficiency: one or two generator levels === Suppose first that :<math> m=1. </math> Then :<math> r(\theta) = e^{a_1\theta/2}u_1. </math> Normalization removes the scalar exponential factor, so :<math> q(\theta) </math> and therefore <math>p(\theta)</math> are constant. A constant trajectory is the degenerate case. Now suppose :<math> m=2. </math> Then :<math> r(\theta) = e^{a_1\theta/2}u_1 + e^{a_2\theta/2}u_2. </math> Therefore :<math> r(\theta) \in \operatorname{span}\{u_1,u_2\} </math> for every <math>\theta</math>. Since <math>q(\theta)</math> differs from <math>r(\theta)</math> only by scalar normalization, :<math> q(\theta) \in \operatorname{span}\{u_1,u_2\}. </math> The vectors <math>u_1</math> and <math>u_2</math> are nonzero and orthogonal, so their span is a two-dimensional linear subspace through the origin. Its intersection with the radius-<math>2</math> sphere is a great circle. Thus the image of the two-level exponential dilation trajectory lies on a Fisher–Rao Levi-Civita geodesic. This proves sufficiency. === 7.6 Necessity: derivative span === Now suppose the generator assumes :<math> m\geq3 </math> distinct values. Differentiate the unnormalized square-root trajectory: :<math> r(\theta) = \sum_{\ell=1}^{m} e^{a_{\ell}\theta/2} u_{\ell}. </math> For every nonnegative integer <math>k</math>, :<math> r^{(k)}(\theta) = \sum_{\ell=1}^{m} \left( \frac{a_{\ell}}{2} \right)^k e^{a_{\ell}\theta/2} u_{\ell}. </math> Fix any :<math> \theta_0\in\mathbb{R}. </math> Consider the vectors :<math> r(\theta_0), r^{(1)}(\theta_0), \ldots, r^{(m-1)}(\theta_0). </math> Their coefficients relative to the basis :<math> u_1,\ldots,u_m </math> form the matrix :<math> C_{k\ell} = \left( \frac{a_{\ell}}{2} \right)^k e^{a_{\ell}\theta_0/2}, </math> where :<math> k=0,\ldots,m-1 </math> and :<math> \ell=1,\ldots,m. </math> === 7.7 Vandermonde argument === Factor the nonzero quantity :<math> e^{a_{\ell}\theta_0/2} </math> from column <math>\ell</math> of the coefficient matrix. The remaining matrix has entries :<math> V_{k\ell} = \left( \frac{a_{\ell}}{2} \right)^k. </math> This is a Vandermonde matrix. Its determinant is nonzero because :<math> a_1,\ldots,a_m </math> are distinct. Therefore the coefficient matrix <math>C</math> is invertible. It follows that :<math> r(\theta_0), r^{(1)}(\theta_0), \ldots, r^{(m-1)}(\theta_0) </math> are linearly independent. Consequently, the linear span generated by the trajectory <math>r(\theta)</math> has dimension at least <math>m</math>. On the other hand, the representation :<math> r(\theta) = \sum_{\ell=1}^{m} e^{a_{\ell}\theta/2}u_{\ell} </math> shows that the trajectory is contained in :<math> \operatorname{span} \{u_1,\ldots,u_m\}, </math> which has dimension <math>m</math>. Hence :<math> \dim \operatorname{span} \{r(\theta):\theta\in\mathbb{R}\} = m. </math> === 7.8 Exclusion of three or more levels === If the square-root trajectory <math>q(\theta)</math> were contained in a great circle, then there would exist a two-dimensional linear subspace <math>W</math> through the origin such that :<math> q(\theta)\in W </math> for every <math>\theta</math>. Since :<math> r(\theta) = \frac{\|r(\theta)\|}{2} q(\theta), </math> the same subspace would contain :<math> r(\theta) </math> for every <math>\theta</math>. Therefore :<math> \dim \operatorname{span} \{r(\theta):\theta\in\mathbb{R}\} \leq2. </math> But Section 7.7 gives :<math> \dim \operatorname{span} \{r(\theta):\theta\in\mathbb{R}\} = m. </math> Thus a great-circle trajectory requires :<math> m\leq2. </math> For :<math> m\geq3, </math> the exponential dilation trajectory cannot be contained in a Fisher–Rao Levi-Civita geodesic. This proves necessity. === 7.9 Conclusion of the proof === Combining Sections 7.5 and 7.8 gives :<math> m\leq2 </math> if and only if the image of the exponential dilation trajectory is contained in a Fisher–Rao Levi-Civita geodesic. Therefore the generator <math>\phi</math> must assume at most two distinct values. This completes the proof. === 7.10 Corollary 1: dimension of the square-root trajectory === '''Corollary 1.''' Under the assumptions of Theorem 1, if the generator <math>\phi</math> assumes exactly <math>m</math> distinct values, then :<math> \dim \operatorname{span} \{r(\theta):\theta\in\mathbb{R}\} = m. </math> Thus the number of distinct generator levels is exactly the dimension of the linear subspace generated by the unnormalized square-root exponential trajectory. '''Proof.''' The vectors <math>u_1,\ldots,u_m</math> are linearly independent, and Section 7.7 shows through the Vandermonde argument that the trajectory spans all of these directions. Therefore its span has dimension <math>m</math>. === 7.11 Corollary 2: three-level obstruction === '''Corollary 2.''' If a strictly positive finite exponential dilation trajectory has a generator assuming three or more distinct values, then its image is not contained in a Fisher–Rao Levi-Civita geodesic. This follows immediately from Theorem 1. The result is exact under the stated hypotheses; it is not merely a generic non-geodesicity statement. === 7.12 Parameterization versus geodesic image === Theorem 1 concerns the image of the trajectory. Even in the two-level case, the exponential parameter <math>\theta</math> is generally not proportional to Fisher–Rao arclength. Thus :<math> p(\theta) </math> traces a Fisher–Rao geodesic path but generally does so with nonconstant Fisher–Rao speed. From Section 6, :<math> \frac{ds}{d\theta} = \sqrt{ \operatorname{Var}_{p(\theta)}(\phi) }. </math> Section 8 derives the exact change of parameter from <math>\theta</math> to Fisher–Rao arclength in the nondegenerate two-level case. === 7.13 Geometric interpretation === The theorem can be understood through the square-root sphere. A generator with one distinct value produces no probability motion. A generator with two distinct values produces two independent exponential directions, :<math> e^{a\theta/2}u </math> and :<math> e^{b\theta/2}v. </math> Their normalized sum remains in a fixed two-dimensional plane through the origin, so its spherical image follows a great circle. With three or more distinct generator values, the trajectory necessarily spans three or more independent linear directions. It therefore cannot remain in any two-dimensional great-circle plane. The distinction between the two-level and multilevel cases is consequently a dimensional property of the exponential rates under the square-root representation. === 7.14 Relation to information-geometric straightness === Theorem 1 does not state that exponential trajectories with three or more levels cease to be e-geodesics. They remain exponential-family trajectories and retain their standard information-geometric interpretation with respect to the e-connection. Rather, the theorem characterizes when this e-geodesic image also coincides with a geodesic image of the Levi-Civita connection associated with the Fisher–Rao metric. Thus the result concerns the coincidence of two distinct notions of geometric straightness. === 7.15 Status of the characterization === The proof above uses established ingredients: * the exponential-family representation; * the Fisher–Rao square-root embedding; * the great-circle characterization of spherical geodesics; * linear independence of vectors with disjoint support; * the Vandermonde determinant. The particular characterization obtained by combining these ingredients is presented here as a result of the present analysis. At this draft stage, no claim of historical priority is made. A complete literature review and independent mathematical scrutiny remain appropriate before describing the characterization as novel. The next section derives an explicit Fisher–Rao arclength parameterization for the nondegenerate two-level case. == Relationship to the Probability Dilation Theory project == This manuscript is part of the broader [[Probability Dilation Theory]] research project on Wikiversity. Technical and exploratory material related to the manuscript is developed on associated PDT subpages, including: * [[Probability Dilation Theory/Measure-Theoretic Foundations|Measure-Theoretic Foundations]] * [[Probability Dilation Theory/Matrix Dilation Operators|Matrix Dilation Operators]] * [[Probability Dilation Theory/Dilation Vector Field|Dilation Vector Field]] * [[Probability Dilation Theory/Dilation Flows|Dilation Flows]] * [[Probability Dilation Theory/Convergence and Fixed Points|Convergence and Fixed Points]] * [[Probability Dilation Theory/Fisher Geometry and Dilation Flows|Fisher Geometry and Dilation Flows]] The present page is intended to develop a concise, standalone manuscript rather than reproduce the complete exploratory PDT project. == Draft status and research note == This manuscript is a work in progress. Some constructions discussed in the paper have direct counterparts in established mathematical literature. These relationships are identified explicitly wherever possible. Results developed specifically within the present formulation are being subjected to continuing literature review, proof checking, numerical verification, and independent mathematical scrutiny before any claim of novelty is made. Readers are encouraged to identify relevant prior literature, mathematical errors, counterexamples, alternative proofs, or useful extensions. == See also == * [[Probability Dilation Theory]] * [[Probability Dilation Theory/Matrix Dilation Operators]] * [[Probability Dilation Theory/Measure-Theoretic Foundations]] * [[Probability Dilation Theory/Fisher Geometry and Dilation Flows]] == Copyright and licensing == Text and original figures © Howard Richardson. Licensed under the [https://creativecommons.org/licenses/by/4.0/ Creative Commons Attribution 4.0 International License (CC BY 4.0)]. Reuse permitted with attribution. 3d7ljqe1vhvu89jvt5mn7qosfhg8s8j 2823784 2823783 2026-08-21T01:45:14Z Howie2024 2995240 /* 7.15 Status of the characterization */ Insert section 8. 2823784 wikitext text/x-wiki {{Research project}} '''Research manuscript — Draft Version 1.0''' ''This page develops a standalone research manuscript arising from the [[Probability Dilation Theory]] project. It is a work in progress and should not be regarded as a peer-reviewed publication.'' = Normalized Probability Dilation: A Unified Framework and Its Fisher–Rao Geometry = '''Howard Richardson''' ''Draft Version 1.0 — August 2026'' == Abstract == This paper develops a unified framework for normalized positive transformations of probability distributions, referred to here as '''Probability Dilation Theory (PDT)'''. The central construction consists of applying a positive transformation to a probability state and subsequently renormalizing the result. In finite dimensions this includes diagonal reweighting, :<math> p_i'= \frac{d_i p_i} {\sum_j d_jp_j}, </math> and the matrix transformation :<math> T_M(p)= \frac{Mp} {\mathbf{1}^{\mathsf T}Mp}, </math> for suitable nonnegative matrices <math>M</math>. A corresponding measure-theoretic formulation is :<math> P_D(A)= \frac{\int_A D\,dP} {\int_X D\,dP}. </math> These constructions are compared explicitly with established mathematical structures including change of measure, normalized positive operators, Perron–Frobenius iteration, Markov operators, replicator-type dynamics, and normalized Feynman–Kac transformations. The purpose of the framework is therefore not to claim these established constructions as new, but to investigate their common dilation-normalization structure and the geometry of the resulting probability trajectories. Particular attention is given to the exponential dilation family :<math> p_i(\theta)= \frac{p_i^{(0)}e^{\theta\phi_i}} {\sum_j p_j^{(0)}e^{\theta\phi_j}}. </math> Using the square-root representation of the Fisher–Rao simplex, we establish that, under finite-dimensional strict-positivity assumptions, the image of this exponential-dilation trajectory is contained in a Fisher–Rao Levi-Civita geodesic, up to reparameterization, if and only if the generator <math>\phi</math> assumes at most two distinct values. An explicit Fisher–Rao arclength parameterization is then obtained for the nondegenerate two-level case. The framework provides a common language for normalized probability transformations while separating results inherited from established theory from geometric properties arising from the particular dilation formulation. == 1. Introduction == Probability distributions are frequently transformed by operations having a common mathematical structure: nonnegative weights are modified by a positive transformation and subsequently normalized so that total probability remains unity. Such constructions occur in numerous areas of probability, statistics, dynamical systems, numerical linear algebra, and mathematical physics. The simplest finite-dimensional example takes a probability vector :<math> p=(p_1,\ldots,p_n)^{\mathsf T}, \qquad p_i\geq 0, \qquad \sum_{i=1}^{n}p_i=1, </math> assigns positive weights <math>d_i</math>, and defines :<math> p_i'= \frac{d_i p_i} {\sum_{j=1}^{n}d_jp_j}. </math> The transformation changes the relative probability assigned to individual states while normalization returns the resulting vector to the probability simplex. This paper uses the term '''probability dilation''' for this general transformation-and-normalization structure and examines a hierarchy of related constructions. In finite dimensions, diagonal dilation extends naturally to the action of a nonnegative matrix, :<math> T_M(p)= \frac{Mp} {\mathbf{1}^{\mathsf T}Mp}, </math> whenever the denominator is positive. At the level of probability measures, multiplication by a positive measurable function <math>D</math> gives :<math> P_D(A)= \frac{\displaystyle\int_A D(x)\,dP(x)} {\displaystyle\int_X D(x)\,dP(x)}. </math> These expressions have substantial connections with existing mathematics. Normalized matrix iteration is closely related to the power method and Perron–Frobenius theory; positive weighting of measures belongs to established change-of-measure constructions; stochastic matrices provide the familiar Markov special case; and normalized potential-weighted measures occur in Feynman–Kac models. Accordingly, the objective of PDT as developed here is '''not''' to rename these established mathematical theories or to assert novelty for normalization itself. Instead, the objective is to examine them through the common structural sequence :<math> \text{positive transformation} \longrightarrow \text{normalization} \longrightarrow \text{iteration} \longrightarrow \text{probability dynamics} \longrightarrow \text{geometry}. </math> This viewpoint leads naturally to questions concerning fixed points, convergence, entropy, state-dependent transformations, and the geometry of trajectories on the probability simplex. === 1.1 Exponential dilation === A particularly useful example is obtained from exponential dilation. Given an initial strictly positive probability vector <math>p^{(0)}</math> and a real-valued generator <math>\phi</math>, define :<math> p_i(\theta)= \frac{p_i^{(0)}e^{\theta\phi_i}} {Z(\theta)}, </math> where :<math> Z(\theta)= \sum_j p_j^{(0)}e^{\theta\phi_j}. </math> This is an exponential-family construction and therefore belongs to well-established information geometry. The question considered here is more specific: :''When is this exponential trajectory also a Levi-Civita geodesic of the Fisher–Rao metric?'' The Fisher–Rao geometry of a finite probability simplex admits a square-root representation on a sphere. Under the mapping :<math> p\longmapsto 2(\sqrt{p_1},\ldots,\sqrt{p_n}), </math> Fisher–Rao geodesics correspond to spherical great-circle arcs. This representation permits a direct characterization of exponential dilation trajectories that are simultaneously Fisher–Rao geodesic. === 1.2 Principal geometric result === The principal geometric result developed below is that, for a strictly positive finite probability vector, an exponential dilation trajectory lies on a Fisher–Rao geodesic, up to reparameterization, precisely when its generator assumes no more than two distinct values. The proof reduces the problem to the dimension of the linear span generated by distinct exponential rates and uses a Vandermonde argument for the converse. The resulting two-level trajectory also admits an explicit Fisher–Rao arclength parameterization. At the present draft stage, this characterization is treated conservatively. Its constituent mathematical ingredients are established results from information geometry and linear algebra. The exact characterization developed here remains subject to further literature review and independent mathematical scrutiny. === 1.3 Organization of the paper === The remainder of the paper is organized as follows: * '''Section 2''' introduces the normalized-dilation framework and notation. * '''Section 3''' develops diagonal and matrix formulations. * '''Section 4''' develops the measure-theoretic formulation. * '''Section 5''' compares the framework explicitly with established mathematics. * '''Section 6''' introduces exponential dilation and its information-geometric representation. * '''Section 7''' states and proves the Fisher–Rao geodesic characterization theorem. * '''Section 8''' derives the two-level Fisher–Rao arclength corollary and illustrative examples. * '''Section 9''' discusses limitations, possible extensions, and open problems. * '''Section 10''' summarizes the principal conclusions. == 2. Normalized-Dilation Framework == This section introduces the common mathematical structure used throughout the paper. The essential operation consists of applying a positive transformation to a probability state and then normalizing the transformed object so that it again represents a probability distribution. === 2.1 Probability simplex === For a finite state space with <math>n</math> states, define the probability simplex :<math> \Delta^{n-1} = \left\{ p\in\mathbb{R}^{n}: p_i\geq 0,\; \sum_{i=1}^{n}p_i=1 \right\}. </math> A probability state is represented by a column vector :<math> p= (p_1,\ldots,p_n)^{\mathsf{T}} \in\Delta^{n-1}. </math> Its components satisfy :<math> p_i\geq 0 </math> and :<math> \mathbf{1}^{\mathsf{T}}p=1, </math> where :<math> \mathbf{1} = (1,\ldots,1)^{\mathsf{T}}. </math> The interior of the simplex is :<math> \Delta_{+}^{n-1} = \left\{ p\in\Delta^{n-1}:p_i>0 \text{ for all }i \right\}. </math> The distinction between the simplex and its interior becomes important later when Fisher–Rao geometry is considered. === 2.2 Positive transformations === Let <math>\mathcal{L}</math> denote a transformation acting on probability states such that :<math> p\geq 0 \quad\Longrightarrow\quad \mathcal{L}(p)\geq 0. </math> The transformed object <math>\mathcal{L}(p)</math> need not itself be normalized. Define its total mass by :<math> \mathcal{N}[\mathcal{L}(p)] = \mathbf{1}^{\mathsf{T}}\mathcal{L}(p). </math> Whenever :<math> 0< \mathcal{N}[\mathcal{L}(p)] < \infty, </math> the normalized transformation is defined by :<math> \mathcal{T}_{\mathcal{L}}(p) = \frac{\mathcal{L}(p)} {\mathcal{N}[\mathcal{L}(p)]}. </math> Equivalently, in the finite-dimensional setting, :<math> \mathcal{T}_{\mathcal{L}}(p) = \frac{\mathcal{L}(p)} {\mathbf{1}^{\mathsf{T}}\mathcal{L}(p)}. </math> By construction, :<math> \mathbf{1}^{\mathsf{T}} \mathcal{T}_{\mathcal{L}}(p) = 1, </math> so :<math> \mathcal{T}_{\mathcal{L}}(p) \in \Delta^{n-1}. </math> This positive-transformation-plus-normalization operation is the basic structure referred to in this paper as '''normalized probability dilation'''. === 2.3 Normalization as projectivization === An immediate property of the normalized transformation is invariance under multiplication by a positive scalar. If <math>c>0</math>, then :<math> \frac{c\mathcal{L}(p)} {\mathbf{1}^{\mathsf{T}}c\mathcal{L}(p)} = \frac{\mathcal{L}(p)} {\mathbf{1}^{\mathsf{T}}\mathcal{L}(p)}. </math> Hence :<math> \mathcal{T}_{c\mathcal{L}}(p) = \mathcal{T}_{\mathcal{L}}(p). </math> The normalized transformation therefore depends on the relative components of <math>\mathcal{L}(p)</math>, rather than on its overall positive scale. This projective feature connects normalized dilation with established theories of positive operators and projective dynamics. No claim of novelty is attached to the normalization or projectivization operation itself. === 2.4 Diagonal dilation === Let :<math> D= \operatorname{diag}(d_1,\ldots,d_n), \qquad d_i>0. </math> Applying <math>D</math> to <math>p</math> gives :<math> Dp= (d_1p_1,\ldots,d_np_n)^{\mathsf{T}}. </math> Normalization produces :<math> T_D(p) = \frac{Dp} {\mathbf{1}^{\mathsf{T}}Dp}. </math> Componentwise, :<math> T_D(p)_i = \frac{d_ip_i} {\sum_{j=1}^{n}d_jp_j}. </math> This is the basic finite-dimensional dilation operation from which the broader PDT formulation developed. The factors <math>d_i</math> alter the relative weights of the probability states, while the denominator restores unit total probability. === 2.5 Matrix dilation === The diagonal transformation can be generalized to a nonnegative matrix :<math> M\in\mathbb{R}^{n\times n}, \qquad M_{ij}\geq 0. </math> For any probability vector <math>p</math> satisfying :<math> \mathbf{1}^{\mathsf{T}}Mp>0, </math> define :<math> T_M(p) = \frac{Mp} {\mathbf{1}^{\mathsf{T}}Mp}. </math> The diagonal case is recovered when :<math> M=D. </math> Off-diagonal entries permit components of the input probability vector to contribute to different output components before normalization. The matrix formulation therefore extends independent componentwise reweighting to coupled positive transformations. The mathematical behavior of this construction is closely related to established positive-matrix theory, normalized power iteration, and Perron–Frobenius theory. These relationships are discussed explicitly in Section 5. === 2.6 Measure-theoretic dilation === The same normalization principle extends naturally from finite probability vectors to probability measures. Let <math>(X,\mathcal{F},P)</math> be a probability space, and let :<math> D:X\rightarrow[0,\infty) </math> be measurable with :<math> 0< \int_X D(x)\,dP(x) < \infty. </math> Define a new probability measure <math>P_D</math> by :<math> P_D(A) = \frac{\displaystyle\int_A D(x)\,dP(x)} {\displaystyle\int_X D(x)\,dP(x)}, \qquad A\in\mathcal{F}. </math> Equivalently, the Radon–Nikodym derivative of <math>P_D</math> with respect to <math>P</math> is :<math> \frac{dP_D}{dP} = \frac{D} {\displaystyle\int_X D\,dP}. </math> Thus the finite-dimensional rule :<math> p_i \longmapsto \frac{d_ip_i} {\sum_jd_jp_j} </math> and the measure-theoretic rule :<math> dP \longmapsto \frac{D\,dP} {\int_XD\,dP} </math> share the same normalized positive-reweighting structure. This construction has direct connections with established change-of-measure and weighted-measure theory. The PDT terminology is used here as an organizing framework rather than as a claim that normalized change of measure is itself new. === 2.7 Iterated dilation === A normalized dilation operator can be iterated. Given an initial state :<math> p^{(0)}\in\Delta^{n-1}, </math> define :<math> p^{(k+1)} = \mathcal{T}_{\mathcal{L}}\left(p^{(k)}\right). </math> This generates an orbit :<math> p^{(0)} \longmapsto p^{(1)} \longmapsto p^{(2)} \longmapsto \cdots </math> on the probability simplex. For a fixed matrix <math>M</math>, :<math> p^{(k+1)} = \frac{Mp^{(k)}} {\mathbf{1}^{\mathsf{T}}Mp^{(k)}}. </math> When all required denominators are positive, repeated normalization gives :<math> p^{(k)} = \frac{M^k p^{(0)}} {\mathbf{1}^{\mathsf{T}}M^k p^{(0)}}. </math> The long-term behavior of this iteration is governed in important cases by established spectral and Perron–Frobenius theory. More general formulations may allow the transformation itself to depend on the iteration index or the current probability state, for example :<math> p^{(k+1)} = \frac{M_kp^{(k)}} {\mathbf{1}^{\mathsf{T}}M_kp^{(k)}} </math> or :<math> p^{(k+1)} = \frac{M(p^{(k)})p^{(k)}} {\mathbf{1}^{\mathsf{T}}M(p^{(k)})p^{(k)}}. </math> These state-dependent and iteration-dependent forms are treated as possible extensions rather than necessary components of the basic framework. === 2.8 Hierarchy of normalized dilation === The constructions above can be summarized by the following hierarchy: :'''diagonal reweighting → matrix transformation → positive operator → measure transformation''' At each level the essential operation is: :'''positive transformation + normalization''' The framework is deliberately broad. Its purpose is not to imply that all normalized positive transformations constitute a new mathematical theory, but to provide a common notation and viewpoint from which their dynamics and geometry can be compared. The following sections specialize this framework before examining its relationship to established mathematical constructions. == 3. Finite-Dimensional and Matrix Dilation == This section develops the finite-dimensional forms of normalized probability dilation in greater detail. The emphasis is on the relationship between diagonal reweighting and nonnegative matrix transformations, together with the basic structural properties required later in the paper. === 3.1 Finite probability states === Let :<math> p=(p_1,\ldots,p_n)^{\mathsf{T}} \in\Delta^{n-1}. </math> A positive weighting vector is written :<math> d=(d_1,\ldots,d_n)^{\mathsf{T}}, \qquad d_i>0. </math> The associated diagonal matrix is :<math> D= \operatorname{diag}(d_1,\ldots,d_n). </math> Applying the weighting gives :<math> Dp= (d_1p_1,\ldots,d_np_n)^{\mathsf{T}}. </math> Its total mass is :<math> Z(p,D) = \mathbf{1}^{\mathsf{T}}Dp = \sum_{i=1}^{n}d_ip_i. </math> Since <math>d_i>0</math> and <math>p</math> is a probability vector, :<math> Z(p,D)>0. </math> The normalized diagonal dilation operator is therefore :<math> T_D(p) = \frac{Dp}{Z(p,D)}. </math> Equivalently, :<math> T_D(p)_i = \frac{d_ip_i} {\sum_{j=1}^{n}d_jp_j}. </math> === 3.2 Relative probability transformation === Diagonal dilation has a simple effect on probability ratios. For any states <math>i</math> and <math>j</math> with <math>p_i>0</math> and <math>p_j>0</math>, :<math> \frac{T_D(p)_i}{T_D(p)_j} = \frac{d_i}{d_j} \frac{p_i}{p_j}. </math> Thus normalization does not alter the relative dilation introduced by the factors <math>d_i</math> and <math>d_j</math>. If :<math> d_i>d_j, </math> then the odds of state <math>i</math> relative to state <math>j</math> increase by the factor :<math> \frac{d_i}{d_j}. </math> This ratio form makes clear that diagonal dilation is fundamentally a relative reweighting operation. === 3.3 Scale invariance === Multiplying every dilation factor by the same positive constant does not change the normalized state. Let :<math> c>0. </math> Then :<math> T_{cD}(p) = \frac{cDp} {\mathbf{1}^{\mathsf{T}}cDp} = \frac{Dp} {\mathbf{1}^{\mathsf{T}}Dp} = T_D(p). </math> Therefore only the relative values of the dilation factors affect the transformed probability distribution. This scale invariance is a basic projective property of normalized positive transformations. === 3.4 Repeated diagonal dilation === Suppose the same diagonal operator <math>D</math> is applied repeatedly. Starting from <math>p^{(0)}</math>, define :<math> p^{(k+1)} = T_D(p^{(k)}). </math> Then :<math> p^{(k)} = \frac{D^k p^{(0)}} {\mathbf{1}^{\mathsf{T}}D^k p^{(0)}}. </math> Since :<math> D^k = \operatorname{diag}(d_1^k,\ldots,d_n^k), </math> the individual components are :<math> p_i^{(k)} = \frac{d_i^k p_i^{(0)}} {\sum_{j=1}^{n}d_j^k p_j^{(0)}}. </math> Consequently, for two initially positive components, :<math> \frac{p_i^{(k)}}{p_j^{(k)}} = \left(\frac{d_i}{d_j}\right)^k \frac{p_i^{(0)}}{p_j^{(0)}}. </math> This expression describes the concentration mechanism directly. If one dilation factor is strictly larger than all others and its corresponding initial probability is positive, repeated dilation concentrates probability on that state. If several states share the maximal dilation factor, probability concentrates on that maximal set while preserving the initial relative proportions within that set. This behavior is a direct consequence of normalized repeated weighting and is not specific to PDT terminology. === 3.5 General nonnegative matrix transformation === Let :<math> M=(M_{ij}) \in\mathbb{R}^{n\times n}, \qquad M_{ij}\geq0. </math> For <math>p\in\Delta^{n-1}</math>, define :<math> q=Mp. </math> Because <math>M</math> and <math>p</math> are nonnegative, :<math> q_i\geq0. </math> Whenever :<math> \mathbf{1}^{\mathsf{T}}Mp>0, </math> the normalized matrix dilation operator is :<math> T_M(p) = \frac{Mp} {\mathbf{1}^{\mathsf{T}}Mp}. </math> Its components are :<math> T_M(p)_i = \frac{\sum_{j=1}^{n}M_{ij}p_j} {\sum_{r=1}^{n}\sum_{j=1}^{n}M_{rj}p_j}. </math> By construction, :<math> \sum_{i=1}^{n}T_M(p)_i=1. </math> Hence :<math> T_M(p)\in\Delta^{n-1}. </math> === 3.6 Diagonal dilation as a special case === If :<math> M=D = \operatorname{diag}(d_1,\ldots,d_n), </math> then :<math> Mp=Dp, </math> and therefore :<math> T_M(p)=T_D(p). </math> Diagonal dilation is thus a special case of normalized matrix dilation. The distinction is structural. For a diagonal matrix, each output component depends only on the corresponding input component: :<math> (Dp)_i=d_ip_i. </math> For a general matrix, :<math> (Mp)_i = \sum_{j=1}^{n}M_{ij}p_j, </math> so multiple input states may contribute to a single output state before normalization. This permits coupled probability evolution. === 3.7 When normalization is unnecessary === There is an important special case. Suppose <math>M</math> satisfies :<math> \mathbf{1}^{\mathsf{T}}M = \mathbf{1}^{\mathsf{T}}. </math> Then for every probability vector <math>p</math>, :<math> \mathbf{1}^{\mathsf{T}}Mp = \mathbf{1}^{\mathsf{T}}p = 1. </math> Consequently, :<math> T_M(p)=Mp. </math> With the column-vector convention used in this paper, the condition :<math> \mathbf{1}^{\mathsf{T}}M = \mathbf{1}^{\mathsf{T}} </math> means that the columns of <math>M</math> sum to one. Thus an ordinary probability-preserving linear transition is contained as a special case of the normalized matrix framework. When <math>M</math> does not preserve total mass, normalization supplies the additional step required to return <math>Mp</math> to the simplex. === 3.8 Fixed points and eigenvectors === Suppose <math>p^{*}</math> is a fixed point of the normalized matrix operator: :<math> T_M(p^{*})=p^{*}. </math> Then :<math> \frac{Mp^{*}} {\mathbf{1}^{\mathsf{T}}Mp^{*}} = p^{*}. </math> Multiplying by the denominator gives :<math> Mp^{*} = \lambda p^{*}, </math> where :<math> \lambda = \mathbf{1}^{\mathsf{T}}Mp^{*}. </math> Therefore every fixed point of the normalized matrix transformation is a nonnegative eigenvector of <math>M</math>, normalized to have unit total mass. Conversely, if <math>v\geq0</math> is a nonzero eigenvector satisfying :<math> Mv=\lambda v, \qquad \lambda>0, </math> then :<math> p^{*} = \frac{v} {\mathbf{1}^{\mathsf{T}}v} </math> is a fixed point of <math>T_M</math>. Thus normalized fixed points and positive eigenvectors are directly related. === 3.9 Repeated matrix dilation === For a fixed nonnegative matrix <math>M</math>, define :<math> p^{(k+1)} = T_M(p^{(k)}). </math> Whenever the required denominators remain positive, :<math> p^{(k)} = \frac{M^k p^{(0)}} {\mathbf{1}^{\mathsf{T}}M^k p^{(0)}}. </math> This identity follows because the scalar normalization introduced at each intermediate step cancels under the next normalization. The iteration is therefore closely related to normalized power iteration. Under suitable positivity or primitivity assumptions, Perron–Frobenius theory describes the dominant eigenvalue and positive eigenvector governing the long-term behavior. Accordingly, convergence of the fixed-matrix case should be understood primarily through established positive-matrix and spectral theory rather than as a separate PDT convergence mechanism. === 3.10 Primitive positive matrices === A particularly important case occurs when <math>M</math> is primitive; that is, some positive integer power of <math>M</math> has strictly positive entries. Perron–Frobenius theory then provides a dominant real eigenvalue :<math> \rho(M)>0 </math> with a corresponding strictly positive eigenvector <math>v</math>. After normalization, :<math> p^{*} = \frac{v} {\mathbf{1}^{\mathsf{T}}v}, </math> this eigenvector gives the distinguished interior fixed point of the normalized matrix transformation. For suitable initial probability vectors, :<math> T_M^{k}(p^{(0)}) </math> converges toward <math>p^{*}</math>. This convergence is an established consequence of Perron–Frobenius theory and normalized power iteration. Its role here is to locate matrix dilation within known mathematics. === 3.11 Interpretation of off-diagonal terms === The off-diagonal entries of <math>M</math> distinguish matrix dilation from independent diagonal reweighting. For :<math> i\neq j, </math> a term :<math> M_{ij}p_j </math> represents a contribution from input state <math>j</math> to output component <math>i</math> before normalization. The matrix therefore combines two operations: * positive redistribution or coupling through <math>M</math>; * restoration of unit total probability through normalization. This interpretation is useful for organizing the framework, but the underlying linear transformation remains standard matrix mathematics. === 3.12 Scope of the matrix formulation === The matrix formulation substantially enlarges the class of transformations expressible within the normalized-dilation notation, but that enlargement should not be confused with mathematical novelty. For a fixed matrix <math>M</math>, the central objects :<math> Mp, \qquad M^kp, \qquad \rho(M), </math> and the associated eigenvectors and convergence properties belong to established linear algebra and positive-operator theory. The role of the PDT framework is to place diagonal reweighting, matrix transformation, iteration, and later measure-theoretic and geometric constructions within a common normalized-probability notation. This distinction between '''framework''' and '''new mathematical result''' will be maintained throughout the paper. == 4. Measure-Theoretic Dilation == The finite-dimensional dilation rule extends naturally to probability measures. In this setting, componentwise multiplication by positive weights is replaced by multiplication of a probability measure by a nonnegative measurable function followed by normalization. This formulation places finite probability dilation within the standard language of measure theory and makes its relationship to change of measure explicit. === 4.1 Probability-space formulation === Let :<math> (X,\mathcal{F},P) </math> be a probability space. Let :<math> D:X\rightarrow[0,\infty) </math> be a measurable function satisfying :<math> 0< \int_X D(x)\,dP(x) < \infty. </math> Define the normalization factor :<math> Z(P,D) = \int_X D(x)\,dP(x). </math> For every measurable set :<math> A\in\mathcal{F}, </math> define :<math> P_D(A) = \frac{\displaystyle\int_A D(x)\,dP(x)} {Z(P,D)}. </math> Equivalently, :<math> P_D(A) = \frac{\displaystyle\int_A D(x)\,dP(x)} {\displaystyle\int_X D(x)\,dP(x)}. </math> The function <math>D</math> acts as a nonnegative weighting or dilation field over the probability space. === 4.2 Normalization === The transformed measure has total mass one because :<math> P_D(X) = \frac{\displaystyle\int_X D(x)\,dP(x)} {\displaystyle\int_X D(x)\,dP(x)} = 1. </math> Also, because <math>D</math> is nonnegative, :<math> P_D(A)\geq0 </math> for every <math>A\in\mathcal{F}</math>. Countable additivity follows from the countable additivity of integration with respect to <math>P</math>. Therefore <math>P_D</math> is a probability measure. === 4.3 Radon–Nikodym representation === The transformed measure <math>P_D</math> is absolutely continuous with respect to <math>P</math>. Its Radon–Nikodym derivative is :<math> \frac{dP_D}{dP}(x) = \frac{D(x)} {\displaystyle\int_X D(y)\,dP(y)}. </math> Thus normalized measure dilation can be written formally as :<math> dP_D(x) = \frac{D(x)\,dP(x)} {\displaystyle\int_X D(y)\,dP(y)}. </math> This expression makes clear that the construction is a normalized change of measure. The Radon–Nikodym framework is established measure theory. The terminology of dilation is used here to emphasize the common transformation-and-normalization structure shared with the finite-dimensional formulation. === 4.4 Scale invariance === As in the finite-dimensional case, multiplication of the dilation field by a positive constant does not change the normalized measure. Let :<math> c>0. </math> Then :<math> P_{cD}(A) = \frac{\displaystyle\int_A cD\,dP} {\displaystyle\int_X cD\,dP}. </math> The common factor cancels, giving :<math> P_{cD}(A)=P_D(A). </math> Hence the transformed probability measure depends only on the relative values of the dilation field <math>D</math>, not on its overall positive scale. === 4.5 Finite probability spaces as a special case === Consider a finite state space :<math> X=\{1,\ldots,n\}. </math> Let :<math> P(\{i\})=p_i </math> and define :<math> D(i)=d_i. </math> Then :<math> \int_X D\,dP = \sum_{j=1}^{n}d_jp_j. </math> For the singleton event <math>\{i\}</math>, :<math> P_D(\{i\}) = \frac{d_ip_i} {\sum_{j=1}^{n}d_jp_j}. </math> Thus the finite diagonal dilation rule :<math> p_i' = \frac{d_ip_i} {\sum_jd_jp_j} </math> is recovered exactly from the measure-theoretic construction. The discrete and measure-theoretic formulations are therefore instances of the same normalized positive-reweighting operation. === 4.6 Expectations under dilation === Let :<math> f:X\rightarrow\mathbb{R} </math> be measurable and integrable with respect to the transformed measure. Then :<math> \mathbb{E}_{P_D}[f] = \int_X f(x)\,dP_D(x). </math> Using the Radon–Nikodym representation, :<math> \mathbb{E}_{P_D}[f] = \frac{\displaystyle\int_X f(x)D(x)\,dP(x)} {\displaystyle\int_X D(x)\,dP(x)}. </math> Equivalently, :<math> \mathbb{E}_{P_D}[f] = \frac{\mathbb{E}_{P}[fD]} {\mathbb{E}_{P}[D]}, </math> provided the required expectations exist. This identity is a standard weighted-expectation formula and will later be useful for exponential dilation. === 4.7 Composition of dilation fields === Suppose a first dilation field <math>D_1</math> transforms <math>P</math> into <math>P_{D_1}</math>, and a second field <math>D_2</math> is then applied. The first transformation gives :<math> dP_{D_1} = \frac{D_1\,dP} {\int_XD_1\,dP}. </math> Applying <math>D_2</math> gives :<math> d(P_{D_1})_{D_2} = \frac{D_2\,dP_{D_1}} {\int_XD_2\,dP_{D_1}}. </math> Substituting the first transformation and simplifying yields :<math> d(P_{D_1})_{D_2} = \frac{D_1D_2\,dP} {\int_XD_1D_2\,dP}, </math> whenever the required integrals are finite and positive. Therefore :<math> (P_{D_1})_{D_2} = P_{D_1D_2}. </math> Sequential scalar dilation fields thus combine multiplicatively before normalization. This composition property is the measure-theoretic analogue of repeated diagonal reweighting. === 4.8 Iterated fixed dilation === If the same dilation field <math>D</math> is applied repeatedly, then after <math>k</math> iterations, :<math> dP^{(k)} = \frac{D^k\,dP^{(0)}} {\displaystyle\int_XD^k\,dP^{(0)}}. </math> Equivalently, for any measurable event <math>A</math>, :<math> P^{(k)}(A) = \frac{\displaystyle\int_A D(x)^k\,dP^{(0)}(x)} {\displaystyle\int_X D(x)^k\,dP^{(0)}(x)}. </math> This is the direct measure-theoretic counterpart of :<math> p_i^{(k)} = \frac{d_i^kp_i^{(0)}} {\sum_jd_j^kp_j^{(0)}}. </math> Regions where <math>D</math> is relatively large receive increasing relative weight under repeated application. The precise limiting behavior depends on the structure of <math>D</math> and the initial measure. === 4.9 Exponential dilation fields === A particularly important family is obtained by choosing :<math> D_{\theta}(x) = e^{\theta\phi(x)}, </math> where <math>\phi:X\rightarrow\mathbb{R}</math> is measurable and <math>\theta</math> is a real parameter for which the normalization integral is finite. Define :<math> Z(\theta) = \int_X e^{\theta\phi(x)}\,dP_0(x). </math> Then :<math> dP_{\theta}(x) = \frac{e^{\theta\phi(x)}} {Z(\theta)} dP_0(x). </math> In a finite state space this becomes :<math> p_i(\theta) = \frac{p_i^{(0)}e^{\theta\phi_i}} {\sum_jp_j^{(0)}e^{\theta\phi_j}}. </math> This is a standard exponential tilting construction and is closely related to exponential families, cumulant-generating functions, and information geometry. Its importance for the present paper is that it provides a continuous one-parameter dilation trajectory whose Fisher–Rao geometry can be studied explicitly. === 4.10 Infinitesimal evolution of exponential dilation === For the finite-dimensional exponential family, :<math> p_i(\theta) = \frac{p_i^{(0)}e^{\theta\phi_i}} {Z(\theta)}, </math> differentiate with respect to <math>\theta</math>. The logarithmic derivative is :<math> \frac{d}{d\theta}\log p_i(\theta) = \phi_i - \frac{d}{d\theta}\log Z(\theta). </math> Since :<math> \frac{d}{d\theta}\log Z(\theta) = \sum_jp_j(\theta)\phi_j, </math> define :<math> \overline{\phi}_{\theta} = \sum_jp_j(\theta)\phi_j. </math> Then :<math> \frac{dp_i}{d\theta} = p_i(\theta) \left( \phi_i-\overline{\phi}_{\theta} \right). </math> This equation has the form of a replicator-type evolution equation with a fixed state-dependent generator <math>\phi_i</math>. The relationship to established replicator dynamics is discussed in Section 5. === 4.11 Conservation of total probability === Summing the infinitesimal evolution equation gives :<math> \sum_i \frac{dp_i}{d\theta} = \sum_i p_i(\theta) \left( \phi_i-\overline{\phi}_{\theta} \right). </math> Since :<math> \sum_ip_i(\theta)\phi_i = \overline{\phi}_{\theta} </math> and :<math> \sum_ip_i(\theta)=1, </math> it follows that :<math> \sum_i \frac{dp_i}{d\theta} = 0. </math> Thus the vector field is tangent to the probability simplex. Normalization is therefore reflected infinitesimally by conservation of total probability. === 4.12 Scope of the measure-theoretic formulation === The measure-theoretic formulation shows that normalized probability dilation is not restricted to finite vectors or matrices. The same structural operation appears as :'''weight → normalize → obtain a new probability measure''' and, for exponential fields, :'''exponential weight → normalize → continuous probability trajectory'''. These constructions overlap directly with established change-of-measure theory, exponential tilting, weighted probability measures, and related probabilistic methods. Their role in the present framework is to connect the finite dilation notation to continuous probability spaces and to provide the bridge to the information-geometric analysis developed later in the paper. The next section therefore compares the normalized-dilation framework systematically with established mathematical constructions before any additional geometric results are introduced. == 5. Relation to Established Mathematics == The normalized-dilation framework overlaps with several established areas of mathematics. This section identifies those relationships explicitly. The purpose is twofold: first, to place the notation used in this paper within its appropriate mathematical context; and second, to distinguish established constructions from the particular synthesis and geometric questions developed later in the paper. The term '''probability dilation''' is therefore used as an organizing description of a transformation-and-normalization structure, not as a claim that the underlying operations of reweighting, normalization, positive matrix iteration, or change of measure are themselves new. === 5.1 Weighted probability and change of measure === The measure-theoretic transformation :<math> dP_D = \frac{D\,dP} {\int_XD\,dP} </math> is a standard normalized change of measure. Its Radon–Nikodym derivative with respect to <math>P</math> is :<math> \frac{dP_D}{dP} = \frac{D} {\int_XD\,dP}. </math> Consequently, for an integrable observable <math>f</math>, :<math> \mathbb{E}_{P_D}[f] = \frac{\mathbb{E}_{P}[fD]} {\mathbb{E}_{P}[D]}. </math> These expressions belong to established measure-theoretic probability. Within the present framework, their role is to show that finite diagonal dilation and continuous weighted change of measure share the same normalized reweighting structure. === 5.2 Bayesian reweighting === A closely related normalization structure occurs in Bayesian inference. If <math>\pi(x)</math> is a prior density and <math>L(y\mid x)</math> is a likelihood for observed data <math>y</math>, Bayes' rule gives :<math> \pi(x\mid y) = \frac{L(y\mid x)\pi(x)} {\int L(y\mid z)\pi(z)\,dz}, </math> when the denominator is finite and nonzero. Structurally, this has the same form as :<math> dP_D = \frac{D\,dP} {\int D\,dP}, </math> with the likelihood acting as a positive weighting function. The statistical interpretation is different: Bayesian updating has a specific inferential meaning associated with conditioning on data. The comparison here concerns only the common mathematical normalization structure. === 5.3 Importance weighting and exponential tilting === Weighted probability measures also arise in importance sampling, exponential tilting, large-deviation methods, and related statistical constructions. For a generator <math>\phi</math>, exponential tilting takes the form :<math> dP_{\theta}(x) = \frac{e^{\theta\phi(x)}} {Z(\theta)} dP_0(x), </math> where :<math> Z(\theta) = \int_Xe^{\theta\phi(x)}\,dP_0(x). </math> This is an established exponential-family construction. The corresponding finite-dimensional expression, :<math> p_i(\theta) = \frac{p_i^{(0)}e^{\theta\phi_i}} {\sum_jp_j^{(0)}e^{\theta\phi_j}}, </math> will be the principal object of the Fisher–Rao analysis in Sections 6 through 8. The geometric analysis developed later concerns this established exponential-tilt family under a particular question about coincidence of information-geometric and Fisher–Rao geodesics. === 5.4 Positive matrices and Perron–Frobenius theory === For a fixed nonnegative matrix <math>M</math>, the normalized transformation :<math> T_M(p) = \frac{Mp} {\mathbf{1}^{\mathsf{T}}Mp} </math> is closely related to classical positive-matrix theory. If <math>M</math> is primitive, Perron–Frobenius theory provides a dominant positive eigenvalue :<math> \rho(M)>0 </math> and a corresponding strictly positive eigenvector. Repeated normalized iteration, :<math> p^{(k)} = \frac{M^kp^{(0)}} {\mathbf{1}^{\mathsf{T}}M^kp^{(0)}}, </math> is therefore closely related to normalized power iteration. Under appropriate hypotheses, its asymptotic direction is governed by the Perron eigenvector. These spectral and convergence results are established mathematics and are not presented here as new consequences of PDT. === 5.5 Markov operators === Suppose <math>M</math> is nonnegative and satisfies :<math> \mathbf{1}^{\mathsf{T}}M = \mathbf{1}^{\mathsf{T}}. </math> With the column-vector convention used in this paper, :<math> \mathbf{1}^{\mathsf{T}}Mp = 1 </math> for every probability vector <math>p</math>. Thus :<math> T_M(p)=Mp. </math> In this mass-preserving case, the normalization step is unnecessary. Accordingly, ordinary finite-state Markov evolution is contained as a special mass-preserving case of the broader positive-transformation framework. This observation is structural. It does not imply that normalized dilation provides a replacement for Markov-chain theory. === 5.6 Replicator-type dynamics === The exponential dilation family satisfies :<math> \frac{dp_i}{d\theta} = p_i \left( \phi_i-\overline{\phi}_{\theta} \right), </math> where :<math> \overline{\phi}_{\theta} = \sum_jp_j(\theta)\phi_j. </math> The standard replicator equation has the form :<math> \frac{dp_i}{dt} = p_i \left( f_i(p)-\overline{f}(p) \right). </math> Thus exponential dilation with fixed generator values <math>\phi_i</math> has the same algebraic structure as a replicator equation with state-independent fitness values. The mean-subtraction term guarantees :<math> \sum_i\frac{dp_i}{d\theta}=0, </math> so the flow remains tangent to the probability simplex. Replicator dynamics and their geometric interpretations are established subjects. The present paper uses this connection to relate normalized dilation to known simplex dynamics. === 5.7 Fisher–Rao and Shahshahani geometry === The interior of the probability simplex carries the Fisher–Rao metric. For tangent vectors <math>u</math> and <math>v</math> satisfying :<math> \sum_i u_i = \sum_i v_i = 0, </math> the finite-dimensional Fisher–Rao metric can be written as :<math> g_p(u,v) = \sum_{i=1}^{n} \frac{u_iv_i}{p_i}. </math> Closely related forms of this metric appear in evolutionary dynamics under the name Shahshahani metric. The square-root mapping :<math> \Psi(p) = 2(\sqrt{p_1},\ldots,\sqrt{p_n}) </math> satisfies :<math> \sum_i\Psi_i(p)^2=4. </math> Thus the simplex interior is represented in the positive orthant of a sphere of radius <math>2</math>. Under this representation, the Fisher–Rao metric becomes the metric induced by the ambient Euclidean space, and Levi-Civita Fisher–Rao geodesics correspond locally to great-circle arcs. This established spherical representation will be the principal geometric tool used in Section 7. === 5.8 Exponential families and the e-connection === The exponential dilation path :<math> p_i(\theta) = \frac{p_i^{(0)}e^{\theta\phi_i}} {Z(\theta)} </math> is a one-parameter exponential family. Taking logarithms gives :<math> \log p_i(\theta) = \log p_i^{(0)} + \theta\phi_i - \log Z(\theta). </math> The natural parameter varies linearly with <math>\theta</math>. In information geometry, exponential families are naturally associated with the exponential, or '''e''', connection. A path linear in natural parameters is an e-geodesic. This notion of geodesic is distinct from a Levi-Civita geodesic of the Fisher–Rao metric. Consequently, an exponential dilation trajectory may be straight with respect to the e-connection while being curved with respect to the Fisher–Rao Levi-Civita connection. This distinction is central to the geometric question investigated later in the paper. === 5.9 Fisher information and variance === For the exponential dilation family, :<math> \frac{d}{d\theta} \log p_i(\theta) = \phi_i-\overline{\phi}_{\theta}. </math> The Fisher information associated with the parameter <math>\theta</math> is therefore :<math> I(\theta) = \sum_i p_i(\theta) \left( \phi_i-\overline{\phi}_{\theta} \right)^2. </math> Hence :<math> I(\theta) = \operatorname{Var}_{p(\theta)}(\phi). </math> The Fisher–Rao speed of the trajectory is :<math> v_{\mathrm{FR}}(\theta) = \sqrt{I(\theta)} = \sqrt{\operatorname{Var}_{p(\theta)}(\phi)}. </math> This variance identity is a standard property of one-parameter exponential families. It will be used later when deriving the arclength parameterization of the two-level case. === 5.10 Normalized Feynman–Kac transformations === Another closely related structure occurs in Feynman–Kac models. At an abstract level, a positive measure may first be weighted by a nonnegative potential and then propagated through a positive or Markov operator, followed by normalization. Schematically, such an evolution has the form :'''weight → propagate → normalize'''. The matrix expression :<math> T_M(p) = \frac{Mp} {\mathbf{1}^{\mathsf{T}}Mp} </math> and the measure expression :<math> dP_D = \frac{D\,dP} {\int D\,dP} </math> therefore have structural analogues within normalized Feynman–Kac theory. The exact interpretation and assumptions differ among applications. The comparison made here is structural rather than an assertion of equivalence between PDT and Feynman–Kac theory. === 5.11 Projective dynamics === Because normalized dilation is invariant under multiplication of the unnormalized transformed state by a positive scalar, it naturally has a projective character. For example, :<math> T_{cM}(p) = T_M(p) </math> for every <math>c>0</math> for which the transformation is defined. Thus the normalized state depends on the ray determined by <math>Mp</math>, rather than its magnitude. Positive projective geometry and projective metrics, including Hilbert-type metrics, are established tools in the study of positive operators and their contraction properties. These methods provide natural mathematical machinery for analyzing normalized positive transformations, particularly in convergence problems. === 5.12 What the PDT framework contributes === The preceding comparisons show that the principal operations used in normalized probability dilation have substantial established precedents. The proposed contribution of the framework is therefore not the isolated operation :'''multiply or transform, then normalize'''. Rather, the framework provides a common notation and organizational viewpoint connecting: * finite diagonal reweighting; * nonnegative matrix transformations; * normalized positive iteration; * weighted change of measure; * exponential probability trajectories; * simplex dynamics; * information geometry. This synthesis is useful only insofar as it clarifies relationships, generates mathematically precise questions, or produces results that are not merely restatements of known theory. For that reason, the remainder of this paper concentrates on a narrower geometric problem. === 5.13 Transition to the geometric question === Every exponential dilation trajectory of the form :<math> p_i(\theta) = \frac{p_i^{(0)}e^{\theta\phi_i}} {Z(\theta)} </math> is an exponential-family trajectory and hence is naturally straight with respect to the e-connection. It does not follow that the same trajectory is a Levi-Civita geodesic of the Fisher–Rao metric. This leads to the central question considered in the remainder of the paper: :''Under what conditions is an exponential dilation trajectory simultaneously an e-geodesic and, up to reparameterization, a Fisher–Rao Levi-Civita geodesic?'' The next section develops the geometric representation required to answer this question. == 6. Exponential Dilation and Fisher–Rao Geometry == This section develops the geometric representation of exponential dilation required for the main characterization theorem. The central object is the one-parameter exponential family :<math> p_i(\theta) = \frac{p_i^{(0)}e^{\theta\phi_i}} {Z(\theta)}, </math> where :<math> Z(\theta) = \sum_{j=1}^{n}p_j^{(0)}e^{\theta\phi_j}. </math> Throughout this section, assume :<math> p_i^{(0)}>0 </math> for all <math>i</math>, and let :<math> \phi=(\phi_1,\ldots,\phi_n) </math> be a real-valued generator. === 6.1 Exponential dilation trajectory === Let :<math> p^{(0)} \in \Delta_{+}^{n-1}. </math> For a real parameter <math>\theta</math>, define :<math> p_i(\theta) = \frac{p_i^{(0)}e^{\theta\phi_i}} {\sum_{j=1}^{n}p_j^{(0)}e^{\theta\phi_j}}. </math> Since every initial component is strictly positive and the exponential function is positive, :<math> p_i(\theta)>0 </math> for every finite <math>\theta</math>. Therefore the trajectory remains in the interior of the probability simplex. The normalization factor satisfies :<math> Z(\theta)>0. </math> Hence the trajectory is well defined for every finite <math>\theta</math> in the finite-dimensional setting. === 6.2 Logarithmic form === Taking logarithms gives :<math> \log p_i(\theta) = \log p_i^{(0)} + \theta\phi_i - \log Z(\theta). </math> Differentiating with respect to <math>\theta</math> gives :<math> \frac{d}{d\theta}\log p_i(\theta) = \phi_i - \frac{d}{d\theta}\log Z(\theta). </math> Now :<math> \frac{dZ}{d\theta} = \sum_j p_j^{(0)} \phi_j e^{\theta\phi_j}. </math> Therefore :<math> \frac{d}{d\theta}\log Z(\theta) = \sum_jp_j(\theta)\phi_j. </math> Define the expectation of the generator by :<math> \mu(\theta) = \mathbb{E}_{p(\theta)}[\phi] = \sum_jp_j(\theta)\phi_j. </math> Then :<math> \frac{d}{d\theta}\log p_i(\theta) = \phi_i-\mu(\theta). </math> === 6.3 Tangent vector === Multiplying the logarithmic derivative by <math>p_i(\theta)</math> gives :<math> \frac{dp_i}{d\theta} = p_i(\theta) \left( \phi_i-\mu(\theta) \right). </math> Define the centered generator :<math> h_i(\theta) = \phi_i-\mu(\theta). </math> Then :<math> \frac{dp_i}{d\theta} = p_i(\theta)h_i(\theta). </math> Because :<math> \sum_i p_i(\theta)h_i(\theta) = 0, </math> we obtain :<math> \sum_i \frac{dp_i}{d\theta} = 0. </math> Thus the velocity vector is tangent to the probability simplex. === 6.4 Fisher information and speed === The Fisher–Rao metric on the simplex interior is :<math> g_p(u,v) = \sum_i \frac{u_iv_i}{p_i}, </math> for tangent vectors <math>u</math> and <math>v</math>. For the exponential dilation trajectory, :<math> \frac{dp_i}{d\theta} = p_i h_i. </math> Its squared Fisher–Rao speed is therefore :<math> v_{\mathrm{FR}}(\theta)^2 = \sum_i \frac{1}{p_i} \left( \frac{dp_i}{d\theta} \right)^2. </math> Substitution gives :<math> v_{\mathrm{FR}}(\theta)^2 = \sum_i p_i(\theta)h_i(\theta)^2. </math> Hence :<math> v_{\mathrm{FR}}(\theta)^2 = \operatorname{Var}_{p(\theta)}(\phi). </math> Therefore :<math> v_{\mathrm{FR}}(\theta) = \sqrt{ \operatorname{Var}_{p(\theta)}(\phi) }. </math> This is the standard Fisher-information identity for a one-parameter exponential family. === 6.5 Square-root representation === Define the square-root map :<math> \Psi: \Delta_{+}^{n-1} \rightarrow \mathbb{R}^{n} </math> by :<math> \Psi(p) = 2(\sqrt{p_1},\ldots,\sqrt{p_n}). </math> Write :<math> q(\theta) = \Psi(p(\theta)). </math> Then :<math> q_i(\theta) = 2\sqrt{p_i(\theta)}. </math> Because :<math> \sum_i p_i(\theta)=1, </math> we have :<math> \sum_iq_i(\theta)^2 = 4. </math> Thus :<math> q(\theta) </math> lies on the positive orthant of the sphere of radius <math>2</math> in <math>\mathbb{R}^{n}</math>. === 6.6 Isometry of the square-root representation === Let <math>u</math> be a tangent vector to the simplex. Differentiating :<math> q_i=2\sqrt{p_i} </math> gives :<math> dq_i = \frac{dp_i}{\sqrt{p_i}}. </math> Therefore the Euclidean squared length of the corresponding tangent displacement on the sphere is :<math> \sum_i(dq_i)^2 = \sum_i \frac{(dp_i)^2}{p_i}. </math> This is precisely the Fisher–Rao line element. Thus the square-root map identifies the Fisher–Rao metric on the simplex interior with the Euclidean metric induced on the positive orthant of the radius-<math>2</math> sphere. Consequently, Fisher–Rao Levi-Civita geodesics correspond locally to great-circle arcs on this sphere. === 6.7 Square-root form of exponential dilation === Substituting the exponential dilation family into the square-root representation gives :<math> q_i(\theta) = \frac{ 2\sqrt{p_i^{(0)}}e^{\theta\phi_i/2} } {\sqrt{Z(\theta)}}. </math> Define the unnormalized square-root vector :<math> r_i(\theta) = \sqrt{p_i^{(0)}}e^{\theta\phi_i/2}. </math> Then :<math> q(\theta) = \frac{2r(\theta)} {\sqrt{Z(\theta)}}. </math> Also, :<math> \|r(\theta)\|^2 = Z(\theta). </math> Hence :<math> q(\theta) = \frac{2r(\theta)} {\|r(\theta)\|}. </math> The normalized square-root trajectory and the unnormalized vector <math>r(\theta)</math> therefore determine the same ray through the origin. This observation allows the Fisher–Rao geodesic question to be reduced to a linear-subspace question in <math>\mathbb{R}^{n}</math>. === 6.8 Distinct generator levels === Suppose the generator <math>\phi</math> assumes exactly <math>m</math> distinct values :<math> a_1,\ldots,a_m. </math> Define the level sets :<math> A_{\ell} = \{i:\phi_i=a_{\ell}\}, </math> for :<math> \ell=1,\ldots,m. </math> For each level, define a vector <math>u_{\ell}</math> by :<math> (u_{\ell})_i = \begin{cases} \sqrt{p_i^{(0)}} & \text{if } i\in A_{\ell},\\ 0 & \text{otherwise}. \end{cases} </math> Because the level sets are disjoint, the vectors :<math> u_1,\ldots,u_m </math> have disjoint supports and are therefore mutually orthogonal. In particular, they are linearly independent. The unnormalized square-root trajectory can now be written as :<math> r(\theta) = \sum_{\ell=1}^{m} e^{a_{\ell}\theta/2} u_{\ell}. </math> This decomposition is central to the geometric characterization developed in the next section. === 6.9 The one-level case === If <math>m=1</math>, then every component of <math>\phi</math> has the same value <math>a</math>. Thus :<math> r(\theta) = e^{a\theta/2}u_1. </math> After normalization, the scalar exponential factor cancels. Therefore :<math> p(\theta)=p^{(0)} </math> for all <math>\theta</math>. The trajectory is constant. This is the degenerate case of exponential dilation. === 6.10 The two-level case === Suppose <math>\phi</math> assumes exactly two distinct values :<math> a </math> and :<math> b, </math> with <math>a\neq b</math>. Then :<math> r(\theta) = e^{a\theta/2}u + e^{b\theta/2}v, </math> where <math>u</math> and <math>v</math> are nonzero orthogonal vectors associated with the two generator levels. Consequently, :<math> r(\theta) \in \operatorname{span}\{u,v\} </math> for every <math>\theta</math>. Since <math>q(\theta)</math> is obtained from <math>r(\theta)</math> by positive scalar normalization, :<math> q(\theta) \in \operatorname{span}\{u,v\} </math> as well. The intersection of a two-dimensional linear subspace through the origin with the radius-<math>2</math> sphere is a great circle. Thus the two-level case naturally produces a Fisher–Rao great-circle trajectory. The formal statement and converse are given in Section 7. === 6.11 Three or more generator levels === If the generator assumes three or more distinct values, then :<math> r(\theta) = \sum_{\ell=1}^{m} e^{a_{\ell}\theta/2}u_{\ell}, </math> with :<math> m\geq3. </math> The vectors <math>u_{\ell}</math> are linearly independent, but this fact alone is not sufficient to conclude that the trajectory spans all <math>m</math> directions. The required result follows from the linear independence of the distinct exponential rates. In Section 7, derivatives of <math>r(\theta)</math> are evaluated at a fixed parameter value. The resulting coefficient matrix is of Vandermonde type and is invertible when the generator levels <math>a_{\ell}</math> are distinct. This shows that a trajectory with <math>m</math> distinct active generator levels spans an <math>m</math>-dimensional linear subspace. Consequently, when <math>m\geq3</math>, the square-root trajectory cannot lie in a two-dimensional great-circle plane. === 6.12 e-geodesic versus Fisher–Rao geodesic === The exponential dilation trajectory is an exponential-family path. In natural coordinates, the parameter <math>\theta</math> enters linearly through :<math> \theta\phi_i. </math> Accordingly, the trajectory is naturally an e-geodesic in the exponential connection of information geometry. The Fisher–Rao Levi-Civita geodesic condition is different. Under the square-root representation, it requires the image of the trajectory to lie on a great-circle arc. Thus the central geometric distinction is: :'''e-geodesic: linearity in exponential-family natural coordinates''' versus :'''Fisher–Rao Levi-Civita geodesic: great-circle geometry under the square-root representation''' The two notions coincide only under additional conditions. === 6.13 Geometric question in linear form === The original probability-geometric question can now be reformulated. Given :<math> r(\theta) = \sum_{\ell=1}^{m} e^{a_{\ell}\theta/2}u_{\ell}, </math> when does the normalized curve :<math> q(\theta) = \frac{2r(\theta)} {\|r(\theta)\|} </math> remain in a fixed two-dimensional linear subspace? If it does, its image lies on a great circle and is therefore a Fisher–Rao Levi-Civita geodesic up to reparameterization. If it does not, the exponential trajectory remains an e-geodesic but is not a Fisher–Rao Levi-Civita geodesic. The next section gives an exact finite-dimensional characterization. == 7. Fisher–Rao Geodesic Characterization == This section gives the principal geometric result of the paper. The question is whether the image of a finite-dimensional exponential dilation trajectory is contained in a Fisher–Rao Levi-Civita geodesic. The parameter <math>\theta</math> itself is not required to be an affine or arclength parameter for that geodesic. === 7.1 Setting and assumptions === Let :<math> p^{(0)} = (p_1^{(0)},\ldots,p_n^{(0)})^{\mathsf{T}} \in \Delta_{+}^{n-1}, </math> so that :<math> p_i^{(0)}>0 </math> for every <math>i</math>. Let :<math> \phi = (\phi_1,\ldots,\phi_n) \in \mathbb{R}^{n}. </math> Define the exponential dilation trajectory :<math> p_i(\theta) = \frac{ p_i^{(0)}e^{\theta\phi_i} } { \sum_{j=1}^{n} p_j^{(0)}e^{\theta\phi_j} }, </math> for :<math> \theta\in\mathbb{R}. </math> Let <math>m</math> denote the number of distinct values assumed by the generator components :<math> \phi_1,\ldots,\phi_n. </math> === 7.2 Theorem 1: two-level Fisher–Rao characterization === '''Theorem 1.''' Under the assumptions above, the image of the exponential dilation trajectory <math>p(\theta)</math> is contained in a Fisher–Rao Levi-Civita geodesic if and only if :<math> m\leq2. </math> Equivalently, the generator <math>\phi</math> must assume at most two distinct values. When <math>m=1</math>, the trajectory is constant. When <math>m=2</math>, the trajectory is nonconstant and its square-root image lies on a great-circle arc. === 7.3 Proof: square-root representation === Define :<math> q_i(\theta) = 2\sqrt{p_i(\theta)}. </math> As shown in Section 6, :<math> q(\theta) </math> lies on the sphere :<math> \sum_iq_i^2=4. </math> The square-root representation is an isometric representation of the Fisher–Rao simplex interior. Therefore the image of <math>p(\theta)</math> is contained in a Fisher–Rao Levi-Civita geodesic if and only if the image of <math>q(\theta)</math> is contained in a great circle of the radius-<math>2</math> sphere. A great circle is the intersection of the sphere with a two-dimensional linear subspace through the origin. === 7.4 Grouping equal generator values === Let the distinct values of <math>\phi</math> be :<math> a_1,\ldots,a_m. </math> For each <math>\ell</math>, define :<math> A_{\ell} = \{i:\phi_i=a_{\ell}\}. </math> Define <math>u_{\ell}\in\mathbb{R}^{n}</math> by :<math> (u_{\ell})_i = \begin{cases} \sqrt{p_i^{(0)}} & \text{if }i\in A_{\ell},\\ 0 & \text{otherwise}. \end{cases} </math> Because the sets <math>A_{\ell}</math> are disjoint and every initial component is strictly positive, the vectors :<math> u_1,\ldots,u_m </math> are nonzero and mutually orthogonal. Hence they are linearly independent. Define the unnormalized square-root trajectory :<math> r(\theta) = \sum_{\ell=1}^{m} e^{a_{\ell}\theta/2} u_{\ell}. </math> Then :<math> q(\theta) = \frac{2r(\theta)} {\|r(\theta)\|}. </math> Since normalization multiplies <math>r(\theta)</math> only by a positive scalar, <math>q(\theta)</math> and <math>r(\theta)</math> lie on the same ray through the origin. === 7.5 Sufficiency: one or two generator levels === Suppose first that :<math> m=1. </math> Then :<math> r(\theta) = e^{a_1\theta/2}u_1. </math> Normalization removes the scalar exponential factor, so :<math> q(\theta) </math> and therefore <math>p(\theta)</math> are constant. A constant trajectory is the degenerate case. Now suppose :<math> m=2. </math> Then :<math> r(\theta) = e^{a_1\theta/2}u_1 + e^{a_2\theta/2}u_2. </math> Therefore :<math> r(\theta) \in \operatorname{span}\{u_1,u_2\} </math> for every <math>\theta</math>. Since <math>q(\theta)</math> differs from <math>r(\theta)</math> only by scalar normalization, :<math> q(\theta) \in \operatorname{span}\{u_1,u_2\}. </math> The vectors <math>u_1</math> and <math>u_2</math> are nonzero and orthogonal, so their span is a two-dimensional linear subspace through the origin. Its intersection with the radius-<math>2</math> sphere is a great circle. Thus the image of the two-level exponential dilation trajectory lies on a Fisher–Rao Levi-Civita geodesic. This proves sufficiency. === 7.6 Necessity: derivative span === Now suppose the generator assumes :<math> m\geq3 </math> distinct values. Differentiate the unnormalized square-root trajectory: :<math> r(\theta) = \sum_{\ell=1}^{m} e^{a_{\ell}\theta/2} u_{\ell}. </math> For every nonnegative integer <math>k</math>, :<math> r^{(k)}(\theta) = \sum_{\ell=1}^{m} \left( \frac{a_{\ell}}{2} \right)^k e^{a_{\ell}\theta/2} u_{\ell}. </math> Fix any :<math> \theta_0\in\mathbb{R}. </math> Consider the vectors :<math> r(\theta_0), r^{(1)}(\theta_0), \ldots, r^{(m-1)}(\theta_0). </math> Their coefficients relative to the basis :<math> u_1,\ldots,u_m </math> form the matrix :<math> C_{k\ell} = \left( \frac{a_{\ell}}{2} \right)^k e^{a_{\ell}\theta_0/2}, </math> where :<math> k=0,\ldots,m-1 </math> and :<math> \ell=1,\ldots,m. </math> === 7.7 Vandermonde argument === Factor the nonzero quantity :<math> e^{a_{\ell}\theta_0/2} </math> from column <math>\ell</math> of the coefficient matrix. The remaining matrix has entries :<math> V_{k\ell} = \left( \frac{a_{\ell}}{2} \right)^k. </math> This is a Vandermonde matrix. Its determinant is nonzero because :<math> a_1,\ldots,a_m </math> are distinct. Therefore the coefficient matrix <math>C</math> is invertible. It follows that :<math> r(\theta_0), r^{(1)}(\theta_0), \ldots, r^{(m-1)}(\theta_0) </math> are linearly independent. Consequently, the linear span generated by the trajectory <math>r(\theta)</math> has dimension at least <math>m</math>. On the other hand, the representation :<math> r(\theta) = \sum_{\ell=1}^{m} e^{a_{\ell}\theta/2}u_{\ell} </math> shows that the trajectory is contained in :<math> \operatorname{span} \{u_1,\ldots,u_m\}, </math> which has dimension <math>m</math>. Hence :<math> \dim \operatorname{span} \{r(\theta):\theta\in\mathbb{R}\} = m. </math> === 7.8 Exclusion of three or more levels === If the square-root trajectory <math>q(\theta)</math> were contained in a great circle, then there would exist a two-dimensional linear subspace <math>W</math> through the origin such that :<math> q(\theta)\in W </math> for every <math>\theta</math>. Since :<math> r(\theta) = \frac{\|r(\theta)\|}{2} q(\theta), </math> the same subspace would contain :<math> r(\theta) </math> for every <math>\theta</math>. Therefore :<math> \dim \operatorname{span} \{r(\theta):\theta\in\mathbb{R}\} \leq2. </math> But Section 7.7 gives :<math> \dim \operatorname{span} \{r(\theta):\theta\in\mathbb{R}\} = m. </math> Thus a great-circle trajectory requires :<math> m\leq2. </math> For :<math> m\geq3, </math> the exponential dilation trajectory cannot be contained in a Fisher–Rao Levi-Civita geodesic. This proves necessity. === 7.9 Conclusion of the proof === Combining Sections 7.5 and 7.8 gives :<math> m\leq2 </math> if and only if the image of the exponential dilation trajectory is contained in a Fisher–Rao Levi-Civita geodesic. Therefore the generator <math>\phi</math> must assume at most two distinct values. This completes the proof. === 7.10 Corollary 1: dimension of the square-root trajectory === '''Corollary 1.''' Under the assumptions of Theorem 1, if the generator <math>\phi</math> assumes exactly <math>m</math> distinct values, then :<math> \dim \operatorname{span} \{r(\theta):\theta\in\mathbb{R}\} = m. </math> Thus the number of distinct generator levels is exactly the dimension of the linear subspace generated by the unnormalized square-root exponential trajectory. '''Proof.''' The vectors <math>u_1,\ldots,u_m</math> are linearly independent, and Section 7.7 shows through the Vandermonde argument that the trajectory spans all of these directions. Therefore its span has dimension <math>m</math>. === 7.11 Corollary 2: three-level obstruction === '''Corollary 2.''' If a strictly positive finite exponential dilation trajectory has a generator assuming three or more distinct values, then its image is not contained in a Fisher–Rao Levi-Civita geodesic. This follows immediately from Theorem 1. The result is exact under the stated hypotheses; it is not merely a generic non-geodesicity statement. === 7.12 Parameterization versus geodesic image === Theorem 1 concerns the image of the trajectory. Even in the two-level case, the exponential parameter <math>\theta</math> is generally not proportional to Fisher–Rao arclength. Thus :<math> p(\theta) </math> traces a Fisher–Rao geodesic path but generally does so with nonconstant Fisher–Rao speed. From Section 6, :<math> \frac{ds}{d\theta} = \sqrt{ \operatorname{Var}_{p(\theta)}(\phi) }. </math> Section 8 derives the exact change of parameter from <math>\theta</math> to Fisher–Rao arclength in the nondegenerate two-level case. === 7.13 Geometric interpretation === The theorem can be understood through the square-root sphere. A generator with one distinct value produces no probability motion. A generator with two distinct values produces two independent exponential directions, :<math> e^{a\theta/2}u </math> and :<math> e^{b\theta/2}v. </math> Their normalized sum remains in a fixed two-dimensional plane through the origin, so its spherical image follows a great circle. With three or more distinct generator values, the trajectory necessarily spans three or more independent linear directions. It therefore cannot remain in any two-dimensional great-circle plane. The distinction between the two-level and multilevel cases is consequently a dimensional property of the exponential rates under the square-root representation. === 7.14 Relation to information-geometric straightness === Theorem 1 does not state that exponential trajectories with three or more levels cease to be e-geodesics. They remain exponential-family trajectories and retain their standard information-geometric interpretation with respect to the e-connection. Rather, the theorem characterizes when this e-geodesic image also coincides with a geodesic image of the Levi-Civita connection associated with the Fisher–Rao metric. Thus the result concerns the coincidence of two distinct notions of geometric straightness. === 7.15 Status of the characterization === The proof above uses established ingredients: * the exponential-family representation; * the Fisher–Rao square-root embedding; * the great-circle characterization of spherical geodesics; * linear independence of vectors with disjoint support; * the Vandermonde determinant. The particular characterization obtained by combining these ingredients is presented here as a result of the present analysis. At this draft stage, no claim of historical priority is made. A complete literature review and independent mathematical scrutiny remain appropriate before describing the characterization as novel. The next section derives an explicit Fisher–Rao arclength parameterization for the nondegenerate two-level case. == 8. Fisher–Rao Arclength in the Two-Level Case == Theorem 1 shows that a nonconstant exponential dilation trajectory is contained in a Fisher–Rao Levi-Civita geodesic precisely when its generator assumes exactly two distinct values. This section derives an explicit Fisher–Rao arclength parameterization for that case. === 8.1 Two generator classes === Suppose the generator <math>\phi</math> assumes exactly two distinct values :<math> a\neq b. </math> Define the corresponding index sets :<math> A= \{i:\phi_i=a\} </math> and :<math> B= \{i:\phi_i=b\}. </math> Let the initial probability masses of the two classes be :<math> r_0 = \sum_{i\in A}p_i^{(0)} </math> and :<math> 1-r_0 = \sum_{i\in B}p_i^{(0)}. </math> Because the initial probability vector is strictly positive and both classes are nonempty, :<math> 0<r_0<1. </math> === 8.2 Evolution of the class probabilities === Let :<math> r(\theta) = \sum_{i\in A}p_i(\theta) </math> denote the total probability assigned to class <math>A</math>. Since every state in <math>A</math> has generator value <math>a</math> and every state in <math>B</math> has generator value <math>b</math>, :<math> r(\theta) = \frac{ r_0e^{a\theta} } { r_0e^{a\theta} + (1-r_0)e^{b\theta} }. </math> Similarly, :<math> 1-r(\theta) = \frac{ (1-r_0)e^{b\theta} } { r_0e^{a\theta} + (1-r_0)e^{b\theta} }. </math> Therefore the class odds satisfy :<math> \frac{r(\theta)} {1-r(\theta)} = \frac{r_0} {1-r_0} e^{(a-b)\theta}. </math> Thus the two-level exponential dilation reduces at the class level to a logistic probability trajectory. === 8.3 Preservation of within-class proportions === For two indices <math>i,j\in A</math>, :<math> \frac{p_i(\theta)} {p_j(\theta)} = \frac{p_i^{(0)}} {p_j^{(0)}}. </math> The same relation holds for indices within <math>B</math>. Therefore exponential dilation changes only the total probability assigned to the two generator classes; it does not change relative probabilities within either class. Define normalized class vectors <math>\widehat{u}</math> and <math>\widehat{v}</math> by :<math> \widehat{u}_i = \begin{cases} \sqrt{p_i^{(0)}/r_0} & \text{if }i\in A,\\ 0 & \text{otherwise}, \end{cases} </math> and :<math> \widehat{v}_i = \begin{cases} \sqrt{p_i^{(0)}/(1-r_0)} & \text{if }i\in B,\\ 0 & \text{otherwise}. \end{cases} </math> These vectors satisfy :<math> \|\widehat{u}\|=1, \qquad \|\widehat{v}\|=1, </math> and :<math> \widehat{u}^{\mathsf{T}}\widehat{v}=0. </math> === 8.4 Great-circle representation === Under the square-root map, :<math> q(\theta) = 2(\sqrt{p_1(\theta)},\ldots,\sqrt{p_n(\theta)}). </math> Using the class decomposition, :<math> q(\theta) = 2 \left( \sqrt{r(\theta)}\,\widehat{u} + \sqrt{1-r(\theta)}\,\widehat{v} \right). </math> Introduce an angular coordinate <math>\alpha(\theta)</math> by :<math> \sqrt{r(\theta)} = \cos\alpha(\theta) </math> and :<math> \sqrt{1-r(\theta)} = \sin\alpha(\theta), </math> with :<math> 0<\alpha(\theta)<\frac{\pi}{2}. </math> Then :<math> q(\theta) = 2 \left( \cos\alpha(\theta)\widehat{u} + \sin\alpha(\theta)\widehat{v} \right). </math> This is the standard angular parameterization of a great circle on a sphere of radius <math>2</math>. === 8.5 Angular coordinate === From the definitions above, :<math> \tan\alpha(\theta) = \sqrt{ \frac{1-r(\theta)} {r(\theta)} }. </math> Using the odds relation, :<math> \frac{1-r(\theta)} {r(\theta)} = \frac{1-r_0} {r_0} e^{(b-a)\theta}. </math> Therefore :<math> \tan\alpha(\theta) = \sqrt{ \frac{1-r_0} {r_0} } e^{(b-a)\theta/2}. </math> Hence :<math> \alpha(\theta) = \arctan \left( \sqrt{ \frac{1-r_0} {r_0} } e^{(b-a)\theta/2} \right). </math> Equivalently, :<math> \alpha(\theta) = \arccos\sqrt{r(\theta)}. </math> === 8.6 Corollary 3: exact Fisher–Rao arclength parameterization === '''Corollary 3.''' Under the hypotheses of Theorem 1, suppose the generator assumes exactly two distinct values <math>a\neq b</math>. Let :<math> r(\theta) </math> denote the total probability assigned to the class with generator value <math>a</math>. Then a signed Fisher–Rao arclength coordinate along the trajectory satisfies :<math> s(\theta)-s(\theta_0) = 2 \left( \alpha(\theta)-\alpha(\theta_0) \right), </math> where :<math> \alpha(\theta) = \arccos\sqrt{r(\theta)}. </math> Thus :<math> s(\theta)-s(\theta_0) = 2 \left( \arccos\sqrt{r(\theta)} - \arccos\sqrt{r(\theta_0)} \right). </math> Equivalently, :<math> s(\theta)-s(\theta_0) = 2 \left[ \arctan \left( \sqrt{ \frac{1-r_0}{r_0} } e^{(b-a)\theta/2} \right) - \arctan \left( \sqrt{ \frac{1-r_0}{r_0} } e^{(b-a)\theta_0/2} \right) \right]. </math> The Fisher–Rao distance traveled between the two parameter values is the absolute value :<math> d_{\mathrm{FR}} = |s(\theta)-s(\theta_0)|. </math> === 8.7 Proof of Corollary 3 === The square-root image is :<math> q(\theta) = 2 \left( \cos\alpha(\theta)\widehat{u} + \sin\alpha(\theta)\widehat{v} \right). </math> Differentiate with respect to <math>\alpha</math>: :<math> \frac{dq}{d\alpha} = 2 \left( -\sin\alpha\,\widehat{u} + \cos\alpha\,\widehat{v} \right). </math> Because <math>\widehat{u}</math> and <math>\widehat{v}</math> are orthonormal, :<math> \left\| \frac{dq}{d\alpha} \right\| = 2. </math> Therefore the spherical arclength element is :<math> ds = 2\,|d\alpha|. </math> For a chosen orientation, signed arclength satisfies :<math> ds=2\,d\alpha. </math> Integrating from <math>\theta_0</math> to <math>\theta</math> gives :<math> s(\theta)-s(\theta_0) = 2 \left( \alpha(\theta)-\alpha(\theta_0) \right). </math> Substituting the expressions for <math>\alpha(\theta)</math> gives the stated formulas. === 8.8 Fisher–Rao speed === Differentiating the angular expression gives :<math> \frac{d\alpha}{d\theta} = \frac{b-a}{2} \sqrt{ r(\theta) \left( 1-r(\theta) \right) }. </math> Therefore the unsigned Fisher–Rao speed is :<math> \left| \frac{ds}{d\theta} \right| = |a-b| \sqrt{ r(\theta) \left( 1-r(\theta) \right) }. </math> This agrees with the variance formula derived in Section 6. Indeed, because <math>\phi</math> takes only the values <math>a</math> and <math>b</math>, :<math> \operatorname{Var}_{p(\theta)}(\phi) = (a-b)^2 r(\theta) \left( 1-r(\theta) \right). </math> Hence :<math> v_{\mathrm{FR}}(\theta) = \sqrt{ \operatorname{Var}_{p(\theta)}(\phi) } = |a-b| \sqrt{ r(\theta) \left( 1-r(\theta) \right) }. </math> The geometric and information-theoretic calculations therefore agree. === 8.9 Nonuniform speed in the exponential parameter === Although the trajectory lies on a Fisher–Rao geodesic, the parameter <math>\theta</math> does not generally move along that geodesic at constant speed. The speed is largest when :<math> r(\theta)=\frac{1}{2}, </math> because the product :<math> r(\theta)(1-r(\theta)) </math> is maximal there. As the trajectory approaches either endpoint, :<math> r(\theta)\rightarrow0 </math> or :<math> r(\theta)\rightarrow1, </math> the Fisher–Rao speed with respect to <math>\theta</math> approaches zero. Thus the exponential parameter stretches the ends of the geodesic trajectory. === 8.10 Limiting behavior === Assume :<math> a>b. </math> Then as :<math> \theta\rightarrow+\infty, </math> we have :<math> r(\theta)\rightarrow1. </math> As :<math> \theta\rightarrow-\infty, </math> we have :<math> r(\theta)\rightarrow0. </math> Therefore :<math> \alpha(\theta)\rightarrow0 </math> as <math>\theta\rightarrow+\infty</math>, while :<math> \alpha(\theta)\rightarrow\frac{\pi}{2} </math> as <math>\theta\rightarrow-\infty</math>. The full two-level trajectory therefore approaches the two boundary class distributions at opposite ends of a quarter of the radius-<math>2</math> great circle. The total Fisher–Rao length between these limiting boundary points is :<math> 2 \left( \frac{\pi}{2} \right) = \pi. </math> The endpoints themselves lie on the boundary of the simplex and are approached only in the infinite-parameter limit. === 8.11 Example === Consider a three-state probability vector :<math> p^{(0)} = \left( \frac{1}{4}, \frac{1}{4}, \frac{1}{2} \right)^{\mathsf{T}} </math> and generator :<math> \phi = (1,1,0). </math> There are two generator classes: :<math> A=\{1,2\}, \qquad B=\{3\}. </math> The initial class mass is :<math> r_0 = \frac{1}{2}. </math> The class probability evolves as :<math> r(\theta) = \frac{e^{\theta}} {e^{\theta}+1}. </math> The individual probabilities are :<math> p_1(\theta) = \frac{1}{2}r(\theta), </math> :<math> p_2(\theta) = \frac{1}{2}r(\theta), </math> and :<math> p_3(\theta) = 1-r(\theta). </math> The angular coordinate is :<math> \alpha(\theta) = \arctan \left( e^{-\theta/2} \right). </math> Thus the trajectory is an exponential-family e-geodesic whose image is simultaneously a Fisher–Rao Levi-Civita geodesic. Its exponential parameterization is nonuniform, while <math>2\alpha</math> provides a signed Fisher–Rao arclength coordinate up to an additive constant and choice of orientation. === 8.12 Interpretation === The two-level result separates the '''path''' from the '''parameterization'''. The exponential parameter <math>\theta</math> generates the probability trajectory through normalized exponential weighting. The Fisher–Rao geometry identifies the same trajectory as a great-circle path. The transformation :<math> \theta \longmapsto \alpha(\theta) \longmapsto s(\theta) </math> provides the exact reparameterization needed to express that path in Fisher–Rao arclength. This provides a concrete example in which exponential-family straightness and Fisher–Rao Levi-Civita straightness describe the same geometric image while using different natural parameters. == Relationship to the Probability Dilation Theory project == This manuscript is part of the broader [[Probability Dilation Theory]] research project on Wikiversity. Technical and exploratory material related to the manuscript is developed on associated PDT subpages, including: * [[Probability Dilation Theory/Measure-Theoretic Foundations|Measure-Theoretic Foundations]] * [[Probability Dilation Theory/Matrix Dilation Operators|Matrix Dilation Operators]] * [[Probability Dilation Theory/Dilation Vector Field|Dilation Vector Field]] * [[Probability Dilation Theory/Dilation Flows|Dilation Flows]] * [[Probability Dilation Theory/Convergence and Fixed Points|Convergence and Fixed Points]] * [[Probability Dilation Theory/Fisher Geometry and Dilation Flows|Fisher Geometry and Dilation Flows]] The present page is intended to develop a concise, standalone manuscript rather than reproduce the complete exploratory PDT project. == Draft status and research note == This manuscript is a work in progress. Some constructions discussed in the paper have direct counterparts in established mathematical literature. These relationships are identified explicitly wherever possible. Results developed specifically within the present formulation are being subjected to continuing literature review, proof checking, numerical verification, and independent mathematical scrutiny before any claim of novelty is made. Readers are encouraged to identify relevant prior literature, mathematical errors, counterexamples, alternative proofs, or useful extensions. == See also == * [[Probability Dilation Theory]] * [[Probability Dilation Theory/Matrix Dilation Operators]] * [[Probability Dilation Theory/Measure-Theoretic Foundations]] * [[Probability Dilation Theory/Fisher Geometry and Dilation Flows]] == Copyright and licensing == Text and original figures © Howard Richardson. Licensed under the [https://creativecommons.org/licenses/by/4.0/ Creative Commons Attribution 4.0 International License (CC BY 4.0)]. Reuse permitted with attribution. 2v5uxi0varbjvy4vzazt43ceammacq7 2823787 2823784 2026-08-21T01:52:42Z Howie2024 2995240 /* 8.12 Interpretation */ insert section 10. 2823787 wikitext text/x-wiki {{Research project}} '''Research manuscript — Draft Version 1.0''' ''This page develops a standalone research manuscript arising from the [[Probability Dilation Theory]] project. It is a work in progress and should not be regarded as a peer-reviewed publication.'' = Normalized Probability Dilation: A Unified Framework and Its Fisher–Rao Geometry = '''Howard Richardson''' ''Draft Version 1.0 — August 2026'' == Abstract == This paper develops a unified framework for normalized positive transformations of probability distributions, referred to here as '''Probability Dilation Theory (PDT)'''. The central construction consists of applying a positive transformation to a probability state and subsequently renormalizing the result. In finite dimensions this includes diagonal reweighting, :<math> p_i'= \frac{d_i p_i} {\sum_j d_jp_j}, </math> and the matrix transformation :<math> T_M(p)= \frac{Mp} {\mathbf{1}^{\mathsf T}Mp}, </math> for suitable nonnegative matrices <math>M</math>. A corresponding measure-theoretic formulation is :<math> P_D(A)= \frac{\int_A D\,dP} {\int_X D\,dP}. </math> These constructions are compared explicitly with established mathematical structures including change of measure, normalized positive operators, Perron–Frobenius iteration, Markov operators, replicator-type dynamics, and normalized Feynman–Kac transformations. The purpose of the framework is therefore not to claim these established constructions as new, but to investigate their common dilation-normalization structure and the geometry of the resulting probability trajectories. Particular attention is given to the exponential dilation family :<math> p_i(\theta)= \frac{p_i^{(0)}e^{\theta\phi_i}} {\sum_j p_j^{(0)}e^{\theta\phi_j}}. </math> Using the square-root representation of the Fisher–Rao simplex, we establish that, under finite-dimensional strict-positivity assumptions, the image of this exponential-dilation trajectory is contained in a Fisher–Rao Levi-Civita geodesic, up to reparameterization, if and only if the generator <math>\phi</math> assumes at most two distinct values. An explicit Fisher–Rao arclength parameterization is then obtained for the nondegenerate two-level case. The framework provides a common language for normalized probability transformations while separating results inherited from established theory from geometric properties arising from the particular dilation formulation. == 1. Introduction == Probability distributions are frequently transformed by operations having a common mathematical structure: nonnegative weights are modified by a positive transformation and subsequently normalized so that total probability remains unity. Such constructions occur in numerous areas of probability, statistics, dynamical systems, numerical linear algebra, and mathematical physics. The simplest finite-dimensional example takes a probability vector :<math> p=(p_1,\ldots,p_n)^{\mathsf T}, \qquad p_i\geq 0, \qquad \sum_{i=1}^{n}p_i=1, </math> assigns positive weights <math>d_i</math>, and defines :<math> p_i'= \frac{d_i p_i} {\sum_{j=1}^{n}d_jp_j}. </math> The transformation changes the relative probability assigned to individual states while normalization returns the resulting vector to the probability simplex. This paper uses the term '''probability dilation''' for this general transformation-and-normalization structure and examines a hierarchy of related constructions. In finite dimensions, diagonal dilation extends naturally to the action of a nonnegative matrix, :<math> T_M(p)= \frac{Mp} {\mathbf{1}^{\mathsf T}Mp}, </math> whenever the denominator is positive. At the level of probability measures, multiplication by a positive measurable function <math>D</math> gives :<math> P_D(A)= \frac{\displaystyle\int_A D(x)\,dP(x)} {\displaystyle\int_X D(x)\,dP(x)}. </math> These expressions have substantial connections with existing mathematics. Normalized matrix iteration is closely related to the power method and Perron–Frobenius theory; positive weighting of measures belongs to established change-of-measure constructions; stochastic matrices provide the familiar Markov special case; and normalized potential-weighted measures occur in Feynman–Kac models. Accordingly, the objective of PDT as developed here is '''not''' to rename these established mathematical theories or to assert novelty for normalization itself. Instead, the objective is to examine them through the common structural sequence :<math> \text{positive transformation} \longrightarrow \text{normalization} \longrightarrow \text{iteration} \longrightarrow \text{probability dynamics} \longrightarrow \text{geometry}. </math> This viewpoint leads naturally to questions concerning fixed points, convergence, entropy, state-dependent transformations, and the geometry of trajectories on the probability simplex. === 1.1 Exponential dilation === A particularly useful example is obtained from exponential dilation. Given an initial strictly positive probability vector <math>p^{(0)}</math> and a real-valued generator <math>\phi</math>, define :<math> p_i(\theta)= \frac{p_i^{(0)}e^{\theta\phi_i}} {Z(\theta)}, </math> where :<math> Z(\theta)= \sum_j p_j^{(0)}e^{\theta\phi_j}. </math> This is an exponential-family construction and therefore belongs to well-established information geometry. The question considered here is more specific: :''When is this exponential trajectory also a Levi-Civita geodesic of the Fisher–Rao metric?'' The Fisher–Rao geometry of a finite probability simplex admits a square-root representation on a sphere. Under the mapping :<math> p\longmapsto 2(\sqrt{p_1},\ldots,\sqrt{p_n}), </math> Fisher–Rao geodesics correspond to spherical great-circle arcs. This representation permits a direct characterization of exponential dilation trajectories that are simultaneously Fisher–Rao geodesic. === 1.2 Principal geometric result === The principal geometric result developed below is that, for a strictly positive finite probability vector, an exponential dilation trajectory lies on a Fisher–Rao geodesic, up to reparameterization, precisely when its generator assumes no more than two distinct values. The proof reduces the problem to the dimension of the linear span generated by distinct exponential rates and uses a Vandermonde argument for the converse. The resulting two-level trajectory also admits an explicit Fisher–Rao arclength parameterization. At the present draft stage, this characterization is treated conservatively. Its constituent mathematical ingredients are established results from information geometry and linear algebra. The exact characterization developed here remains subject to further literature review and independent mathematical scrutiny. === 1.3 Organization of the paper === The remainder of the paper is organized as follows: * '''Section 2''' introduces the normalized-dilation framework and notation. * '''Section 3''' develops diagonal and matrix formulations. * '''Section 4''' develops the measure-theoretic formulation. * '''Section 5''' compares the framework explicitly with established mathematics. * '''Section 6''' introduces exponential dilation and its information-geometric representation. * '''Section 7''' states and proves the Fisher–Rao geodesic characterization theorem. * '''Section 8''' derives the two-level Fisher–Rao arclength corollary and illustrative examples. * '''Section 9''' discusses limitations, possible extensions, and open problems. * '''Section 10''' summarizes the principal conclusions. == 2. Normalized-Dilation Framework == This section introduces the common mathematical structure used throughout the paper. The essential operation consists of applying a positive transformation to a probability state and then normalizing the transformed object so that it again represents a probability distribution. === 2.1 Probability simplex === For a finite state space with <math>n</math> states, define the probability simplex :<math> \Delta^{n-1} = \left\{ p\in\mathbb{R}^{n}: p_i\geq 0,\; \sum_{i=1}^{n}p_i=1 \right\}. </math> A probability state is represented by a column vector :<math> p= (p_1,\ldots,p_n)^{\mathsf{T}} \in\Delta^{n-1}. </math> Its components satisfy :<math> p_i\geq 0 </math> and :<math> \mathbf{1}^{\mathsf{T}}p=1, </math> where :<math> \mathbf{1} = (1,\ldots,1)^{\mathsf{T}}. </math> The interior of the simplex is :<math> \Delta_{+}^{n-1} = \left\{ p\in\Delta^{n-1}:p_i>0 \text{ for all }i \right\}. </math> The distinction between the simplex and its interior becomes important later when Fisher–Rao geometry is considered. === 2.2 Positive transformations === Let <math>\mathcal{L}</math> denote a transformation acting on probability states such that :<math> p\geq 0 \quad\Longrightarrow\quad \mathcal{L}(p)\geq 0. </math> The transformed object <math>\mathcal{L}(p)</math> need not itself be normalized. Define its total mass by :<math> \mathcal{N}[\mathcal{L}(p)] = \mathbf{1}^{\mathsf{T}}\mathcal{L}(p). </math> Whenever :<math> 0< \mathcal{N}[\mathcal{L}(p)] < \infty, </math> the normalized transformation is defined by :<math> \mathcal{T}_{\mathcal{L}}(p) = \frac{\mathcal{L}(p)} {\mathcal{N}[\mathcal{L}(p)]}. </math> Equivalently, in the finite-dimensional setting, :<math> \mathcal{T}_{\mathcal{L}}(p) = \frac{\mathcal{L}(p)} {\mathbf{1}^{\mathsf{T}}\mathcal{L}(p)}. </math> By construction, :<math> \mathbf{1}^{\mathsf{T}} \mathcal{T}_{\mathcal{L}}(p) = 1, </math> so :<math> \mathcal{T}_{\mathcal{L}}(p) \in \Delta^{n-1}. </math> This positive-transformation-plus-normalization operation is the basic structure referred to in this paper as '''normalized probability dilation'''. === 2.3 Normalization as projectivization === An immediate property of the normalized transformation is invariance under multiplication by a positive scalar. If <math>c>0</math>, then :<math> \frac{c\mathcal{L}(p)} {\mathbf{1}^{\mathsf{T}}c\mathcal{L}(p)} = \frac{\mathcal{L}(p)} {\mathbf{1}^{\mathsf{T}}\mathcal{L}(p)}. </math> Hence :<math> \mathcal{T}_{c\mathcal{L}}(p) = \mathcal{T}_{\mathcal{L}}(p). </math> The normalized transformation therefore depends on the relative components of <math>\mathcal{L}(p)</math>, rather than on its overall positive scale. This projective feature connects normalized dilation with established theories of positive operators and projective dynamics. No claim of novelty is attached to the normalization or projectivization operation itself. === 2.4 Diagonal dilation === Let :<math> D= \operatorname{diag}(d_1,\ldots,d_n), \qquad d_i>0. </math> Applying <math>D</math> to <math>p</math> gives :<math> Dp= (d_1p_1,\ldots,d_np_n)^{\mathsf{T}}. </math> Normalization produces :<math> T_D(p) = \frac{Dp} {\mathbf{1}^{\mathsf{T}}Dp}. </math> Componentwise, :<math> T_D(p)_i = \frac{d_ip_i} {\sum_{j=1}^{n}d_jp_j}. </math> This is the basic finite-dimensional dilation operation from which the broader PDT formulation developed. The factors <math>d_i</math> alter the relative weights of the probability states, while the denominator restores unit total probability. === 2.5 Matrix dilation === The diagonal transformation can be generalized to a nonnegative matrix :<math> M\in\mathbb{R}^{n\times n}, \qquad M_{ij}\geq 0. </math> For any probability vector <math>p</math> satisfying :<math> \mathbf{1}^{\mathsf{T}}Mp>0, </math> define :<math> T_M(p) = \frac{Mp} {\mathbf{1}^{\mathsf{T}}Mp}. </math> The diagonal case is recovered when :<math> M=D. </math> Off-diagonal entries permit components of the input probability vector to contribute to different output components before normalization. The matrix formulation therefore extends independent componentwise reweighting to coupled positive transformations. The mathematical behavior of this construction is closely related to established positive-matrix theory, normalized power iteration, and Perron–Frobenius theory. These relationships are discussed explicitly in Section 5. === 2.6 Measure-theoretic dilation === The same normalization principle extends naturally from finite probability vectors to probability measures. Let <math>(X,\mathcal{F},P)</math> be a probability space, and let :<math> D:X\rightarrow[0,\infty) </math> be measurable with :<math> 0< \int_X D(x)\,dP(x) < \infty. </math> Define a new probability measure <math>P_D</math> by :<math> P_D(A) = \frac{\displaystyle\int_A D(x)\,dP(x)} {\displaystyle\int_X D(x)\,dP(x)}, \qquad A\in\mathcal{F}. </math> Equivalently, the Radon–Nikodym derivative of <math>P_D</math> with respect to <math>P</math> is :<math> \frac{dP_D}{dP} = \frac{D} {\displaystyle\int_X D\,dP}. </math> Thus the finite-dimensional rule :<math> p_i \longmapsto \frac{d_ip_i} {\sum_jd_jp_j} </math> and the measure-theoretic rule :<math> dP \longmapsto \frac{D\,dP} {\int_XD\,dP} </math> share the same normalized positive-reweighting structure. This construction has direct connections with established change-of-measure and weighted-measure theory. The PDT terminology is used here as an organizing framework rather than as a claim that normalized change of measure is itself new. === 2.7 Iterated dilation === A normalized dilation operator can be iterated. Given an initial state :<math> p^{(0)}\in\Delta^{n-1}, </math> define :<math> p^{(k+1)} = \mathcal{T}_{\mathcal{L}}\left(p^{(k)}\right). </math> This generates an orbit :<math> p^{(0)} \longmapsto p^{(1)} \longmapsto p^{(2)} \longmapsto \cdots </math> on the probability simplex. For a fixed matrix <math>M</math>, :<math> p^{(k+1)} = \frac{Mp^{(k)}} {\mathbf{1}^{\mathsf{T}}Mp^{(k)}}. </math> When all required denominators are positive, repeated normalization gives :<math> p^{(k)} = \frac{M^k p^{(0)}} {\mathbf{1}^{\mathsf{T}}M^k p^{(0)}}. </math> The long-term behavior of this iteration is governed in important cases by established spectral and Perron–Frobenius theory. More general formulations may allow the transformation itself to depend on the iteration index or the current probability state, for example :<math> p^{(k+1)} = \frac{M_kp^{(k)}} {\mathbf{1}^{\mathsf{T}}M_kp^{(k)}} </math> or :<math> p^{(k+1)} = \frac{M(p^{(k)})p^{(k)}} {\mathbf{1}^{\mathsf{T}}M(p^{(k)})p^{(k)}}. </math> These state-dependent and iteration-dependent forms are treated as possible extensions rather than necessary components of the basic framework. === 2.8 Hierarchy of normalized dilation === The constructions above can be summarized by the following hierarchy: :'''diagonal reweighting → matrix transformation → positive operator → measure transformation''' At each level the essential operation is: :'''positive transformation + normalization''' The framework is deliberately broad. Its purpose is not to imply that all normalized positive transformations constitute a new mathematical theory, but to provide a common notation and viewpoint from which their dynamics and geometry can be compared. The following sections specialize this framework before examining its relationship to established mathematical constructions. == 3. Finite-Dimensional and Matrix Dilation == This section develops the finite-dimensional forms of normalized probability dilation in greater detail. The emphasis is on the relationship between diagonal reweighting and nonnegative matrix transformations, together with the basic structural properties required later in the paper. === 3.1 Finite probability states === Let :<math> p=(p_1,\ldots,p_n)^{\mathsf{T}} \in\Delta^{n-1}. </math> A positive weighting vector is written :<math> d=(d_1,\ldots,d_n)^{\mathsf{T}}, \qquad d_i>0. </math> The associated diagonal matrix is :<math> D= \operatorname{diag}(d_1,\ldots,d_n). </math> Applying the weighting gives :<math> Dp= (d_1p_1,\ldots,d_np_n)^{\mathsf{T}}. </math> Its total mass is :<math> Z(p,D) = \mathbf{1}^{\mathsf{T}}Dp = \sum_{i=1}^{n}d_ip_i. </math> Since <math>d_i>0</math> and <math>p</math> is a probability vector, :<math> Z(p,D)>0. </math> The normalized diagonal dilation operator is therefore :<math> T_D(p) = \frac{Dp}{Z(p,D)}. </math> Equivalently, :<math> T_D(p)_i = \frac{d_ip_i} {\sum_{j=1}^{n}d_jp_j}. </math> === 3.2 Relative probability transformation === Diagonal dilation has a simple effect on probability ratios. For any states <math>i</math> and <math>j</math> with <math>p_i>0</math> and <math>p_j>0</math>, :<math> \frac{T_D(p)_i}{T_D(p)_j} = \frac{d_i}{d_j} \frac{p_i}{p_j}. </math> Thus normalization does not alter the relative dilation introduced by the factors <math>d_i</math> and <math>d_j</math>. If :<math> d_i>d_j, </math> then the odds of state <math>i</math> relative to state <math>j</math> increase by the factor :<math> \frac{d_i}{d_j}. </math> This ratio form makes clear that diagonal dilation is fundamentally a relative reweighting operation. === 3.3 Scale invariance === Multiplying every dilation factor by the same positive constant does not change the normalized state. Let :<math> c>0. </math> Then :<math> T_{cD}(p) = \frac{cDp} {\mathbf{1}^{\mathsf{T}}cDp} = \frac{Dp} {\mathbf{1}^{\mathsf{T}}Dp} = T_D(p). </math> Therefore only the relative values of the dilation factors affect the transformed probability distribution. This scale invariance is a basic projective property of normalized positive transformations. === 3.4 Repeated diagonal dilation === Suppose the same diagonal operator <math>D</math> is applied repeatedly. Starting from <math>p^{(0)}</math>, define :<math> p^{(k+1)} = T_D(p^{(k)}). </math> Then :<math> p^{(k)} = \frac{D^k p^{(0)}} {\mathbf{1}^{\mathsf{T}}D^k p^{(0)}}. </math> Since :<math> D^k = \operatorname{diag}(d_1^k,\ldots,d_n^k), </math> the individual components are :<math> p_i^{(k)} = \frac{d_i^k p_i^{(0)}} {\sum_{j=1}^{n}d_j^k p_j^{(0)}}. </math> Consequently, for two initially positive components, :<math> \frac{p_i^{(k)}}{p_j^{(k)}} = \left(\frac{d_i}{d_j}\right)^k \frac{p_i^{(0)}}{p_j^{(0)}}. </math> This expression describes the concentration mechanism directly. If one dilation factor is strictly larger than all others and its corresponding initial probability is positive, repeated dilation concentrates probability on that state. If several states share the maximal dilation factor, probability concentrates on that maximal set while preserving the initial relative proportions within that set. This behavior is a direct consequence of normalized repeated weighting and is not specific to PDT terminology. === 3.5 General nonnegative matrix transformation === Let :<math> M=(M_{ij}) \in\mathbb{R}^{n\times n}, \qquad M_{ij}\geq0. </math> For <math>p\in\Delta^{n-1}</math>, define :<math> q=Mp. </math> Because <math>M</math> and <math>p</math> are nonnegative, :<math> q_i\geq0. </math> Whenever :<math> \mathbf{1}^{\mathsf{T}}Mp>0, </math> the normalized matrix dilation operator is :<math> T_M(p) = \frac{Mp} {\mathbf{1}^{\mathsf{T}}Mp}. </math> Its components are :<math> T_M(p)_i = \frac{\sum_{j=1}^{n}M_{ij}p_j} {\sum_{r=1}^{n}\sum_{j=1}^{n}M_{rj}p_j}. </math> By construction, :<math> \sum_{i=1}^{n}T_M(p)_i=1. </math> Hence :<math> T_M(p)\in\Delta^{n-1}. </math> === 3.6 Diagonal dilation as a special case === If :<math> M=D = \operatorname{diag}(d_1,\ldots,d_n), </math> then :<math> Mp=Dp, </math> and therefore :<math> T_M(p)=T_D(p). </math> Diagonal dilation is thus a special case of normalized matrix dilation. The distinction is structural. For a diagonal matrix, each output component depends only on the corresponding input component: :<math> (Dp)_i=d_ip_i. </math> For a general matrix, :<math> (Mp)_i = \sum_{j=1}^{n}M_{ij}p_j, </math> so multiple input states may contribute to a single output state before normalization. This permits coupled probability evolution. === 3.7 When normalization is unnecessary === There is an important special case. Suppose <math>M</math> satisfies :<math> \mathbf{1}^{\mathsf{T}}M = \mathbf{1}^{\mathsf{T}}. </math> Then for every probability vector <math>p</math>, :<math> \mathbf{1}^{\mathsf{T}}Mp = \mathbf{1}^{\mathsf{T}}p = 1. </math> Consequently, :<math> T_M(p)=Mp. </math> With the column-vector convention used in this paper, the condition :<math> \mathbf{1}^{\mathsf{T}}M = \mathbf{1}^{\mathsf{T}} </math> means that the columns of <math>M</math> sum to one. Thus an ordinary probability-preserving linear transition is contained as a special case of the normalized matrix framework. When <math>M</math> does not preserve total mass, normalization supplies the additional step required to return <math>Mp</math> to the simplex. === 3.8 Fixed points and eigenvectors === Suppose <math>p^{*}</math> is a fixed point of the normalized matrix operator: :<math> T_M(p^{*})=p^{*}. </math> Then :<math> \frac{Mp^{*}} {\mathbf{1}^{\mathsf{T}}Mp^{*}} = p^{*}. </math> Multiplying by the denominator gives :<math> Mp^{*} = \lambda p^{*}, </math> where :<math> \lambda = \mathbf{1}^{\mathsf{T}}Mp^{*}. </math> Therefore every fixed point of the normalized matrix transformation is a nonnegative eigenvector of <math>M</math>, normalized to have unit total mass. Conversely, if <math>v\geq0</math> is a nonzero eigenvector satisfying :<math> Mv=\lambda v, \qquad \lambda>0, </math> then :<math> p^{*} = \frac{v} {\mathbf{1}^{\mathsf{T}}v} </math> is a fixed point of <math>T_M</math>. Thus normalized fixed points and positive eigenvectors are directly related. === 3.9 Repeated matrix dilation === For a fixed nonnegative matrix <math>M</math>, define :<math> p^{(k+1)} = T_M(p^{(k)}). </math> Whenever the required denominators remain positive, :<math> p^{(k)} = \frac{M^k p^{(0)}} {\mathbf{1}^{\mathsf{T}}M^k p^{(0)}}. </math> This identity follows because the scalar normalization introduced at each intermediate step cancels under the next normalization. The iteration is therefore closely related to normalized power iteration. Under suitable positivity or primitivity assumptions, Perron–Frobenius theory describes the dominant eigenvalue and positive eigenvector governing the long-term behavior. Accordingly, convergence of the fixed-matrix case should be understood primarily through established positive-matrix and spectral theory rather than as a separate PDT convergence mechanism. === 3.10 Primitive positive matrices === A particularly important case occurs when <math>M</math> is primitive; that is, some positive integer power of <math>M</math> has strictly positive entries. Perron–Frobenius theory then provides a dominant real eigenvalue :<math> \rho(M)>0 </math> with a corresponding strictly positive eigenvector <math>v</math>. After normalization, :<math> p^{*} = \frac{v} {\mathbf{1}^{\mathsf{T}}v}, </math> this eigenvector gives the distinguished interior fixed point of the normalized matrix transformation. For suitable initial probability vectors, :<math> T_M^{k}(p^{(0)}) </math> converges toward <math>p^{*}</math>. This convergence is an established consequence of Perron–Frobenius theory and normalized power iteration. Its role here is to locate matrix dilation within known mathematics. === 3.11 Interpretation of off-diagonal terms === The off-diagonal entries of <math>M</math> distinguish matrix dilation from independent diagonal reweighting. For :<math> i\neq j, </math> a term :<math> M_{ij}p_j </math> represents a contribution from input state <math>j</math> to output component <math>i</math> before normalization. The matrix therefore combines two operations: * positive redistribution or coupling through <math>M</math>; * restoration of unit total probability through normalization. This interpretation is useful for organizing the framework, but the underlying linear transformation remains standard matrix mathematics. === 3.12 Scope of the matrix formulation === The matrix formulation substantially enlarges the class of transformations expressible within the normalized-dilation notation, but that enlargement should not be confused with mathematical novelty. For a fixed matrix <math>M</math>, the central objects :<math> Mp, \qquad M^kp, \qquad \rho(M), </math> and the associated eigenvectors and convergence properties belong to established linear algebra and positive-operator theory. The role of the PDT framework is to place diagonal reweighting, matrix transformation, iteration, and later measure-theoretic and geometric constructions within a common normalized-probability notation. This distinction between '''framework''' and '''new mathematical result''' will be maintained throughout the paper. == 4. Measure-Theoretic Dilation == The finite-dimensional dilation rule extends naturally to probability measures. In this setting, componentwise multiplication by positive weights is replaced by multiplication of a probability measure by a nonnegative measurable function followed by normalization. This formulation places finite probability dilation within the standard language of measure theory and makes its relationship to change of measure explicit. === 4.1 Probability-space formulation === Let :<math> (X,\mathcal{F},P) </math> be a probability space. Let :<math> D:X\rightarrow[0,\infty) </math> be a measurable function satisfying :<math> 0< \int_X D(x)\,dP(x) < \infty. </math> Define the normalization factor :<math> Z(P,D) = \int_X D(x)\,dP(x). </math> For every measurable set :<math> A\in\mathcal{F}, </math> define :<math> P_D(A) = \frac{\displaystyle\int_A D(x)\,dP(x)} {Z(P,D)}. </math> Equivalently, :<math> P_D(A) = \frac{\displaystyle\int_A D(x)\,dP(x)} {\displaystyle\int_X D(x)\,dP(x)}. </math> The function <math>D</math> acts as a nonnegative weighting or dilation field over the probability space. === 4.2 Normalization === The transformed measure has total mass one because :<math> P_D(X) = \frac{\displaystyle\int_X D(x)\,dP(x)} {\displaystyle\int_X D(x)\,dP(x)} = 1. </math> Also, because <math>D</math> is nonnegative, :<math> P_D(A)\geq0 </math> for every <math>A\in\mathcal{F}</math>. Countable additivity follows from the countable additivity of integration with respect to <math>P</math>. Therefore <math>P_D</math> is a probability measure. === 4.3 Radon–Nikodym representation === The transformed measure <math>P_D</math> is absolutely continuous with respect to <math>P</math>. Its Radon–Nikodym derivative is :<math> \frac{dP_D}{dP}(x) = \frac{D(x)} {\displaystyle\int_X D(y)\,dP(y)}. </math> Thus normalized measure dilation can be written formally as :<math> dP_D(x) = \frac{D(x)\,dP(x)} {\displaystyle\int_X D(y)\,dP(y)}. </math> This expression makes clear that the construction is a normalized change of measure. The Radon–Nikodym framework is established measure theory. The terminology of dilation is used here to emphasize the common transformation-and-normalization structure shared with the finite-dimensional formulation. === 4.4 Scale invariance === As in the finite-dimensional case, multiplication of the dilation field by a positive constant does not change the normalized measure. Let :<math> c>0. </math> Then :<math> P_{cD}(A) = \frac{\displaystyle\int_A cD\,dP} {\displaystyle\int_X cD\,dP}. </math> The common factor cancels, giving :<math> P_{cD}(A)=P_D(A). </math> Hence the transformed probability measure depends only on the relative values of the dilation field <math>D</math>, not on its overall positive scale. === 4.5 Finite probability spaces as a special case === Consider a finite state space :<math> X=\{1,\ldots,n\}. </math> Let :<math> P(\{i\})=p_i </math> and define :<math> D(i)=d_i. </math> Then :<math> \int_X D\,dP = \sum_{j=1}^{n}d_jp_j. </math> For the singleton event <math>\{i\}</math>, :<math> P_D(\{i\}) = \frac{d_ip_i} {\sum_{j=1}^{n}d_jp_j}. </math> Thus the finite diagonal dilation rule :<math> p_i' = \frac{d_ip_i} {\sum_jd_jp_j} </math> is recovered exactly from the measure-theoretic construction. The discrete and measure-theoretic formulations are therefore instances of the same normalized positive-reweighting operation. === 4.6 Expectations under dilation === Let :<math> f:X\rightarrow\mathbb{R} </math> be measurable and integrable with respect to the transformed measure. Then :<math> \mathbb{E}_{P_D}[f] = \int_X f(x)\,dP_D(x). </math> Using the Radon–Nikodym representation, :<math> \mathbb{E}_{P_D}[f] = \frac{\displaystyle\int_X f(x)D(x)\,dP(x)} {\displaystyle\int_X D(x)\,dP(x)}. </math> Equivalently, :<math> \mathbb{E}_{P_D}[f] = \frac{\mathbb{E}_{P}[fD]} {\mathbb{E}_{P}[D]}, </math> provided the required expectations exist. This identity is a standard weighted-expectation formula and will later be useful for exponential dilation. === 4.7 Composition of dilation fields === Suppose a first dilation field <math>D_1</math> transforms <math>P</math> into <math>P_{D_1}</math>, and a second field <math>D_2</math> is then applied. The first transformation gives :<math> dP_{D_1} = \frac{D_1\,dP} {\int_XD_1\,dP}. </math> Applying <math>D_2</math> gives :<math> d(P_{D_1})_{D_2} = \frac{D_2\,dP_{D_1}} {\int_XD_2\,dP_{D_1}}. </math> Substituting the first transformation and simplifying yields :<math> d(P_{D_1})_{D_2} = \frac{D_1D_2\,dP} {\int_XD_1D_2\,dP}, </math> whenever the required integrals are finite and positive. Therefore :<math> (P_{D_1})_{D_2} = P_{D_1D_2}. </math> Sequential scalar dilation fields thus combine multiplicatively before normalization. This composition property is the measure-theoretic analogue of repeated diagonal reweighting. === 4.8 Iterated fixed dilation === If the same dilation field <math>D</math> is applied repeatedly, then after <math>k</math> iterations, :<math> dP^{(k)} = \frac{D^k\,dP^{(0)}} {\displaystyle\int_XD^k\,dP^{(0)}}. </math> Equivalently, for any measurable event <math>A</math>, :<math> P^{(k)}(A) = \frac{\displaystyle\int_A D(x)^k\,dP^{(0)}(x)} {\displaystyle\int_X D(x)^k\,dP^{(0)}(x)}. </math> This is the direct measure-theoretic counterpart of :<math> p_i^{(k)} = \frac{d_i^kp_i^{(0)}} {\sum_jd_j^kp_j^{(0)}}. </math> Regions where <math>D</math> is relatively large receive increasing relative weight under repeated application. The precise limiting behavior depends on the structure of <math>D</math> and the initial measure. === 4.9 Exponential dilation fields === A particularly important family is obtained by choosing :<math> D_{\theta}(x) = e^{\theta\phi(x)}, </math> where <math>\phi:X\rightarrow\mathbb{R}</math> is measurable and <math>\theta</math> is a real parameter for which the normalization integral is finite. Define :<math> Z(\theta) = \int_X e^{\theta\phi(x)}\,dP_0(x). </math> Then :<math> dP_{\theta}(x) = \frac{e^{\theta\phi(x)}} {Z(\theta)} dP_0(x). </math> In a finite state space this becomes :<math> p_i(\theta) = \frac{p_i^{(0)}e^{\theta\phi_i}} {\sum_jp_j^{(0)}e^{\theta\phi_j}}. </math> This is a standard exponential tilting construction and is closely related to exponential families, cumulant-generating functions, and information geometry. Its importance for the present paper is that it provides a continuous one-parameter dilation trajectory whose Fisher–Rao geometry can be studied explicitly. === 4.10 Infinitesimal evolution of exponential dilation === For the finite-dimensional exponential family, :<math> p_i(\theta) = \frac{p_i^{(0)}e^{\theta\phi_i}} {Z(\theta)}, </math> differentiate with respect to <math>\theta</math>. The logarithmic derivative is :<math> \frac{d}{d\theta}\log p_i(\theta) = \phi_i - \frac{d}{d\theta}\log Z(\theta). </math> Since :<math> \frac{d}{d\theta}\log Z(\theta) = \sum_jp_j(\theta)\phi_j, </math> define :<math> \overline{\phi}_{\theta} = \sum_jp_j(\theta)\phi_j. </math> Then :<math> \frac{dp_i}{d\theta} = p_i(\theta) \left( \phi_i-\overline{\phi}_{\theta} \right). </math> This equation has the form of a replicator-type evolution equation with a fixed state-dependent generator <math>\phi_i</math>. The relationship to established replicator dynamics is discussed in Section 5. === 4.11 Conservation of total probability === Summing the infinitesimal evolution equation gives :<math> \sum_i \frac{dp_i}{d\theta} = \sum_i p_i(\theta) \left( \phi_i-\overline{\phi}_{\theta} \right). </math> Since :<math> \sum_ip_i(\theta)\phi_i = \overline{\phi}_{\theta} </math> and :<math> \sum_ip_i(\theta)=1, </math> it follows that :<math> \sum_i \frac{dp_i}{d\theta} = 0. </math> Thus the vector field is tangent to the probability simplex. Normalization is therefore reflected infinitesimally by conservation of total probability. === 4.12 Scope of the measure-theoretic formulation === The measure-theoretic formulation shows that normalized probability dilation is not restricted to finite vectors or matrices. The same structural operation appears as :'''weight → normalize → obtain a new probability measure''' and, for exponential fields, :'''exponential weight → normalize → continuous probability trajectory'''. These constructions overlap directly with established change-of-measure theory, exponential tilting, weighted probability measures, and related probabilistic methods. Their role in the present framework is to connect the finite dilation notation to continuous probability spaces and to provide the bridge to the information-geometric analysis developed later in the paper. The next section therefore compares the normalized-dilation framework systematically with established mathematical constructions before any additional geometric results are introduced. == 5. Relation to Established Mathematics == The normalized-dilation framework overlaps with several established areas of mathematics. This section identifies those relationships explicitly. The purpose is twofold: first, to place the notation used in this paper within its appropriate mathematical context; and second, to distinguish established constructions from the particular synthesis and geometric questions developed later in the paper. The term '''probability dilation''' is therefore used as an organizing description of a transformation-and-normalization structure, not as a claim that the underlying operations of reweighting, normalization, positive matrix iteration, or change of measure are themselves new. === 5.1 Weighted probability and change of measure === The measure-theoretic transformation :<math> dP_D = \frac{D\,dP} {\int_XD\,dP} </math> is a standard normalized change of measure. Its Radon–Nikodym derivative with respect to <math>P</math> is :<math> \frac{dP_D}{dP} = \frac{D} {\int_XD\,dP}. </math> Consequently, for an integrable observable <math>f</math>, :<math> \mathbb{E}_{P_D}[f] = \frac{\mathbb{E}_{P}[fD]} {\mathbb{E}_{P}[D]}. </math> These expressions belong to established measure-theoretic probability. Within the present framework, their role is to show that finite diagonal dilation and continuous weighted change of measure share the same normalized reweighting structure. === 5.2 Bayesian reweighting === A closely related normalization structure occurs in Bayesian inference. If <math>\pi(x)</math> is a prior density and <math>L(y\mid x)</math> is a likelihood for observed data <math>y</math>, Bayes' rule gives :<math> \pi(x\mid y) = \frac{L(y\mid x)\pi(x)} {\int L(y\mid z)\pi(z)\,dz}, </math> when the denominator is finite and nonzero. Structurally, this has the same form as :<math> dP_D = \frac{D\,dP} {\int D\,dP}, </math> with the likelihood acting as a positive weighting function. The statistical interpretation is different: Bayesian updating has a specific inferential meaning associated with conditioning on data. The comparison here concerns only the common mathematical normalization structure. === 5.3 Importance weighting and exponential tilting === Weighted probability measures also arise in importance sampling, exponential tilting, large-deviation methods, and related statistical constructions. For a generator <math>\phi</math>, exponential tilting takes the form :<math> dP_{\theta}(x) = \frac{e^{\theta\phi(x)}} {Z(\theta)} dP_0(x), </math> where :<math> Z(\theta) = \int_Xe^{\theta\phi(x)}\,dP_0(x). </math> This is an established exponential-family construction. The corresponding finite-dimensional expression, :<math> p_i(\theta) = \frac{p_i^{(0)}e^{\theta\phi_i}} {\sum_jp_j^{(0)}e^{\theta\phi_j}}, </math> will be the principal object of the Fisher–Rao analysis in Sections 6 through 8. The geometric analysis developed later concerns this established exponential-tilt family under a particular question about coincidence of information-geometric and Fisher–Rao geodesics. === 5.4 Positive matrices and Perron–Frobenius theory === For a fixed nonnegative matrix <math>M</math>, the normalized transformation :<math> T_M(p) = \frac{Mp} {\mathbf{1}^{\mathsf{T}}Mp} </math> is closely related to classical positive-matrix theory. If <math>M</math> is primitive, Perron–Frobenius theory provides a dominant positive eigenvalue :<math> \rho(M)>0 </math> and a corresponding strictly positive eigenvector. Repeated normalized iteration, :<math> p^{(k)} = \frac{M^kp^{(0)}} {\mathbf{1}^{\mathsf{T}}M^kp^{(0)}}, </math> is therefore closely related to normalized power iteration. Under appropriate hypotheses, its asymptotic direction is governed by the Perron eigenvector. These spectral and convergence results are established mathematics and are not presented here as new consequences of PDT. === 5.5 Markov operators === Suppose <math>M</math> is nonnegative and satisfies :<math> \mathbf{1}^{\mathsf{T}}M = \mathbf{1}^{\mathsf{T}}. </math> With the column-vector convention used in this paper, :<math> \mathbf{1}^{\mathsf{T}}Mp = 1 </math> for every probability vector <math>p</math>. Thus :<math> T_M(p)=Mp. </math> In this mass-preserving case, the normalization step is unnecessary. Accordingly, ordinary finite-state Markov evolution is contained as a special mass-preserving case of the broader positive-transformation framework. This observation is structural. It does not imply that normalized dilation provides a replacement for Markov-chain theory. === 5.6 Replicator-type dynamics === The exponential dilation family satisfies :<math> \frac{dp_i}{d\theta} = p_i \left( \phi_i-\overline{\phi}_{\theta} \right), </math> where :<math> \overline{\phi}_{\theta} = \sum_jp_j(\theta)\phi_j. </math> The standard replicator equation has the form :<math> \frac{dp_i}{dt} = p_i \left( f_i(p)-\overline{f}(p) \right). </math> Thus exponential dilation with fixed generator values <math>\phi_i</math> has the same algebraic structure as a replicator equation with state-independent fitness values. The mean-subtraction term guarantees :<math> \sum_i\frac{dp_i}{d\theta}=0, </math> so the flow remains tangent to the probability simplex. Replicator dynamics and their geometric interpretations are established subjects. The present paper uses this connection to relate normalized dilation to known simplex dynamics. === 5.7 Fisher–Rao and Shahshahani geometry === The interior of the probability simplex carries the Fisher–Rao metric. For tangent vectors <math>u</math> and <math>v</math> satisfying :<math> \sum_i u_i = \sum_i v_i = 0, </math> the finite-dimensional Fisher–Rao metric can be written as :<math> g_p(u,v) = \sum_{i=1}^{n} \frac{u_iv_i}{p_i}. </math> Closely related forms of this metric appear in evolutionary dynamics under the name Shahshahani metric. The square-root mapping :<math> \Psi(p) = 2(\sqrt{p_1},\ldots,\sqrt{p_n}) </math> satisfies :<math> \sum_i\Psi_i(p)^2=4. </math> Thus the simplex interior is represented in the positive orthant of a sphere of radius <math>2</math>. Under this representation, the Fisher–Rao metric becomes the metric induced by the ambient Euclidean space, and Levi-Civita Fisher–Rao geodesics correspond locally to great-circle arcs. This established spherical representation will be the principal geometric tool used in Section 7. === 5.8 Exponential families and the e-connection === The exponential dilation path :<math> p_i(\theta) = \frac{p_i^{(0)}e^{\theta\phi_i}} {Z(\theta)} </math> is a one-parameter exponential family. Taking logarithms gives :<math> \log p_i(\theta) = \log p_i^{(0)} + \theta\phi_i - \log Z(\theta). </math> The natural parameter varies linearly with <math>\theta</math>. In information geometry, exponential families are naturally associated with the exponential, or '''e''', connection. A path linear in natural parameters is an e-geodesic. This notion of geodesic is distinct from a Levi-Civita geodesic of the Fisher–Rao metric. Consequently, an exponential dilation trajectory may be straight with respect to the e-connection while being curved with respect to the Fisher–Rao Levi-Civita connection. This distinction is central to the geometric question investigated later in the paper. === 5.9 Fisher information and variance === For the exponential dilation family, :<math> \frac{d}{d\theta} \log p_i(\theta) = \phi_i-\overline{\phi}_{\theta}. </math> The Fisher information associated with the parameter <math>\theta</math> is therefore :<math> I(\theta) = \sum_i p_i(\theta) \left( \phi_i-\overline{\phi}_{\theta} \right)^2. </math> Hence :<math> I(\theta) = \operatorname{Var}_{p(\theta)}(\phi). </math> The Fisher–Rao speed of the trajectory is :<math> v_{\mathrm{FR}}(\theta) = \sqrt{I(\theta)} = \sqrt{\operatorname{Var}_{p(\theta)}(\phi)}. </math> This variance identity is a standard property of one-parameter exponential families. It will be used later when deriving the arclength parameterization of the two-level case. === 5.10 Normalized Feynman–Kac transformations === Another closely related structure occurs in Feynman–Kac models. At an abstract level, a positive measure may first be weighted by a nonnegative potential and then propagated through a positive or Markov operator, followed by normalization. Schematically, such an evolution has the form :'''weight → propagate → normalize'''. The matrix expression :<math> T_M(p) = \frac{Mp} {\mathbf{1}^{\mathsf{T}}Mp} </math> and the measure expression :<math> dP_D = \frac{D\,dP} {\int D\,dP} </math> therefore have structural analogues within normalized Feynman–Kac theory. The exact interpretation and assumptions differ among applications. The comparison made here is structural rather than an assertion of equivalence between PDT and Feynman–Kac theory. === 5.11 Projective dynamics === Because normalized dilation is invariant under multiplication of the unnormalized transformed state by a positive scalar, it naturally has a projective character. For example, :<math> T_{cM}(p) = T_M(p) </math> for every <math>c>0</math> for which the transformation is defined. Thus the normalized state depends on the ray determined by <math>Mp</math>, rather than its magnitude. Positive projective geometry and projective metrics, including Hilbert-type metrics, are established tools in the study of positive operators and their contraction properties. These methods provide natural mathematical machinery for analyzing normalized positive transformations, particularly in convergence problems. === 5.12 What the PDT framework contributes === The preceding comparisons show that the principal operations used in normalized probability dilation have substantial established precedents. The proposed contribution of the framework is therefore not the isolated operation :'''multiply or transform, then normalize'''. Rather, the framework provides a common notation and organizational viewpoint connecting: * finite diagonal reweighting; * nonnegative matrix transformations; * normalized positive iteration; * weighted change of measure; * exponential probability trajectories; * simplex dynamics; * information geometry. This synthesis is useful only insofar as it clarifies relationships, generates mathematically precise questions, or produces results that are not merely restatements of known theory. For that reason, the remainder of this paper concentrates on a narrower geometric problem. === 5.13 Transition to the geometric question === Every exponential dilation trajectory of the form :<math> p_i(\theta) = \frac{p_i^{(0)}e^{\theta\phi_i}} {Z(\theta)} </math> is an exponential-family trajectory and hence is naturally straight with respect to the e-connection. It does not follow that the same trajectory is a Levi-Civita geodesic of the Fisher–Rao metric. This leads to the central question considered in the remainder of the paper: :''Under what conditions is an exponential dilation trajectory simultaneously an e-geodesic and, up to reparameterization, a Fisher–Rao Levi-Civita geodesic?'' The next section develops the geometric representation required to answer this question. == 6. Exponential Dilation and Fisher–Rao Geometry == This section develops the geometric representation of exponential dilation required for the main characterization theorem. The central object is the one-parameter exponential family :<math> p_i(\theta) = \frac{p_i^{(0)}e^{\theta\phi_i}} {Z(\theta)}, </math> where :<math> Z(\theta) = \sum_{j=1}^{n}p_j^{(0)}e^{\theta\phi_j}. </math> Throughout this section, assume :<math> p_i^{(0)}>0 </math> for all <math>i</math>, and let :<math> \phi=(\phi_1,\ldots,\phi_n) </math> be a real-valued generator. === 6.1 Exponential dilation trajectory === Let :<math> p^{(0)} \in \Delta_{+}^{n-1}. </math> For a real parameter <math>\theta</math>, define :<math> p_i(\theta) = \frac{p_i^{(0)}e^{\theta\phi_i}} {\sum_{j=1}^{n}p_j^{(0)}e^{\theta\phi_j}}. </math> Since every initial component is strictly positive and the exponential function is positive, :<math> p_i(\theta)>0 </math> for every finite <math>\theta</math>. Therefore the trajectory remains in the interior of the probability simplex. The normalization factor satisfies :<math> Z(\theta)>0. </math> Hence the trajectory is well defined for every finite <math>\theta</math> in the finite-dimensional setting. === 6.2 Logarithmic form === Taking logarithms gives :<math> \log p_i(\theta) = \log p_i^{(0)} + \theta\phi_i - \log Z(\theta). </math> Differentiating with respect to <math>\theta</math> gives :<math> \frac{d}{d\theta}\log p_i(\theta) = \phi_i - \frac{d}{d\theta}\log Z(\theta). </math> Now :<math> \frac{dZ}{d\theta} = \sum_j p_j^{(0)} \phi_j e^{\theta\phi_j}. </math> Therefore :<math> \frac{d}{d\theta}\log Z(\theta) = \sum_jp_j(\theta)\phi_j. </math> Define the expectation of the generator by :<math> \mu(\theta) = \mathbb{E}_{p(\theta)}[\phi] = \sum_jp_j(\theta)\phi_j. </math> Then :<math> \frac{d}{d\theta}\log p_i(\theta) = \phi_i-\mu(\theta). </math> === 6.3 Tangent vector === Multiplying the logarithmic derivative by <math>p_i(\theta)</math> gives :<math> \frac{dp_i}{d\theta} = p_i(\theta) \left( \phi_i-\mu(\theta) \right). </math> Define the centered generator :<math> h_i(\theta) = \phi_i-\mu(\theta). </math> Then :<math> \frac{dp_i}{d\theta} = p_i(\theta)h_i(\theta). </math> Because :<math> \sum_i p_i(\theta)h_i(\theta) = 0, </math> we obtain :<math> \sum_i \frac{dp_i}{d\theta} = 0. </math> Thus the velocity vector is tangent to the probability simplex. === 6.4 Fisher information and speed === The Fisher–Rao metric on the simplex interior is :<math> g_p(u,v) = \sum_i \frac{u_iv_i}{p_i}, </math> for tangent vectors <math>u</math> and <math>v</math>. For the exponential dilation trajectory, :<math> \frac{dp_i}{d\theta} = p_i h_i. </math> Its squared Fisher–Rao speed is therefore :<math> v_{\mathrm{FR}}(\theta)^2 = \sum_i \frac{1}{p_i} \left( \frac{dp_i}{d\theta} \right)^2. </math> Substitution gives :<math> v_{\mathrm{FR}}(\theta)^2 = \sum_i p_i(\theta)h_i(\theta)^2. </math> Hence :<math> v_{\mathrm{FR}}(\theta)^2 = \operatorname{Var}_{p(\theta)}(\phi). </math> Therefore :<math> v_{\mathrm{FR}}(\theta) = \sqrt{ \operatorname{Var}_{p(\theta)}(\phi) }. </math> This is the standard Fisher-information identity for a one-parameter exponential family. === 6.5 Square-root representation === Define the square-root map :<math> \Psi: \Delta_{+}^{n-1} \rightarrow \mathbb{R}^{n} </math> by :<math> \Psi(p) = 2(\sqrt{p_1},\ldots,\sqrt{p_n}). </math> Write :<math> q(\theta) = \Psi(p(\theta)). </math> Then :<math> q_i(\theta) = 2\sqrt{p_i(\theta)}. </math> Because :<math> \sum_i p_i(\theta)=1, </math> we have :<math> \sum_iq_i(\theta)^2 = 4. </math> Thus :<math> q(\theta) </math> lies on the positive orthant of the sphere of radius <math>2</math> in <math>\mathbb{R}^{n}</math>. === 6.6 Isometry of the square-root representation === Let <math>u</math> be a tangent vector to the simplex. Differentiating :<math> q_i=2\sqrt{p_i} </math> gives :<math> dq_i = \frac{dp_i}{\sqrt{p_i}}. </math> Therefore the Euclidean squared length of the corresponding tangent displacement on the sphere is :<math> \sum_i(dq_i)^2 = \sum_i \frac{(dp_i)^2}{p_i}. </math> This is precisely the Fisher–Rao line element. Thus the square-root map identifies the Fisher–Rao metric on the simplex interior with the Euclidean metric induced on the positive orthant of the radius-<math>2</math> sphere. Consequently, Fisher–Rao Levi-Civita geodesics correspond locally to great-circle arcs on this sphere. === 6.7 Square-root form of exponential dilation === Substituting the exponential dilation family into the square-root representation gives :<math> q_i(\theta) = \frac{ 2\sqrt{p_i^{(0)}}e^{\theta\phi_i/2} } {\sqrt{Z(\theta)}}. </math> Define the unnormalized square-root vector :<math> r_i(\theta) = \sqrt{p_i^{(0)}}e^{\theta\phi_i/2}. </math> Then :<math> q(\theta) = \frac{2r(\theta)} {\sqrt{Z(\theta)}}. </math> Also, :<math> \|r(\theta)\|^2 = Z(\theta). </math> Hence :<math> q(\theta) = \frac{2r(\theta)} {\|r(\theta)\|}. </math> The normalized square-root trajectory and the unnormalized vector <math>r(\theta)</math> therefore determine the same ray through the origin. This observation allows the Fisher–Rao geodesic question to be reduced to a linear-subspace question in <math>\mathbb{R}^{n}</math>. === 6.8 Distinct generator levels === Suppose the generator <math>\phi</math> assumes exactly <math>m</math> distinct values :<math> a_1,\ldots,a_m. </math> Define the level sets :<math> A_{\ell} = \{i:\phi_i=a_{\ell}\}, </math> for :<math> \ell=1,\ldots,m. </math> For each level, define a vector <math>u_{\ell}</math> by :<math> (u_{\ell})_i = \begin{cases} \sqrt{p_i^{(0)}} & \text{if } i\in A_{\ell},\\ 0 & \text{otherwise}. \end{cases} </math> Because the level sets are disjoint, the vectors :<math> u_1,\ldots,u_m </math> have disjoint supports and are therefore mutually orthogonal. In particular, they are linearly independent. The unnormalized square-root trajectory can now be written as :<math> r(\theta) = \sum_{\ell=1}^{m} e^{a_{\ell}\theta/2} u_{\ell}. </math> This decomposition is central to the geometric characterization developed in the next section. === 6.9 The one-level case === If <math>m=1</math>, then every component of <math>\phi</math> has the same value <math>a</math>. Thus :<math> r(\theta) = e^{a\theta/2}u_1. </math> After normalization, the scalar exponential factor cancels. Therefore :<math> p(\theta)=p^{(0)} </math> for all <math>\theta</math>. The trajectory is constant. This is the degenerate case of exponential dilation. === 6.10 The two-level case === Suppose <math>\phi</math> assumes exactly two distinct values :<math> a </math> and :<math> b, </math> with <math>a\neq b</math>. Then :<math> r(\theta) = e^{a\theta/2}u + e^{b\theta/2}v, </math> where <math>u</math> and <math>v</math> are nonzero orthogonal vectors associated with the two generator levels. Consequently, :<math> r(\theta) \in \operatorname{span}\{u,v\} </math> for every <math>\theta</math>. Since <math>q(\theta)</math> is obtained from <math>r(\theta)</math> by positive scalar normalization, :<math> q(\theta) \in \operatorname{span}\{u,v\} </math> as well. The intersection of a two-dimensional linear subspace through the origin with the radius-<math>2</math> sphere is a great circle. Thus the two-level case naturally produces a Fisher–Rao great-circle trajectory. The formal statement and converse are given in Section 7. === 6.11 Three or more generator levels === If the generator assumes three or more distinct values, then :<math> r(\theta) = \sum_{\ell=1}^{m} e^{a_{\ell}\theta/2}u_{\ell}, </math> with :<math> m\geq3. </math> The vectors <math>u_{\ell}</math> are linearly independent, but this fact alone is not sufficient to conclude that the trajectory spans all <math>m</math> directions. The required result follows from the linear independence of the distinct exponential rates. In Section 7, derivatives of <math>r(\theta)</math> are evaluated at a fixed parameter value. The resulting coefficient matrix is of Vandermonde type and is invertible when the generator levels <math>a_{\ell}</math> are distinct. This shows that a trajectory with <math>m</math> distinct active generator levels spans an <math>m</math>-dimensional linear subspace. Consequently, when <math>m\geq3</math>, the square-root trajectory cannot lie in a two-dimensional great-circle plane. === 6.12 e-geodesic versus Fisher–Rao geodesic === The exponential dilation trajectory is an exponential-family path. In natural coordinates, the parameter <math>\theta</math> enters linearly through :<math> \theta\phi_i. </math> Accordingly, the trajectory is naturally an e-geodesic in the exponential connection of information geometry. The Fisher–Rao Levi-Civita geodesic condition is different. Under the square-root representation, it requires the image of the trajectory to lie on a great-circle arc. Thus the central geometric distinction is: :'''e-geodesic: linearity in exponential-family natural coordinates''' versus :'''Fisher–Rao Levi-Civita geodesic: great-circle geometry under the square-root representation''' The two notions coincide only under additional conditions. === 6.13 Geometric question in linear form === The original probability-geometric question can now be reformulated. Given :<math> r(\theta) = \sum_{\ell=1}^{m} e^{a_{\ell}\theta/2}u_{\ell}, </math> when does the normalized curve :<math> q(\theta) = \frac{2r(\theta)} {\|r(\theta)\|} </math> remain in a fixed two-dimensional linear subspace? If it does, its image lies on a great circle and is therefore a Fisher–Rao Levi-Civita geodesic up to reparameterization. If it does not, the exponential trajectory remains an e-geodesic but is not a Fisher–Rao Levi-Civita geodesic. The next section gives an exact finite-dimensional characterization. == 7. Fisher–Rao Geodesic Characterization == This section gives the principal geometric result of the paper. The question is whether the image of a finite-dimensional exponential dilation trajectory is contained in a Fisher–Rao Levi-Civita geodesic. The parameter <math>\theta</math> itself is not required to be an affine or arclength parameter for that geodesic. === 7.1 Setting and assumptions === Let :<math> p^{(0)} = (p_1^{(0)},\ldots,p_n^{(0)})^{\mathsf{T}} \in \Delta_{+}^{n-1}, </math> so that :<math> p_i^{(0)}>0 </math> for every <math>i</math>. Let :<math> \phi = (\phi_1,\ldots,\phi_n) \in \mathbb{R}^{n}. </math> Define the exponential dilation trajectory :<math> p_i(\theta) = \frac{ p_i^{(0)}e^{\theta\phi_i} } { \sum_{j=1}^{n} p_j^{(0)}e^{\theta\phi_j} }, </math> for :<math> \theta\in\mathbb{R}. </math> Let <math>m</math> denote the number of distinct values assumed by the generator components :<math> \phi_1,\ldots,\phi_n. </math> === 7.2 Theorem 1: two-level Fisher–Rao characterization === '''Theorem 1.''' Under the assumptions above, the image of the exponential dilation trajectory <math>p(\theta)</math> is contained in a Fisher–Rao Levi-Civita geodesic if and only if :<math> m\leq2. </math> Equivalently, the generator <math>\phi</math> must assume at most two distinct values. When <math>m=1</math>, the trajectory is constant. When <math>m=2</math>, the trajectory is nonconstant and its square-root image lies on a great-circle arc. === 7.3 Proof: square-root representation === Define :<math> q_i(\theta) = 2\sqrt{p_i(\theta)}. </math> As shown in Section 6, :<math> q(\theta) </math> lies on the sphere :<math> \sum_iq_i^2=4. </math> The square-root representation is an isometric representation of the Fisher–Rao simplex interior. Therefore the image of <math>p(\theta)</math> is contained in a Fisher–Rao Levi-Civita geodesic if and only if the image of <math>q(\theta)</math> is contained in a great circle of the radius-<math>2</math> sphere. A great circle is the intersection of the sphere with a two-dimensional linear subspace through the origin. === 7.4 Grouping equal generator values === Let the distinct values of <math>\phi</math> be :<math> a_1,\ldots,a_m. </math> For each <math>\ell</math>, define :<math> A_{\ell} = \{i:\phi_i=a_{\ell}\}. </math> Define <math>u_{\ell}\in\mathbb{R}^{n}</math> by :<math> (u_{\ell})_i = \begin{cases} \sqrt{p_i^{(0)}} & \text{if }i\in A_{\ell},\\ 0 & \text{otherwise}. \end{cases} </math> Because the sets <math>A_{\ell}</math> are disjoint and every initial component is strictly positive, the vectors :<math> u_1,\ldots,u_m </math> are nonzero and mutually orthogonal. Hence they are linearly independent. Define the unnormalized square-root trajectory :<math> r(\theta) = \sum_{\ell=1}^{m} e^{a_{\ell}\theta/2} u_{\ell}. </math> Then :<math> q(\theta) = \frac{2r(\theta)} {\|r(\theta)\|}. </math> Since normalization multiplies <math>r(\theta)</math> only by a positive scalar, <math>q(\theta)</math> and <math>r(\theta)</math> lie on the same ray through the origin. === 7.5 Sufficiency: one or two generator levels === Suppose first that :<math> m=1. </math> Then :<math> r(\theta) = e^{a_1\theta/2}u_1. </math> Normalization removes the scalar exponential factor, so :<math> q(\theta) </math> and therefore <math>p(\theta)</math> are constant. A constant trajectory is the degenerate case. Now suppose :<math> m=2. </math> Then :<math> r(\theta) = e^{a_1\theta/2}u_1 + e^{a_2\theta/2}u_2. </math> Therefore :<math> r(\theta) \in \operatorname{span}\{u_1,u_2\} </math> for every <math>\theta</math>. Since <math>q(\theta)</math> differs from <math>r(\theta)</math> only by scalar normalization, :<math> q(\theta) \in \operatorname{span}\{u_1,u_2\}. </math> The vectors <math>u_1</math> and <math>u_2</math> are nonzero and orthogonal, so their span is a two-dimensional linear subspace through the origin. Its intersection with the radius-<math>2</math> sphere is a great circle. Thus the image of the two-level exponential dilation trajectory lies on a Fisher–Rao Levi-Civita geodesic. This proves sufficiency. === 7.6 Necessity: derivative span === Now suppose the generator assumes :<math> m\geq3 </math> distinct values. Differentiate the unnormalized square-root trajectory: :<math> r(\theta) = \sum_{\ell=1}^{m} e^{a_{\ell}\theta/2} u_{\ell}. </math> For every nonnegative integer <math>k</math>, :<math> r^{(k)}(\theta) = \sum_{\ell=1}^{m} \left( \frac{a_{\ell}}{2} \right)^k e^{a_{\ell}\theta/2} u_{\ell}. </math> Fix any :<math> \theta_0\in\mathbb{R}. </math> Consider the vectors :<math> r(\theta_0), r^{(1)}(\theta_0), \ldots, r^{(m-1)}(\theta_0). </math> Their coefficients relative to the basis :<math> u_1,\ldots,u_m </math> form the matrix :<math> C_{k\ell} = \left( \frac{a_{\ell}}{2} \right)^k e^{a_{\ell}\theta_0/2}, </math> where :<math> k=0,\ldots,m-1 </math> and :<math> \ell=1,\ldots,m. </math> === 7.7 Vandermonde argument === Factor the nonzero quantity :<math> e^{a_{\ell}\theta_0/2} </math> from column <math>\ell</math> of the coefficient matrix. The remaining matrix has entries :<math> V_{k\ell} = \left( \frac{a_{\ell}}{2} \right)^k. </math> This is a Vandermonde matrix. Its determinant is nonzero because :<math> a_1,\ldots,a_m </math> are distinct. Therefore the coefficient matrix <math>C</math> is invertible. It follows that :<math> r(\theta_0), r^{(1)}(\theta_0), \ldots, r^{(m-1)}(\theta_0) </math> are linearly independent. Consequently, the linear span generated by the trajectory <math>r(\theta)</math> has dimension at least <math>m</math>. On the other hand, the representation :<math> r(\theta) = \sum_{\ell=1}^{m} e^{a_{\ell}\theta/2}u_{\ell} </math> shows that the trajectory is contained in :<math> \operatorname{span} \{u_1,\ldots,u_m\}, </math> which has dimension <math>m</math>. Hence :<math> \dim \operatorname{span} \{r(\theta):\theta\in\mathbb{R}\} = m. </math> === 7.8 Exclusion of three or more levels === If the square-root trajectory <math>q(\theta)</math> were contained in a great circle, then there would exist a two-dimensional linear subspace <math>W</math> through the origin such that :<math> q(\theta)\in W </math> for every <math>\theta</math>. Since :<math> r(\theta) = \frac{\|r(\theta)\|}{2} q(\theta), </math> the same subspace would contain :<math> r(\theta) </math> for every <math>\theta</math>. Therefore :<math> \dim \operatorname{span} \{r(\theta):\theta\in\mathbb{R}\} \leq2. </math> But Section 7.7 gives :<math> \dim \operatorname{span} \{r(\theta):\theta\in\mathbb{R}\} = m. </math> Thus a great-circle trajectory requires :<math> m\leq2. </math> For :<math> m\geq3, </math> the exponential dilation trajectory cannot be contained in a Fisher–Rao Levi-Civita geodesic. This proves necessity. === 7.9 Conclusion of the proof === Combining Sections 7.5 and 7.8 gives :<math> m\leq2 </math> if and only if the image of the exponential dilation trajectory is contained in a Fisher–Rao Levi-Civita geodesic. Therefore the generator <math>\phi</math> must assume at most two distinct values. This completes the proof. === 7.10 Corollary 1: dimension of the square-root trajectory === '''Corollary 1.''' Under the assumptions of Theorem 1, if the generator <math>\phi</math> assumes exactly <math>m</math> distinct values, then :<math> \dim \operatorname{span} \{r(\theta):\theta\in\mathbb{R}\} = m. </math> Thus the number of distinct generator levels is exactly the dimension of the linear subspace generated by the unnormalized square-root exponential trajectory. '''Proof.''' The vectors <math>u_1,\ldots,u_m</math> are linearly independent, and Section 7.7 shows through the Vandermonde argument that the trajectory spans all of these directions. Therefore its span has dimension <math>m</math>. === 7.11 Corollary 2: three-level obstruction === '''Corollary 2.''' If a strictly positive finite exponential dilation trajectory has a generator assuming three or more distinct values, then its image is not contained in a Fisher–Rao Levi-Civita geodesic. This follows immediately from Theorem 1. The result is exact under the stated hypotheses; it is not merely a generic non-geodesicity statement. === 7.12 Parameterization versus geodesic image === Theorem 1 concerns the image of the trajectory. Even in the two-level case, the exponential parameter <math>\theta</math> is generally not proportional to Fisher–Rao arclength. Thus :<math> p(\theta) </math> traces a Fisher–Rao geodesic path but generally does so with nonconstant Fisher–Rao speed. From Section 6, :<math> \frac{ds}{d\theta} = \sqrt{ \operatorname{Var}_{p(\theta)}(\phi) }. </math> Section 8 derives the exact change of parameter from <math>\theta</math> to Fisher–Rao arclength in the nondegenerate two-level case. === 7.13 Geometric interpretation === The theorem can be understood through the square-root sphere. A generator with one distinct value produces no probability motion. A generator with two distinct values produces two independent exponential directions, :<math> e^{a\theta/2}u </math> and :<math> e^{b\theta/2}v. </math> Their normalized sum remains in a fixed two-dimensional plane through the origin, so its spherical image follows a great circle. With three or more distinct generator values, the trajectory necessarily spans three or more independent linear directions. It therefore cannot remain in any two-dimensional great-circle plane. The distinction between the two-level and multilevel cases is consequently a dimensional property of the exponential rates under the square-root representation. === 7.14 Relation to information-geometric straightness === Theorem 1 does not state that exponential trajectories with three or more levels cease to be e-geodesics. They remain exponential-family trajectories and retain their standard information-geometric interpretation with respect to the e-connection. Rather, the theorem characterizes when this e-geodesic image also coincides with a geodesic image of the Levi-Civita connection associated with the Fisher–Rao metric. Thus the result concerns the coincidence of two distinct notions of geometric straightness. === 7.15 Status of the characterization === The proof above uses established ingredients: * the exponential-family representation; * the Fisher–Rao square-root embedding; * the great-circle characterization of spherical geodesics; * linear independence of vectors with disjoint support; * the Vandermonde determinant. The particular characterization obtained by combining these ingredients is presented here as a result of the present analysis. At this draft stage, no claim of historical priority is made. A complete literature review and independent mathematical scrutiny remain appropriate before describing the characterization as novel. The next section derives an explicit Fisher–Rao arclength parameterization for the nondegenerate two-level case. == 8. Fisher–Rao Arclength in the Two-Level Case == Theorem 1 shows that a nonconstant exponential dilation trajectory is contained in a Fisher–Rao Levi-Civita geodesic precisely when its generator assumes exactly two distinct values. This section derives an explicit Fisher–Rao arclength parameterization for that case. === 8.1 Two generator classes === Suppose the generator <math>\phi</math> assumes exactly two distinct values :<math> a\neq b. </math> Define the corresponding index sets :<math> A= \{i:\phi_i=a\} </math> and :<math> B= \{i:\phi_i=b\}. </math> Let the initial probability masses of the two classes be :<math> r_0 = \sum_{i\in A}p_i^{(0)} </math> and :<math> 1-r_0 = \sum_{i\in B}p_i^{(0)}. </math> Because the initial probability vector is strictly positive and both classes are nonempty, :<math> 0<r_0<1. </math> === 8.2 Evolution of the class probabilities === Let :<math> r(\theta) = \sum_{i\in A}p_i(\theta) </math> denote the total probability assigned to class <math>A</math>. Since every state in <math>A</math> has generator value <math>a</math> and every state in <math>B</math> has generator value <math>b</math>, :<math> r(\theta) = \frac{ r_0e^{a\theta} } { r_0e^{a\theta} + (1-r_0)e^{b\theta} }. </math> Similarly, :<math> 1-r(\theta) = \frac{ (1-r_0)e^{b\theta} } { r_0e^{a\theta} + (1-r_0)e^{b\theta} }. </math> Therefore the class odds satisfy :<math> \frac{r(\theta)} {1-r(\theta)} = \frac{r_0} {1-r_0} e^{(a-b)\theta}. </math> Thus the two-level exponential dilation reduces at the class level to a logistic probability trajectory. === 8.3 Preservation of within-class proportions === For two indices <math>i,j\in A</math>, :<math> \frac{p_i(\theta)} {p_j(\theta)} = \frac{p_i^{(0)}} {p_j^{(0)}}. </math> The same relation holds for indices within <math>B</math>. Therefore exponential dilation changes only the total probability assigned to the two generator classes; it does not change relative probabilities within either class. Define normalized class vectors <math>\widehat{u}</math> and <math>\widehat{v}</math> by :<math> \widehat{u}_i = \begin{cases} \sqrt{p_i^{(0)}/r_0} & \text{if }i\in A,\\ 0 & \text{otherwise}, \end{cases} </math> and :<math> \widehat{v}_i = \begin{cases} \sqrt{p_i^{(0)}/(1-r_0)} & \text{if }i\in B,\\ 0 & \text{otherwise}. \end{cases} </math> These vectors satisfy :<math> \|\widehat{u}\|=1, \qquad \|\widehat{v}\|=1, </math> and :<math> \widehat{u}^{\mathsf{T}}\widehat{v}=0. </math> === 8.4 Great-circle representation === Under the square-root map, :<math> q(\theta) = 2(\sqrt{p_1(\theta)},\ldots,\sqrt{p_n(\theta)}). </math> Using the class decomposition, :<math> q(\theta) = 2 \left( \sqrt{r(\theta)}\,\widehat{u} + \sqrt{1-r(\theta)}\,\widehat{v} \right). </math> Introduce an angular coordinate <math>\alpha(\theta)</math> by :<math> \sqrt{r(\theta)} = \cos\alpha(\theta) </math> and :<math> \sqrt{1-r(\theta)} = \sin\alpha(\theta), </math> with :<math> 0<\alpha(\theta)<\frac{\pi}{2}. </math> Then :<math> q(\theta) = 2 \left( \cos\alpha(\theta)\widehat{u} + \sin\alpha(\theta)\widehat{v} \right). </math> This is the standard angular parameterization of a great circle on a sphere of radius <math>2</math>. === 8.5 Angular coordinate === From the definitions above, :<math> \tan\alpha(\theta) = \sqrt{ \frac{1-r(\theta)} {r(\theta)} }. </math> Using the odds relation, :<math> \frac{1-r(\theta)} {r(\theta)} = \frac{1-r_0} {r_0} e^{(b-a)\theta}. </math> Therefore :<math> \tan\alpha(\theta) = \sqrt{ \frac{1-r_0} {r_0} } e^{(b-a)\theta/2}. </math> Hence :<math> \alpha(\theta) = \arctan \left( \sqrt{ \frac{1-r_0} {r_0} } e^{(b-a)\theta/2} \right). </math> Equivalently, :<math> \alpha(\theta) = \arccos\sqrt{r(\theta)}. </math> === 8.6 Corollary 3: exact Fisher–Rao arclength parameterization === '''Corollary 3.''' Under the hypotheses of Theorem 1, suppose the generator assumes exactly two distinct values <math>a\neq b</math>. Let :<math> r(\theta) </math> denote the total probability assigned to the class with generator value <math>a</math>. Then a signed Fisher–Rao arclength coordinate along the trajectory satisfies :<math> s(\theta)-s(\theta_0) = 2 \left( \alpha(\theta)-\alpha(\theta_0) \right), </math> where :<math> \alpha(\theta) = \arccos\sqrt{r(\theta)}. </math> Thus :<math> s(\theta)-s(\theta_0) = 2 \left( \arccos\sqrt{r(\theta)} - \arccos\sqrt{r(\theta_0)} \right). </math> Equivalently, :<math> s(\theta)-s(\theta_0) = 2 \left[ \arctan \left( \sqrt{ \frac{1-r_0}{r_0} } e^{(b-a)\theta/2} \right) - \arctan \left( \sqrt{ \frac{1-r_0}{r_0} } e^{(b-a)\theta_0/2} \right) \right]. </math> The Fisher–Rao distance traveled between the two parameter values is the absolute value :<math> d_{\mathrm{FR}} = |s(\theta)-s(\theta_0)|. </math> === 8.7 Proof of Corollary 3 === The square-root image is :<math> q(\theta) = 2 \left( \cos\alpha(\theta)\widehat{u} + \sin\alpha(\theta)\widehat{v} \right). </math> Differentiate with respect to <math>\alpha</math>: :<math> \frac{dq}{d\alpha} = 2 \left( -\sin\alpha\,\widehat{u} + \cos\alpha\,\widehat{v} \right). </math> Because <math>\widehat{u}</math> and <math>\widehat{v}</math> are orthonormal, :<math> \left\| \frac{dq}{d\alpha} \right\| = 2. </math> Therefore the spherical arclength element is :<math> ds = 2\,|d\alpha|. </math> For a chosen orientation, signed arclength satisfies :<math> ds=2\,d\alpha. </math> Integrating from <math>\theta_0</math> to <math>\theta</math> gives :<math> s(\theta)-s(\theta_0) = 2 \left( \alpha(\theta)-\alpha(\theta_0) \right). </math> Substituting the expressions for <math>\alpha(\theta)</math> gives the stated formulas. === 8.8 Fisher–Rao speed === Differentiating the angular expression gives :<math> \frac{d\alpha}{d\theta} = \frac{b-a}{2} \sqrt{ r(\theta) \left( 1-r(\theta) \right) }. </math> Therefore the unsigned Fisher–Rao speed is :<math> \left| \frac{ds}{d\theta} \right| = |a-b| \sqrt{ r(\theta) \left( 1-r(\theta) \right) }. </math> This agrees with the variance formula derived in Section 6. Indeed, because <math>\phi</math> takes only the values <math>a</math> and <math>b</math>, :<math> \operatorname{Var}_{p(\theta)}(\phi) = (a-b)^2 r(\theta) \left( 1-r(\theta) \right). </math> Hence :<math> v_{\mathrm{FR}}(\theta) = \sqrt{ \operatorname{Var}_{p(\theta)}(\phi) } = |a-b| \sqrt{ r(\theta) \left( 1-r(\theta) \right) }. </math> The geometric and information-theoretic calculations therefore agree. === 8.9 Nonuniform speed in the exponential parameter === Although the trajectory lies on a Fisher–Rao geodesic, the parameter <math>\theta</math> does not generally move along that geodesic at constant speed. The speed is largest when :<math> r(\theta)=\frac{1}{2}, </math> because the product :<math> r(\theta)(1-r(\theta)) </math> is maximal there. As the trajectory approaches either endpoint, :<math> r(\theta)\rightarrow0 </math> or :<math> r(\theta)\rightarrow1, </math> the Fisher–Rao speed with respect to <math>\theta</math> approaches zero. Thus the exponential parameter stretches the ends of the geodesic trajectory. === 8.10 Limiting behavior === Assume :<math> a>b. </math> Then as :<math> \theta\rightarrow+\infty, </math> we have :<math> r(\theta)\rightarrow1. </math> As :<math> \theta\rightarrow-\infty, </math> we have :<math> r(\theta)\rightarrow0. </math> Therefore :<math> \alpha(\theta)\rightarrow0 </math> as <math>\theta\rightarrow+\infty</math>, while :<math> \alpha(\theta)\rightarrow\frac{\pi}{2} </math> as <math>\theta\rightarrow-\infty</math>. The full two-level trajectory therefore approaches the two boundary class distributions at opposite ends of a quarter of the radius-<math>2</math> great circle. The total Fisher–Rao length between these limiting boundary points is :<math> 2 \left( \frac{\pi}{2} \right) = \pi. </math> The endpoints themselves lie on the boundary of the simplex and are approached only in the infinite-parameter limit. === 8.11 Example === Consider a three-state probability vector :<math> p^{(0)} = \left( \frac{1}{4}, \frac{1}{4}, \frac{1}{2} \right)^{\mathsf{T}} </math> and generator :<math> \phi = (1,1,0). </math> There are two generator classes: :<math> A=\{1,2\}, \qquad B=\{3\}. </math> The initial class mass is :<math> r_0 = \frac{1}{2}. </math> The class probability evolves as :<math> r(\theta) = \frac{e^{\theta}} {e^{\theta}+1}. </math> The individual probabilities are :<math> p_1(\theta) = \frac{1}{2}r(\theta), </math> :<math> p_2(\theta) = \frac{1}{2}r(\theta), </math> and :<math> p_3(\theta) = 1-r(\theta). </math> The angular coordinate is :<math> \alpha(\theta) = \arctan \left( e^{-\theta/2} \right). </math> Thus the trajectory is an exponential-family e-geodesic whose image is simultaneously a Fisher–Rao Levi-Civita geodesic. Its exponential parameterization is nonuniform, while <math>2\alpha</math> provides a signed Fisher–Rao arclength coordinate up to an additive constant and choice of orientation. === 8.12 Interpretation === The two-level result separates the '''path''' from the '''parameterization'''. The exponential parameter <math>\theta</math> generates the probability trajectory through normalized exponential weighting. The Fisher–Rao geometry identifies the same trajectory as a great-circle path. The transformation :<math> \theta \longmapsto \alpha(\theta) \longmapsto s(\theta) </math> provides the exact reparameterization needed to express that path in Fisher–Rao arclength. This provides a concrete example in which exponential-family straightness and Fisher–Rao Levi-Civita straightness describe the same geometric image while using different natural parameters. == 9. Discussion, Limitations, and Open Problems == The preceding sections developed normalized probability dilation as a common framework for positive transformation followed by normalization, and then considered a specific geometric question for exponential dilation. This section summarizes the mathematical interpretation of those results, identifies their limitations, and outlines several directions requiring further investigation. === 9.1 Scope of the framework === The normalized-dilation framework contains the basic operation :'''positive transformation → normalization → probability state'''. In finite dimensions this includes :<math> p \longmapsto \frac{Dp} {\mathbf{1}^{\mathsf{T}}Dp} </math> and :<math> p \longmapsto \frac{Mp} {\mathbf{1}^{\mathsf{T}}Mp}. </math> For probability measures it includes :<math> dP \longmapsto \frac{D\,dP} {\int_XD\,dP}. </math> These operations overlap substantially with established mathematical constructions. Accordingly, the value of the framework should not be judged by whether transformation followed by normalization is itself new. Rather, its usefulness depends on whether a common formulation clarifies relationships among existing constructions, suggests useful questions, or leads to additional mathematical results. === 9.2 Established mathematics and the PDT formulation === Several central components of the paper belong directly to established theory. These include: * normalized weighted probability measures; * Radon–Nikodym change of measure; * exponential tilting; * exponential families; * positive matrix iteration; * Perron–Frobenius theory; * normalized power iteration; * Markov operators; * replicator-type equations; * Fisher information; * Fisher–Rao geometry; * the square-root representation of the probability simplex. The PDT formulation does not replace these theories. Instead, it organizes them around a recurring transformation-and-normalization structure. This distinction is important when assessing both the mathematical contribution and the appropriate claims of the paper. === 9.3 The geometric characterization === The principal result developed in Section 7 concerns the exponential dilation family :<math> p_i(\theta) = \frac{ p_i^{(0)}e^{\theta\phi_i} } { \sum_jp_j^{(0)}e^{\theta\phi_j} }. </math> Under the finite-dimensional strict-positivity assumptions used in the theorem, the image of this trajectory is contained in a Fisher–Rao Levi-Civita geodesic if and only if the generator <math>\phi</math> assumes at most two distinct values. The proof uses the square-root representation :<math> q_i(\theta) = 2\sqrt{p_i(\theta)} </math> and the unnormalized trajectory :<math> r(\theta) = \sum_{\ell=1}^{m} e^{a_{\ell}\theta/2}u_{\ell}. </math> The Vandermonde argument shows that if the generator assumes exactly <math>m</math> distinct active values, then :<math> \dim \operatorname{span} \{r(\theta):\theta\in\mathbb{R}\} = m. </math> A Fisher–Rao geodesic requires the square-root image to lie in a two-dimensional linear subspace through the origin. This yields the two-level characterization. === 9.4 What the theorem does not claim === Theorem 1 should be interpreted narrowly. It does not claim that exponential trajectories with three or more generator levels are geometrically uninteresting. It does not claim that such trajectories cease to be e-geodesics. It does not claim that the exponential parameter <math>\theta</math> is an affine Fisher–Rao geodesic parameter in the two-level case. It does not characterize arbitrary curves on the probability simplex. It does not characterize arbitrary state-dependent dilation fields. It does not establish an analogous result for infinite-dimensional statistical manifolds. The theorem concerns a specific finite-dimensional exponential family and the coincidence of its trajectory image with a Fisher–Rao Levi-Civita geodesic. === 9.5 Boundary behavior === The main theorem assumes :<math> p_i^{(0)}>0 </math> for every state. This places the trajectory in the interior of the probability simplex for every finite <math>\theta</math>. The square-root representation remains meaningful at the boundary, but the usual coordinate expression of the Fisher–Rao metric becomes singular when one or more probabilities vanish. Boundary points therefore require separate care. In the two-level case, the exponential trajectory approaches boundary distributions only asymptotically as :<math> |\theta|\rightarrow\infty. </math> A systematic treatment of trajectories beginning on, reaching, or moving between lower-dimensional faces of the simplex is outside the scope of the present paper. === 9.6 Zero initial probabilities === If some initial components satisfy :<math> p_i^{(0)}=0, </math> then exponential dilation preserves those zeros: :<math> p_i(\theta)=0. </math> The effective trajectory then lies in a lower-dimensional face of the simplex. In such a case, the number of relevant generator levels should be counted only among states with positive initial probability. The theorem can therefore be expected to admit a support-restricted formulation, but the present statement uses strict positivity to avoid unnecessary boundary qualifications. === 9.7 Fixed versus state-dependent dilation === Much of the analysis in this paper concerns a fixed positive matrix, a fixed weighting field, or a fixed generator. More general transformations may depend on the current probability state: :<math> p^{(k+1)} = \frac{ M(p^{(k)})p^{(k)} } { \mathbf{1}^{\mathsf{T}} M(p^{(k)})p^{(k)} }. </math> Similarly, a continuous generator may depend on <math>p</math> or on the evolution parameter. Such systems may display behavior not reducible to ordinary fixed-matrix spectral theory or fixed-generator exponential tilting. Their study would require tools from nonlinear dynamical systems, nonlinear positive operators, differential geometry, and related fields. No general convergence claim for state-dependent dilation is made here. === 9.8 Entropy === Normalized dilation can either increase or decrease Shannon entropy depending on the transformation and the initial state. For :<math> H(p) = -\sum_i p_i\log p_i, </math> there is no general principle requiring :<math> H(T_M(p)) \leq H(p) </math> or the reverse inequality for arbitrary nonnegative matrices. In repeated diagonal dilation with a unique dominant weight, probability concentration generally drives the limiting distribution toward a point mass and therefore toward zero Shannon entropy. However, this special concentration behavior should not be generalized to arbitrary matrix or state-dependent dilation. A useful open problem is to identify classes of dilation operators for which entropy, relative entropy, or another information functional is monotone. === 9.9 Projective metrics and contraction === Because normalized positive transformations are invariant under positive scalar multiplication, projective geometry provides a natural language for their analysis. For positive matrices and positive operators, Hilbert-type projective metrics and contraction theorems may provide convergence estimates stronger than those obtained from elementary normalization arguments. A systematic comparison between normalized matrix dilation and established projective contraction theory would clarify which convergence properties follow immediately from known results and which, if any, require additional hypotheses. This is an important direction for further study. === 9.10 Curvature beyond the two-level case === Theorem 1 distinguishes exactly between the two-level geodesic case and trajectories generated by three or more distinct levels. The next geometric question is quantitative rather than binary. For :<math> m\geq3, </math> one may ask how far the exponential trajectory departs from a Fisher–Rao Levi-Civita geodesic. Possible quantities include: * geodesic curvature; * covariant acceleration; * deviation from the great-circle plane; * Fisher–Rao distance from an appropriate comparison geodesic; * integrated curvature along the trajectory. Such quantities could provide a graded measure of geometric departure rather than the yes-or-no characterization of Theorem 1. === 9.11 Relation between generator levels and geometric dimension === Corollary 1 gives :<math> \dim \operatorname{span} \{r(\theta)\} = m, </math> where <math>m</math> is the number of distinct active generator values. This suggests a direct relationship between the algebraic complexity of the generator and the linear dimension required to contain its square-root trajectory. The two-level Fisher–Rao result is the first consequence of this dimensional relation. Further work could investigate whether analogous dimension-counting principles arise for multiparameter exponential families or other normalized positive flows. === 9.12 Multiparameter exponential dilation === A natural extension is :<math> p_i(\theta_1,\ldots,\theta_k) = \frac{ p_i^{(0)} \exp \left( \sum_{r=1}^{k}\theta_r\phi_i^{(r)} \right) } { Z(\theta_1,\ldots,\theta_k) }. </math> This defines a multiparameter exponential family. Questions then arise concerning the dimension and curvature of its square-root image and the conditions under which particular parameter curves or submanifolds are totally geodesic with respect to the Fisher–Rao Levi-Civita connection. The one-parameter theorem in this paper does not answer these questions. === 9.13 Infinite-dimensional extension === The measure-theoretic formulation suggests possible extensions beyond finite probability simplices. For a reference probability measure <math>P_0</math>, consider :<math> dP_{\theta} = \frac{ e^{\theta\phi} } { \int e^{\theta\phi}\,dP_0 } dP_0. </math> This is the natural measure-theoretic analogue of finite exponential dilation. An infinite-dimensional version of the geodesic characterization would require careful specification of the statistical manifold, admissible tangent spaces, regularity conditions, and the appropriate Fisher–Rao geometry. The finite-dimensional Vandermonde argument does not by itself establish such a result. === 9.14 Numerical verification === The analytical results in Sections 7 and 8 can be supplemented by numerical experiments. For two generator levels, numerical calculations should verify that the square-root trajectory remains in a fixed two-dimensional plane to numerical precision. For three or more distinct levels, rank calculations can verify the predicted increase in the dimension of the trajectory span. Numerical differentiation can also compare :<math> \left| \frac{ds}{d\theta} \right| </math> with :<math> \sqrt{ \operatorname{Var}_{p(\theta)}(\phi) }. </math> Such computations do not replace proof, but they provide useful checks against algebraic or implementation errors. === 9.15 Literature and priority limitations === The mathematical ingredients used in this paper draw from established areas with extensive literatures. A literature search performed during development has identified substantial prior theory surrounding exponential families, Fisher–Rao geometry, positive operators, normalized matrix iteration, replicator dynamics, and related constructions. At the present draft stage, the exact two-level characterization proved in Section 7 has not been identified by the author in the literature in the same form. This absence should not be interpreted as proof of novelty. Equivalent results may exist under different terminology or as consequences of more general theorems. Accordingly, no claim of historical priority is made. Further literature review and expert scrutiny are required before any stronger novelty statement would be appropriate. === 9.16 Open problems === The framework suggests several specific open questions: # Can the finite-dimensional characterization be formulated cleanly for probability vectors with restricted support? # Is there an established information-geometric theorem equivalent to the two-level characterization? # What is the Fisher–Rao geodesic curvature of an exponential dilation trajectory with three distinct generator levels? # Can that curvature be expressed directly in terms of moments or cumulants of the generator <math>\phi</math>? # Which normalized matrix transformations are contractions in a natural projective or information-geometric metric? # Under what conditions is Shannon entropy monotone under repeated dilation? # What aspects of the framework survive for nonlinear state-dependent operators? # Is there a useful infinite-dimensional analogue of the generator-level dimension result? # How does the characterization generalize to multiparameter exponential families? These questions provide possible directions for extending the present work while maintaining a clear distinction between established theory and additional results. === 9.17 Summary of the discussion === The normalized-dilation viewpoint provides a common structural language for several familiar probability transformations. Its mathematical usefulness depends on what can be learned from that organization rather than on the normalization operation itself. Within the finite-dimensional exponential setting, the Fisher–Rao analysis leads to a precise characterization: the exponential trajectory has a Fisher–Rao geodesic image exactly in the one-level or two-level cases under the stated assumptions. The two-level case additionally admits an explicit Fisher–Rao arclength parameterization. These results motivate further study of curvature, dimensional structure, nonlinear dilation, and measure-theoretic extensions while leaving their broader significance open to mathematical evaluation. == 10. Conclusion == This paper has developed '''normalized probability dilation''' as a common framework for probability transformations having the form :'''positive transformation → normalization → probability state'''. In finite dimensions, the framework includes diagonal reweighting :<math> p_i' = \frac{d_ip_i} {\sum_jd_jp_j}, </math> and normalized nonnegative matrix transformations :<math> T_M(p) = \frac{Mp} {\mathbf{1}^{\mathsf{T}}Mp}. </math> At the level of probability measures, the corresponding construction is :<math> dP_D = \frac{D\,dP} {\int_XD\,dP}. </math> These constructions have direct relationships with established mathematics, including change of measure, exponential tilting, positive matrix theory, Perron–Frobenius theory, normalized power iteration, Markov operators, replicator-type dynamics, Feynman–Kac constructions, exponential families, and Fisher–Rao information geometry. The purpose of the PDT framework is therefore not to claim these established operations as new, but to place them within a common transformation-and-normalization language and to use that organization to formulate precise mathematical questions. === 10.1 Principal geometric result === For the finite-dimensional exponential dilation family :<math> p_i(\theta) = \frac{ p_i^{(0)}e^{\theta\phi_i} } { \sum_jp_j^{(0)}e^{\theta\phi_j} }, </math> the square-root representation :<math> q_i(\theta) = 2\sqrt{p_i(\theta)} </math> converts the Fisher–Rao geometry of the probability simplex into spherical geometry. Grouping equal generator values gives the unnormalized square-root trajectory :<math> r(\theta) = \sum_{\ell=1}^{m} e^{a_{\ell}\theta/2}u_{\ell}, </math> where <math>a_1,\ldots,a_m</math> are the distinct generator levels. The Vandermonde argument developed in Section 7 gives :<math> \dim \operatorname{span} \{r(\theta):\theta\in\mathbb{R}\} = m. </math> Because a spherical great circle lies in a two-dimensional linear subspace through the origin, the exponential dilation trajectory has a Fisher–Rao Levi-Civita geodesic image if and only if :<math> m\leq2. </math> Thus, under the finite-dimensional strict-positivity assumptions of the theorem, the generator must assume at most two distinct values. === 10.2 Two-level arclength === For the nondegenerate two-level case, the trajectory can be written in square-root coordinates as :<math> q(\theta) = 2 \left( \cos\alpha(\theta)\widehat{u} + \sin\alpha(\theta)\widehat{v} \right), </math> where :<math> \alpha(\theta) = \arctan \left( \sqrt{ \frac{1-r_0}{r_0} } e^{(b-a)\theta/2} \right). </math> A signed Fisher–Rao arclength coordinate therefore satisfies :<math> s(\theta)-s(\theta_0) = 2 \left( \alpha(\theta)-\alpha(\theta_0) \right). </math> This makes explicit the distinction between the exponential parameter <math>\theta</math> and Fisher–Rao arclength. The exponential trajectory may follow the correct Fisher–Rao geodesic image without moving along it at constant Fisher–Rao speed. === 10.3 Final perspective === The results illustrate a broader methodological point. A common mathematical framework is most useful when it does more than rename existing constructions. It should clarify relationships among established theories, expose structural distinctions, or lead to questions that can be answered precisely. For normalized probability dilation, the distinction between exponential-family straightness and Fisher–Rao Levi-Civita straightness provides one such question. The resulting two-level characterization and arclength formula provide a concrete starting point for further investigation. Important directions remain open, including curvature of multilevel exponential trajectories, projective contraction properties, entropy conditions, nonlinear state-dependent dilation, multiparameter families, and possible infinite-dimensional extensions. The present manuscript should therefore be regarded as a mathematical framework and initial geometric analysis rather than a completed general theory. The characterization developed here remains subject to further literature review, independent proof checking, and external mathematical evaluation before any claim of historical priority or novelty is made. == Relationship to the Probability Dilation Theory project == This manuscript is part of the broader [[Probability Dilation Theory]] research project on Wikiversity. Technical and exploratory material related to the manuscript is developed on associated PDT subpages, including: * [[Probability Dilation Theory/Measure-Theoretic Foundations|Measure-Theoretic Foundations]] * [[Probability Dilation Theory/Matrix Dilation Operators|Matrix Dilation Operators]] * [[Probability Dilation Theory/Dilation Vector Field|Dilation Vector Field]] * [[Probability Dilation Theory/Dilation Flows|Dilation Flows]] * [[Probability Dilation Theory/Convergence and Fixed Points|Convergence and Fixed Points]] * [[Probability Dilation Theory/Fisher Geometry and Dilation Flows|Fisher Geometry and Dilation Flows]] The present page is intended to develop a concise, standalone manuscript rather than reproduce the complete exploratory PDT project. == Draft status and research note == This manuscript is a work in progress. Some constructions discussed in the paper have direct counterparts in established mathematical literature. These relationships are identified explicitly wherever possible. Results developed specifically within the present formulation are being subjected to continuing literature review, proof checking, numerical verification, and independent mathematical scrutiny before any claim of novelty is made. Readers are encouraged to identify relevant prior literature, mathematical errors, counterexamples, alternative proofs, or useful extensions. == See also == * [[Probability Dilation Theory]] * [[Probability Dilation Theory/Matrix Dilation Operators]] * [[Probability Dilation Theory/Measure-Theoretic Foundations]] * [[Probability Dilation Theory/Fisher Geometry and Dilation Flows]] == Copyright and licensing == Text and original figures © Howard Richardson. Licensed under the [https://creativecommons.org/licenses/by/4.0/ Creative Commons Attribution 4.0 International License (CC BY 4.0)]. Reuse permitted with attribution. 90ftwpxc2f1roor97w0jfmok4xtn4iu 2823788 2823787 2026-08-21T01:55:23Z Howie2024 2995240 /* 10.3 Final perspective */ 2823788 wikitext text/x-wiki {{Research project}} '''Research manuscript — Draft Version 1.0''' ''This page develops a standalone research manuscript arising from the [[Probability Dilation Theory]] project. It is a work in progress and should not be regarded as a peer-reviewed publication.'' = Normalized Probability Dilation: A Unified Framework and Its Fisher–Rao Geometry = '''Howard Richardson''' ''Draft Version 1.0 — August 2026'' == Abstract == This paper develops a unified framework for normalized positive transformations of probability distributions, referred to here as '''Probability Dilation Theory (PDT)'''. The central construction consists of applying a positive transformation to a probability state and subsequently renormalizing the result. In finite dimensions this includes diagonal reweighting, :<math> p_i'= \frac{d_i p_i} {\sum_j d_jp_j}, </math> and the matrix transformation :<math> T_M(p)= \frac{Mp} {\mathbf{1}^{\mathsf T}Mp}, </math> for suitable nonnegative matrices <math>M</math>. A corresponding measure-theoretic formulation is :<math> P_D(A)= \frac{\int_A D\,dP} {\int_X D\,dP}. </math> These constructions are compared explicitly with established mathematical structures including change of measure, normalized positive operators, Perron–Frobenius iteration, Markov operators, replicator-type dynamics, and normalized Feynman–Kac transformations. The purpose of the framework is therefore not to claim these established constructions as new, but to investigate their common dilation-normalization structure and the geometry of the resulting probability trajectories. Particular attention is given to the exponential dilation family :<math> p_i(\theta)= \frac{p_i^{(0)}e^{\theta\phi_i}} {\sum_j p_j^{(0)}e^{\theta\phi_j}}. </math> Using the square-root representation of the Fisher–Rao simplex, we establish that, under finite-dimensional strict-positivity assumptions, the image of this exponential-dilation trajectory is contained in a Fisher–Rao Levi-Civita geodesic, up to reparameterization, if and only if the generator <math>\phi</math> assumes at most two distinct values. An explicit Fisher–Rao arclength parameterization is then obtained for the nondegenerate two-level case. The framework provides a common language for normalized probability transformations while separating results inherited from established theory from geometric properties arising from the particular dilation formulation. == 1. Introduction == Probability distributions are frequently transformed by operations having a common mathematical structure: nonnegative weights are modified by a positive transformation and subsequently normalized so that total probability remains unity. Such constructions occur in numerous areas of probability, statistics, dynamical systems, numerical linear algebra, and mathematical physics. The simplest finite-dimensional example takes a probability vector :<math> p=(p_1,\ldots,p_n)^{\mathsf T}, \qquad p_i\geq 0, \qquad \sum_{i=1}^{n}p_i=1, </math> assigns positive weights <math>d_i</math>, and defines :<math> p_i'= \frac{d_i p_i} {\sum_{j=1}^{n}d_jp_j}. </math> The transformation changes the relative probability assigned to individual states while normalization returns the resulting vector to the probability simplex. This paper uses the term '''probability dilation''' for this general transformation-and-normalization structure and examines a hierarchy of related constructions. In finite dimensions, diagonal dilation extends naturally to the action of a nonnegative matrix, :<math> T_M(p)= \frac{Mp} {\mathbf{1}^{\mathsf T}Mp}, </math> whenever the denominator is positive. At the level of probability measures, multiplication by a positive measurable function <math>D</math> gives :<math> P_D(A)= \frac{\displaystyle\int_A D(x)\,dP(x)} {\displaystyle\int_X D(x)\,dP(x)}. </math> These expressions have substantial connections with existing mathematics. Normalized matrix iteration is closely related to the power method and Perron–Frobenius theory; positive weighting of measures belongs to established change-of-measure constructions; stochastic matrices provide the familiar Markov special case; and normalized potential-weighted measures occur in Feynman–Kac models. Accordingly, the objective of PDT as developed here is '''not''' to rename these established mathematical theories or to assert novelty for normalization itself. Instead, the objective is to examine them through the common structural sequence :<math> \text{positive transformation} \longrightarrow \text{normalization} \longrightarrow \text{iteration} \longrightarrow \text{probability dynamics} \longrightarrow \text{geometry}. </math> This viewpoint leads naturally to questions concerning fixed points, convergence, entropy, state-dependent transformations, and the geometry of trajectories on the probability simplex. === 1.1 Exponential dilation === A particularly useful example is obtained from exponential dilation. Given an initial strictly positive probability vector <math>p^{(0)}</math> and a real-valued generator <math>\phi</math>, define :<math> p_i(\theta)= \frac{p_i^{(0)}e^{\theta\phi_i}} {Z(\theta)}, </math> where :<math> Z(\theta)= \sum_j p_j^{(0)}e^{\theta\phi_j}. </math> This is an exponential-family construction and therefore belongs to well-established information geometry. The question considered here is more specific: :''When is this exponential trajectory also a Levi-Civita geodesic of the Fisher–Rao metric?'' The Fisher–Rao geometry of a finite probability simplex admits a square-root representation on a sphere. Under the mapping :<math> p\longmapsto 2(\sqrt{p_1},\ldots,\sqrt{p_n}), </math> Fisher–Rao geodesics correspond to spherical great-circle arcs. This representation permits a direct characterization of exponential dilation trajectories that are simultaneously Fisher–Rao geodesic. === 1.2 Principal geometric result === The principal geometric result developed below is that, for a strictly positive finite probability vector, an exponential dilation trajectory lies on a Fisher–Rao geodesic, up to reparameterization, precisely when its generator assumes no more than two distinct values. The proof reduces the problem to the dimension of the linear span generated by distinct exponential rates and uses a Vandermonde argument for the converse. The resulting two-level trajectory also admits an explicit Fisher–Rao arclength parameterization. At the present draft stage, this characterization is treated conservatively. Its constituent mathematical ingredients are established results from information geometry and linear algebra. The exact characterization developed here remains subject to further literature review and independent mathematical scrutiny. === 1.3 Organization of the paper === The remainder of the paper is organized as follows: * '''Section 2''' introduces the normalized-dilation framework and notation. * '''Section 3''' develops diagonal and matrix formulations. * '''Section 4''' develops the measure-theoretic formulation. * '''Section 5''' compares the framework explicitly with established mathematics. * '''Section 6''' introduces exponential dilation and its information-geometric representation. * '''Section 7''' states and proves the Fisher–Rao geodesic characterization theorem. * '''Section 8''' derives the two-level Fisher–Rao arclength corollary and illustrative examples. * '''Section 9''' discusses limitations, possible extensions, and open problems. * '''Section 10''' summarizes the principal conclusions. == 2. Normalized-Dilation Framework == This section introduces the common mathematical structure used throughout the paper. The essential operation consists of applying a positive transformation to a probability state and then normalizing the transformed object so that it again represents a probability distribution. === 2.1 Probability simplex === For a finite state space with <math>n</math> states, define the probability simplex :<math> \Delta^{n-1} = \left\{ p\in\mathbb{R}^{n}: p_i\geq 0,\; \sum_{i=1}^{n}p_i=1 \right\}. </math> A probability state is represented by a column vector :<math> p= (p_1,\ldots,p_n)^{\mathsf{T}} \in\Delta^{n-1}. </math> Its components satisfy :<math> p_i\geq 0 </math> and :<math> \mathbf{1}^{\mathsf{T}}p=1, </math> where :<math> \mathbf{1} = (1,\ldots,1)^{\mathsf{T}}. </math> The interior of the simplex is :<math> \Delta_{+}^{n-1} = \left\{ p\in\Delta^{n-1}:p_i>0 \text{ for all }i \right\}. </math> The distinction between the simplex and its interior becomes important later when Fisher–Rao geometry is considered. === 2.2 Positive transformations === Let <math>\mathcal{L}</math> denote a transformation acting on probability states such that :<math> p\geq 0 \quad\Longrightarrow\quad \mathcal{L}(p)\geq 0. </math> The transformed object <math>\mathcal{L}(p)</math> need not itself be normalized. Define its total mass by :<math> \mathcal{N}[\mathcal{L}(p)] = \mathbf{1}^{\mathsf{T}}\mathcal{L}(p). </math> Whenever :<math> 0< \mathcal{N}[\mathcal{L}(p)] < \infty, </math> the normalized transformation is defined by :<math> \mathcal{T}_{\mathcal{L}}(p) = \frac{\mathcal{L}(p)} {\mathcal{N}[\mathcal{L}(p)]}. </math> Equivalently, in the finite-dimensional setting, :<math> \mathcal{T}_{\mathcal{L}}(p) = \frac{\mathcal{L}(p)} {\mathbf{1}^{\mathsf{T}}\mathcal{L}(p)}. </math> By construction, :<math> \mathbf{1}^{\mathsf{T}} \mathcal{T}_{\mathcal{L}}(p) = 1, </math> so :<math> \mathcal{T}_{\mathcal{L}}(p) \in \Delta^{n-1}. </math> This positive-transformation-plus-normalization operation is the basic structure referred to in this paper as '''normalized probability dilation'''. === 2.3 Normalization as projectivization === An immediate property of the normalized transformation is invariance under multiplication by a positive scalar. If <math>c>0</math>, then :<math> \frac{c\mathcal{L}(p)} {\mathbf{1}^{\mathsf{T}}c\mathcal{L}(p)} = \frac{\mathcal{L}(p)} {\mathbf{1}^{\mathsf{T}}\mathcal{L}(p)}. </math> Hence :<math> \mathcal{T}_{c\mathcal{L}}(p) = \mathcal{T}_{\mathcal{L}}(p). </math> The normalized transformation therefore depends on the relative components of <math>\mathcal{L}(p)</math>, rather than on its overall positive scale. This projective feature connects normalized dilation with established theories of positive operators and projective dynamics. No claim of novelty is attached to the normalization or projectivization operation itself. === 2.4 Diagonal dilation === Let :<math> D= \operatorname{diag}(d_1,\ldots,d_n), \qquad d_i>0. </math> Applying <math>D</math> to <math>p</math> gives :<math> Dp= (d_1p_1,\ldots,d_np_n)^{\mathsf{T}}. </math> Normalization produces :<math> T_D(p) = \frac{Dp} {\mathbf{1}^{\mathsf{T}}Dp}. </math> Componentwise, :<math> T_D(p)_i = \frac{d_ip_i} {\sum_{j=1}^{n}d_jp_j}. </math> This is the basic finite-dimensional dilation operation from which the broader PDT formulation developed. The factors <math>d_i</math> alter the relative weights of the probability states, while the denominator restores unit total probability. === 2.5 Matrix dilation === The diagonal transformation can be generalized to a nonnegative matrix :<math> M\in\mathbb{R}^{n\times n}, \qquad M_{ij}\geq 0. </math> For any probability vector <math>p</math> satisfying :<math> \mathbf{1}^{\mathsf{T}}Mp>0, </math> define :<math> T_M(p) = \frac{Mp} {\mathbf{1}^{\mathsf{T}}Mp}. </math> The diagonal case is recovered when :<math> M=D. </math> Off-diagonal entries permit components of the input probability vector to contribute to different output components before normalization. The matrix formulation therefore extends independent componentwise reweighting to coupled positive transformations. The mathematical behavior of this construction is closely related to established positive-matrix theory, normalized power iteration, and Perron–Frobenius theory. These relationships are discussed explicitly in Section 5. === 2.6 Measure-theoretic dilation === The same normalization principle extends naturally from finite probability vectors to probability measures. Let <math>(X,\mathcal{F},P)</math> be a probability space, and let :<math> D:X\rightarrow[0,\infty) </math> be measurable with :<math> 0< \int_X D(x)\,dP(x) < \infty. </math> Define a new probability measure <math>P_D</math> by :<math> P_D(A) = \frac{\displaystyle\int_A D(x)\,dP(x)} {\displaystyle\int_X D(x)\,dP(x)}, \qquad A\in\mathcal{F}. </math> Equivalently, the Radon–Nikodym derivative of <math>P_D</math> with respect to <math>P</math> is :<math> \frac{dP_D}{dP} = \frac{D} {\displaystyle\int_X D\,dP}. </math> Thus the finite-dimensional rule :<math> p_i \longmapsto \frac{d_ip_i} {\sum_jd_jp_j} </math> and the measure-theoretic rule :<math> dP \longmapsto \frac{D\,dP} {\int_XD\,dP} </math> share the same normalized positive-reweighting structure. This construction has direct connections with established change-of-measure and weighted-measure theory. The PDT terminology is used here as an organizing framework rather than as a claim that normalized change of measure is itself new. === 2.7 Iterated dilation === A normalized dilation operator can be iterated. Given an initial state :<math> p^{(0)}\in\Delta^{n-1}, </math> define :<math> p^{(k+1)} = \mathcal{T}_{\mathcal{L}}\left(p^{(k)}\right). </math> This generates an orbit :<math> p^{(0)} \longmapsto p^{(1)} \longmapsto p^{(2)} \longmapsto \cdots </math> on the probability simplex. For a fixed matrix <math>M</math>, :<math> p^{(k+1)} = \frac{Mp^{(k)}} {\mathbf{1}^{\mathsf{T}}Mp^{(k)}}. </math> When all required denominators are positive, repeated normalization gives :<math> p^{(k)} = \frac{M^k p^{(0)}} {\mathbf{1}^{\mathsf{T}}M^k p^{(0)}}. </math> The long-term behavior of this iteration is governed in important cases by established spectral and Perron–Frobenius theory. More general formulations may allow the transformation itself to depend on the iteration index or the current probability state, for example :<math> p^{(k+1)} = \frac{M_kp^{(k)}} {\mathbf{1}^{\mathsf{T}}M_kp^{(k)}} </math> or :<math> p^{(k+1)} = \frac{M(p^{(k)})p^{(k)}} {\mathbf{1}^{\mathsf{T}}M(p^{(k)})p^{(k)}}. </math> These state-dependent and iteration-dependent forms are treated as possible extensions rather than necessary components of the basic framework. === 2.8 Hierarchy of normalized dilation === The constructions above can be summarized by the following hierarchy: :'''diagonal reweighting → matrix transformation → positive operator → measure transformation''' At each level the essential operation is: :'''positive transformation + normalization''' The framework is deliberately broad. Its purpose is not to imply that all normalized positive transformations constitute a new mathematical theory, but to provide a common notation and viewpoint from which their dynamics and geometry can be compared. The following sections specialize this framework before examining its relationship to established mathematical constructions. == 3. Finite-Dimensional and Matrix Dilation == This section develops the finite-dimensional forms of normalized probability dilation in greater detail. The emphasis is on the relationship between diagonal reweighting and nonnegative matrix transformations, together with the basic structural properties required later in the paper. === 3.1 Finite probability states === Let :<math> p=(p_1,\ldots,p_n)^{\mathsf{T}} \in\Delta^{n-1}. </math> A positive weighting vector is written :<math> d=(d_1,\ldots,d_n)^{\mathsf{T}}, \qquad d_i>0. </math> The associated diagonal matrix is :<math> D= \operatorname{diag}(d_1,\ldots,d_n). </math> Applying the weighting gives :<math> Dp= (d_1p_1,\ldots,d_np_n)^{\mathsf{T}}. </math> Its total mass is :<math> Z(p,D) = \mathbf{1}^{\mathsf{T}}Dp = \sum_{i=1}^{n}d_ip_i. </math> Since <math>d_i>0</math> and <math>p</math> is a probability vector, :<math> Z(p,D)>0. </math> The normalized diagonal dilation operator is therefore :<math> T_D(p) = \frac{Dp}{Z(p,D)}. </math> Equivalently, :<math> T_D(p)_i = \frac{d_ip_i} {\sum_{j=1}^{n}d_jp_j}. </math> === 3.2 Relative probability transformation === Diagonal dilation has a simple effect on probability ratios. For any states <math>i</math> and <math>j</math> with <math>p_i>0</math> and <math>p_j>0</math>, :<math> \frac{T_D(p)_i}{T_D(p)_j} = \frac{d_i}{d_j} \frac{p_i}{p_j}. </math> Thus normalization does not alter the relative dilation introduced by the factors <math>d_i</math> and <math>d_j</math>. If :<math> d_i>d_j, </math> then the odds of state <math>i</math> relative to state <math>j</math> increase by the factor :<math> \frac{d_i}{d_j}. </math> This ratio form makes clear that diagonal dilation is fundamentally a relative reweighting operation. === 3.3 Scale invariance === Multiplying every dilation factor by the same positive constant does not change the normalized state. Let :<math> c>0. </math> Then :<math> T_{cD}(p) = \frac{cDp} {\mathbf{1}^{\mathsf{T}}cDp} = \frac{Dp} {\mathbf{1}^{\mathsf{T}}Dp} = T_D(p). </math> Therefore only the relative values of the dilation factors affect the transformed probability distribution. This scale invariance is a basic projective property of normalized positive transformations. === 3.4 Repeated diagonal dilation === Suppose the same diagonal operator <math>D</math> is applied repeatedly. Starting from <math>p^{(0)}</math>, define :<math> p^{(k+1)} = T_D(p^{(k)}). </math> Then :<math> p^{(k)} = \frac{D^k p^{(0)}} {\mathbf{1}^{\mathsf{T}}D^k p^{(0)}}. </math> Since :<math> D^k = \operatorname{diag}(d_1^k,\ldots,d_n^k), </math> the individual components are :<math> p_i^{(k)} = \frac{d_i^k p_i^{(0)}} {\sum_{j=1}^{n}d_j^k p_j^{(0)}}. </math> Consequently, for two initially positive components, :<math> \frac{p_i^{(k)}}{p_j^{(k)}} = \left(\frac{d_i}{d_j}\right)^k \frac{p_i^{(0)}}{p_j^{(0)}}. </math> This expression describes the concentration mechanism directly. If one dilation factor is strictly larger than all others and its corresponding initial probability is positive, repeated dilation concentrates probability on that state. If several states share the maximal dilation factor, probability concentrates on that maximal set while preserving the initial relative proportions within that set. This behavior is a direct consequence of normalized repeated weighting and is not specific to PDT terminology. === 3.5 General nonnegative matrix transformation === Let :<math> M=(M_{ij}) \in\mathbb{R}^{n\times n}, \qquad M_{ij}\geq0. </math> For <math>p\in\Delta^{n-1}</math>, define :<math> q=Mp. </math> Because <math>M</math> and <math>p</math> are nonnegative, :<math> q_i\geq0. </math> Whenever :<math> \mathbf{1}^{\mathsf{T}}Mp>0, </math> the normalized matrix dilation operator is :<math> T_M(p) = \frac{Mp} {\mathbf{1}^{\mathsf{T}}Mp}. </math> Its components are :<math> T_M(p)_i = \frac{\sum_{j=1}^{n}M_{ij}p_j} {\sum_{r=1}^{n}\sum_{j=1}^{n}M_{rj}p_j}. </math> By construction, :<math> \sum_{i=1}^{n}T_M(p)_i=1. </math> Hence :<math> T_M(p)\in\Delta^{n-1}. </math> === 3.6 Diagonal dilation as a special case === If :<math> M=D = \operatorname{diag}(d_1,\ldots,d_n), </math> then :<math> Mp=Dp, </math> and therefore :<math> T_M(p)=T_D(p). </math> Diagonal dilation is thus a special case of normalized matrix dilation. The distinction is structural. For a diagonal matrix, each output component depends only on the corresponding input component: :<math> (Dp)_i=d_ip_i. </math> For a general matrix, :<math> (Mp)_i = \sum_{j=1}^{n}M_{ij}p_j, </math> so multiple input states may contribute to a single output state before normalization. This permits coupled probability evolution. === 3.7 When normalization is unnecessary === There is an important special case. Suppose <math>M</math> satisfies :<math> \mathbf{1}^{\mathsf{T}}M = \mathbf{1}^{\mathsf{T}}. </math> Then for every probability vector <math>p</math>, :<math> \mathbf{1}^{\mathsf{T}}Mp = \mathbf{1}^{\mathsf{T}}p = 1. </math> Consequently, :<math> T_M(p)=Mp. </math> With the column-vector convention used in this paper, the condition :<math> \mathbf{1}^{\mathsf{T}}M = \mathbf{1}^{\mathsf{T}} </math> means that the columns of <math>M</math> sum to one. Thus an ordinary probability-preserving linear transition is contained as a special case of the normalized matrix framework. When <math>M</math> does not preserve total mass, normalization supplies the additional step required to return <math>Mp</math> to the simplex. === 3.8 Fixed points and eigenvectors === Suppose <math>p^{*}</math> is a fixed point of the normalized matrix operator: :<math> T_M(p^{*})=p^{*}. </math> Then :<math> \frac{Mp^{*}} {\mathbf{1}^{\mathsf{T}}Mp^{*}} = p^{*}. </math> Multiplying by the denominator gives :<math> Mp^{*} = \lambda p^{*}, </math> where :<math> \lambda = \mathbf{1}^{\mathsf{T}}Mp^{*}. </math> Therefore every fixed point of the normalized matrix transformation is a nonnegative eigenvector of <math>M</math>, normalized to have unit total mass. Conversely, if <math>v\geq0</math> is a nonzero eigenvector satisfying :<math> Mv=\lambda v, \qquad \lambda>0, </math> then :<math> p^{*} = \frac{v} {\mathbf{1}^{\mathsf{T}}v} </math> is a fixed point of <math>T_M</math>. Thus normalized fixed points and positive eigenvectors are directly related. === 3.9 Repeated matrix dilation === For a fixed nonnegative matrix <math>M</math>, define :<math> p^{(k+1)} = T_M(p^{(k)}). </math> Whenever the required denominators remain positive, :<math> p^{(k)} = \frac{M^k p^{(0)}} {\mathbf{1}^{\mathsf{T}}M^k p^{(0)}}. </math> This identity follows because the scalar normalization introduced at each intermediate step cancels under the next normalization. The iteration is therefore closely related to normalized power iteration. Under suitable positivity or primitivity assumptions, Perron–Frobenius theory describes the dominant eigenvalue and positive eigenvector governing the long-term behavior. Accordingly, convergence of the fixed-matrix case should be understood primarily through established positive-matrix and spectral theory rather than as a separate PDT convergence mechanism. === 3.10 Primitive positive matrices === A particularly important case occurs when <math>M</math> is primitive; that is, some positive integer power of <math>M</math> has strictly positive entries. Perron–Frobenius theory then provides a dominant real eigenvalue :<math> \rho(M)>0 </math> with a corresponding strictly positive eigenvector <math>v</math>. After normalization, :<math> p^{*} = \frac{v} {\mathbf{1}^{\mathsf{T}}v}, </math> this eigenvector gives the distinguished interior fixed point of the normalized matrix transformation. For suitable initial probability vectors, :<math> T_M^{k}(p^{(0)}) </math> converges toward <math>p^{*}</math>. This convergence is an established consequence of Perron–Frobenius theory and normalized power iteration. Its role here is to locate matrix dilation within known mathematics. === 3.11 Interpretation of off-diagonal terms === The off-diagonal entries of <math>M</math> distinguish matrix dilation from independent diagonal reweighting. For :<math> i\neq j, </math> a term :<math> M_{ij}p_j </math> represents a contribution from input state <math>j</math> to output component <math>i</math> before normalization. The matrix therefore combines two operations: * positive redistribution or coupling through <math>M</math>; * restoration of unit total probability through normalization. This interpretation is useful for organizing the framework, but the underlying linear transformation remains standard matrix mathematics. === 3.12 Scope of the matrix formulation === The matrix formulation substantially enlarges the class of transformations expressible within the normalized-dilation notation, but that enlargement should not be confused with mathematical novelty. For a fixed matrix <math>M</math>, the central objects :<math> Mp, \qquad M^kp, \qquad \rho(M), </math> and the associated eigenvectors and convergence properties belong to established linear algebra and positive-operator theory. The role of the PDT framework is to place diagonal reweighting, matrix transformation, iteration, and later measure-theoretic and geometric constructions within a common normalized-probability notation. This distinction between '''framework''' and '''new mathematical result''' will be maintained throughout the paper. == 4. Measure-Theoretic Dilation == The finite-dimensional dilation rule extends naturally to probability measures. In this setting, componentwise multiplication by positive weights is replaced by multiplication of a probability measure by a nonnegative measurable function followed by normalization. This formulation places finite probability dilation within the standard language of measure theory and makes its relationship to change of measure explicit. === 4.1 Probability-space formulation === Let :<math> (X,\mathcal{F},P) </math> be a probability space. Let :<math> D:X\rightarrow[0,\infty) </math> be a measurable function satisfying :<math> 0< \int_X D(x)\,dP(x) < \infty. </math> Define the normalization factor :<math> Z(P,D) = \int_X D(x)\,dP(x). </math> For every measurable set :<math> A\in\mathcal{F}, </math> define :<math> P_D(A) = \frac{\displaystyle\int_A D(x)\,dP(x)} {Z(P,D)}. </math> Equivalently, :<math> P_D(A) = \frac{\displaystyle\int_A D(x)\,dP(x)} {\displaystyle\int_X D(x)\,dP(x)}. </math> The function <math>D</math> acts as a nonnegative weighting or dilation field over the probability space. === 4.2 Normalization === The transformed measure has total mass one because :<math> P_D(X) = \frac{\displaystyle\int_X D(x)\,dP(x)} {\displaystyle\int_X D(x)\,dP(x)} = 1. </math> Also, because <math>D</math> is nonnegative, :<math> P_D(A)\geq0 </math> for every <math>A\in\mathcal{F}</math>. Countable additivity follows from the countable additivity of integration with respect to <math>P</math>. Therefore <math>P_D</math> is a probability measure. === 4.3 Radon–Nikodym representation === The transformed measure <math>P_D</math> is absolutely continuous with respect to <math>P</math>. Its Radon–Nikodym derivative is :<math> \frac{dP_D}{dP}(x) = \frac{D(x)} {\displaystyle\int_X D(y)\,dP(y)}. </math> Thus normalized measure dilation can be written formally as :<math> dP_D(x) = \frac{D(x)\,dP(x)} {\displaystyle\int_X D(y)\,dP(y)}. </math> This expression makes clear that the construction is a normalized change of measure. The Radon–Nikodym framework is established measure theory. The terminology of dilation is used here to emphasize the common transformation-and-normalization structure shared with the finite-dimensional formulation. === 4.4 Scale invariance === As in the finite-dimensional case, multiplication of the dilation field by a positive constant does not change the normalized measure. Let :<math> c>0. </math> Then :<math> P_{cD}(A) = \frac{\displaystyle\int_A cD\,dP} {\displaystyle\int_X cD\,dP}. </math> The common factor cancels, giving :<math> P_{cD}(A)=P_D(A). </math> Hence the transformed probability measure depends only on the relative values of the dilation field <math>D</math>, not on its overall positive scale. === 4.5 Finite probability spaces as a special case === Consider a finite state space :<math> X=\{1,\ldots,n\}. </math> Let :<math> P(\{i\})=p_i </math> and define :<math> D(i)=d_i. </math> Then :<math> \int_X D\,dP = \sum_{j=1}^{n}d_jp_j. </math> For the singleton event <math>\{i\}</math>, :<math> P_D(\{i\}) = \frac{d_ip_i} {\sum_{j=1}^{n}d_jp_j}. </math> Thus the finite diagonal dilation rule :<math> p_i' = \frac{d_ip_i} {\sum_jd_jp_j} </math> is recovered exactly from the measure-theoretic construction. The discrete and measure-theoretic formulations are therefore instances of the same normalized positive-reweighting operation. === 4.6 Expectations under dilation === Let :<math> f:X\rightarrow\mathbb{R} </math> be measurable and integrable with respect to the transformed measure. Then :<math> \mathbb{E}_{P_D}[f] = \int_X f(x)\,dP_D(x). </math> Using the Radon–Nikodym representation, :<math> \mathbb{E}_{P_D}[f] = \frac{\displaystyle\int_X f(x)D(x)\,dP(x)} {\displaystyle\int_X D(x)\,dP(x)}. </math> Equivalently, :<math> \mathbb{E}_{P_D}[f] = \frac{\mathbb{E}_{P}[fD]} {\mathbb{E}_{P}[D]}, </math> provided the required expectations exist. This identity is a standard weighted-expectation formula and will later be useful for exponential dilation. === 4.7 Composition of dilation fields === Suppose a first dilation field <math>D_1</math> transforms <math>P</math> into <math>P_{D_1}</math>, and a second field <math>D_2</math> is then applied. The first transformation gives :<math> dP_{D_1} = \frac{D_1\,dP} {\int_XD_1\,dP}. </math> Applying <math>D_2</math> gives :<math> d(P_{D_1})_{D_2} = \frac{D_2\,dP_{D_1}} {\int_XD_2\,dP_{D_1}}. </math> Substituting the first transformation and simplifying yields :<math> d(P_{D_1})_{D_2} = \frac{D_1D_2\,dP} {\int_XD_1D_2\,dP}, </math> whenever the required integrals are finite and positive. Therefore :<math> (P_{D_1})_{D_2} = P_{D_1D_2}. </math> Sequential scalar dilation fields thus combine multiplicatively before normalization. This composition property is the measure-theoretic analogue of repeated diagonal reweighting. === 4.8 Iterated fixed dilation === If the same dilation field <math>D</math> is applied repeatedly, then after <math>k</math> iterations, :<math> dP^{(k)} = \frac{D^k\,dP^{(0)}} {\displaystyle\int_XD^k\,dP^{(0)}}. </math> Equivalently, for any measurable event <math>A</math>, :<math> P^{(k)}(A) = \frac{\displaystyle\int_A D(x)^k\,dP^{(0)}(x)} {\displaystyle\int_X D(x)^k\,dP^{(0)}(x)}. </math> This is the direct measure-theoretic counterpart of :<math> p_i^{(k)} = \frac{d_i^kp_i^{(0)}} {\sum_jd_j^kp_j^{(0)}}. </math> Regions where <math>D</math> is relatively large receive increasing relative weight under repeated application. The precise limiting behavior depends on the structure of <math>D</math> and the initial measure. === 4.9 Exponential dilation fields === A particularly important family is obtained by choosing :<math> D_{\theta}(x) = e^{\theta\phi(x)}, </math> where <math>\phi:X\rightarrow\mathbb{R}</math> is measurable and <math>\theta</math> is a real parameter for which the normalization integral is finite. Define :<math> Z(\theta) = \int_X e^{\theta\phi(x)}\,dP_0(x). </math> Then :<math> dP_{\theta}(x) = \frac{e^{\theta\phi(x)}} {Z(\theta)} dP_0(x). </math> In a finite state space this becomes :<math> p_i(\theta) = \frac{p_i^{(0)}e^{\theta\phi_i}} {\sum_jp_j^{(0)}e^{\theta\phi_j}}. </math> This is a standard exponential tilting construction and is closely related to exponential families, cumulant-generating functions, and information geometry. Its importance for the present paper is that it provides a continuous one-parameter dilation trajectory whose Fisher–Rao geometry can be studied explicitly. === 4.10 Infinitesimal evolution of exponential dilation === For the finite-dimensional exponential family, :<math> p_i(\theta) = \frac{p_i^{(0)}e^{\theta\phi_i}} {Z(\theta)}, </math> differentiate with respect to <math>\theta</math>. The logarithmic derivative is :<math> \frac{d}{d\theta}\log p_i(\theta) = \phi_i - \frac{d}{d\theta}\log Z(\theta). </math> Since :<math> \frac{d}{d\theta}\log Z(\theta) = \sum_jp_j(\theta)\phi_j, </math> define :<math> \overline{\phi}_{\theta} = \sum_jp_j(\theta)\phi_j. </math> Then :<math> \frac{dp_i}{d\theta} = p_i(\theta) \left( \phi_i-\overline{\phi}_{\theta} \right). </math> This equation has the form of a replicator-type evolution equation with a fixed state-dependent generator <math>\phi_i</math>. The relationship to established replicator dynamics is discussed in Section 5. === 4.11 Conservation of total probability === Summing the infinitesimal evolution equation gives :<math> \sum_i \frac{dp_i}{d\theta} = \sum_i p_i(\theta) \left( \phi_i-\overline{\phi}_{\theta} \right). </math> Since :<math> \sum_ip_i(\theta)\phi_i = \overline{\phi}_{\theta} </math> and :<math> \sum_ip_i(\theta)=1, </math> it follows that :<math> \sum_i \frac{dp_i}{d\theta} = 0. </math> Thus the vector field is tangent to the probability simplex. Normalization is therefore reflected infinitesimally by conservation of total probability. === 4.12 Scope of the measure-theoretic formulation === The measure-theoretic formulation shows that normalized probability dilation is not restricted to finite vectors or matrices. The same structural operation appears as :'''weight → normalize → obtain a new probability measure''' and, for exponential fields, :'''exponential weight → normalize → continuous probability trajectory'''. These constructions overlap directly with established change-of-measure theory, exponential tilting, weighted probability measures, and related probabilistic methods. Their role in the present framework is to connect the finite dilation notation to continuous probability spaces and to provide the bridge to the information-geometric analysis developed later in the paper. The next section therefore compares the normalized-dilation framework systematically with established mathematical constructions before any additional geometric results are introduced. == 5. Relation to Established Mathematics == The normalized-dilation framework overlaps with several established areas of mathematics. This section identifies those relationships explicitly. The purpose is twofold: first, to place the notation used in this paper within its appropriate mathematical context; and second, to distinguish established constructions from the particular synthesis and geometric questions developed later in the paper. The term '''probability dilation''' is therefore used as an organizing description of a transformation-and-normalization structure, not as a claim that the underlying operations of reweighting, normalization, positive matrix iteration, or change of measure are themselves new. === 5.1 Weighted probability and change of measure === The measure-theoretic transformation :<math> dP_D = \frac{D\,dP} {\int_XD\,dP} </math> is a standard normalized change of measure. Its Radon–Nikodym derivative with respect to <math>P</math> is :<math> \frac{dP_D}{dP} = \frac{D} {\int_XD\,dP}. </math> Consequently, for an integrable observable <math>f</math>, :<math> \mathbb{E}_{P_D}[f] = \frac{\mathbb{E}_{P}[fD]} {\mathbb{E}_{P}[D]}. </math> These expressions belong to established measure-theoretic probability. Within the present framework, their role is to show that finite diagonal dilation and continuous weighted change of measure share the same normalized reweighting structure. === 5.2 Bayesian reweighting === A closely related normalization structure occurs in Bayesian inference. If <math>\pi(x)</math> is a prior density and <math>L(y\mid x)</math> is a likelihood for observed data <math>y</math>, Bayes' rule gives :<math> \pi(x\mid y) = \frac{L(y\mid x)\pi(x)} {\int L(y\mid z)\pi(z)\,dz}, </math> when the denominator is finite and nonzero. Structurally, this has the same form as :<math> dP_D = \frac{D\,dP} {\int D\,dP}, </math> with the likelihood acting as a positive weighting function. The statistical interpretation is different: Bayesian updating has a specific inferential meaning associated with conditioning on data. The comparison here concerns only the common mathematical normalization structure. === 5.3 Importance weighting and exponential tilting === Weighted probability measures also arise in importance sampling, exponential tilting, large-deviation methods, and related statistical constructions. For a generator <math>\phi</math>, exponential tilting takes the form :<math> dP_{\theta}(x) = \frac{e^{\theta\phi(x)}} {Z(\theta)} dP_0(x), </math> where :<math> Z(\theta) = \int_Xe^{\theta\phi(x)}\,dP_0(x). </math> This is an established exponential-family construction. The corresponding finite-dimensional expression, :<math> p_i(\theta) = \frac{p_i^{(0)}e^{\theta\phi_i}} {\sum_jp_j^{(0)}e^{\theta\phi_j}}, </math> will be the principal object of the Fisher–Rao analysis in Sections 6 through 8. The geometric analysis developed later concerns this established exponential-tilt family under a particular question about coincidence of information-geometric and Fisher–Rao geodesics. === 5.4 Positive matrices and Perron–Frobenius theory === For a fixed nonnegative matrix <math>M</math>, the normalized transformation :<math> T_M(p) = \frac{Mp} {\mathbf{1}^{\mathsf{T}}Mp} </math> is closely related to classical positive-matrix theory. If <math>M</math> is primitive, Perron–Frobenius theory provides a dominant positive eigenvalue :<math> \rho(M)>0 </math> and a corresponding strictly positive eigenvector. Repeated normalized iteration, :<math> p^{(k)} = \frac{M^kp^{(0)}} {\mathbf{1}^{\mathsf{T}}M^kp^{(0)}}, </math> is therefore closely related to normalized power iteration. Under appropriate hypotheses, its asymptotic direction is governed by the Perron eigenvector. These spectral and convergence results are established mathematics and are not presented here as new consequences of PDT. === 5.5 Markov operators === Suppose <math>M</math> is nonnegative and satisfies :<math> \mathbf{1}^{\mathsf{T}}M = \mathbf{1}^{\mathsf{T}}. </math> With the column-vector convention used in this paper, :<math> \mathbf{1}^{\mathsf{T}}Mp = 1 </math> for every probability vector <math>p</math>. Thus :<math> T_M(p)=Mp. </math> In this mass-preserving case, the normalization step is unnecessary. Accordingly, ordinary finite-state Markov evolution is contained as a special mass-preserving case of the broader positive-transformation framework. This observation is structural. It does not imply that normalized dilation provides a replacement for Markov-chain theory. === 5.6 Replicator-type dynamics === The exponential dilation family satisfies :<math> \frac{dp_i}{d\theta} = p_i \left( \phi_i-\overline{\phi}_{\theta} \right), </math> where :<math> \overline{\phi}_{\theta} = \sum_jp_j(\theta)\phi_j. </math> The standard replicator equation has the form :<math> \frac{dp_i}{dt} = p_i \left( f_i(p)-\overline{f}(p) \right). </math> Thus exponential dilation with fixed generator values <math>\phi_i</math> has the same algebraic structure as a replicator equation with state-independent fitness values. The mean-subtraction term guarantees :<math> \sum_i\frac{dp_i}{d\theta}=0, </math> so the flow remains tangent to the probability simplex. Replicator dynamics and their geometric interpretations are established subjects. The present paper uses this connection to relate normalized dilation to known simplex dynamics. === 5.7 Fisher–Rao and Shahshahani geometry === The interior of the probability simplex carries the Fisher–Rao metric. For tangent vectors <math>u</math> and <math>v</math> satisfying :<math> \sum_i u_i = \sum_i v_i = 0, </math> the finite-dimensional Fisher–Rao metric can be written as :<math> g_p(u,v) = \sum_{i=1}^{n} \frac{u_iv_i}{p_i}. </math> Closely related forms of this metric appear in evolutionary dynamics under the name Shahshahani metric. The square-root mapping :<math> \Psi(p) = 2(\sqrt{p_1},\ldots,\sqrt{p_n}) </math> satisfies :<math> \sum_i\Psi_i(p)^2=4. </math> Thus the simplex interior is represented in the positive orthant of a sphere of radius <math>2</math>. Under this representation, the Fisher–Rao metric becomes the metric induced by the ambient Euclidean space, and Levi-Civita Fisher–Rao geodesics correspond locally to great-circle arcs. This established spherical representation will be the principal geometric tool used in Section 7. === 5.8 Exponential families and the e-connection === The exponential dilation path :<math> p_i(\theta) = \frac{p_i^{(0)}e^{\theta\phi_i}} {Z(\theta)} </math> is a one-parameter exponential family. Taking logarithms gives :<math> \log p_i(\theta) = \log p_i^{(0)} + \theta\phi_i - \log Z(\theta). </math> The natural parameter varies linearly with <math>\theta</math>. In information geometry, exponential families are naturally associated with the exponential, or '''e''', connection. A path linear in natural parameters is an e-geodesic. This notion of geodesic is distinct from a Levi-Civita geodesic of the Fisher–Rao metric. Consequently, an exponential dilation trajectory may be straight with respect to the e-connection while being curved with respect to the Fisher–Rao Levi-Civita connection. This distinction is central to the geometric question investigated later in the paper. === 5.9 Fisher information and variance === For the exponential dilation family, :<math> \frac{d}{d\theta} \log p_i(\theta) = \phi_i-\overline{\phi}_{\theta}. </math> The Fisher information associated with the parameter <math>\theta</math> is therefore :<math> I(\theta) = \sum_i p_i(\theta) \left( \phi_i-\overline{\phi}_{\theta} \right)^2. </math> Hence :<math> I(\theta) = \operatorname{Var}_{p(\theta)}(\phi). </math> The Fisher–Rao speed of the trajectory is :<math> v_{\mathrm{FR}}(\theta) = \sqrt{I(\theta)} = \sqrt{\operatorname{Var}_{p(\theta)}(\phi)}. </math> This variance identity is a standard property of one-parameter exponential families. It will be used later when deriving the arclength parameterization of the two-level case. === 5.10 Normalized Feynman–Kac transformations === Another closely related structure occurs in Feynman–Kac models. At an abstract level, a positive measure may first be weighted by a nonnegative potential and then propagated through a positive or Markov operator, followed by normalization. Schematically, such an evolution has the form :'''weight → propagate → normalize'''. The matrix expression :<math> T_M(p) = \frac{Mp} {\mathbf{1}^{\mathsf{T}}Mp} </math> and the measure expression :<math> dP_D = \frac{D\,dP} {\int D\,dP} </math> therefore have structural analogues within normalized Feynman–Kac theory. The exact interpretation and assumptions differ among applications. The comparison made here is structural rather than an assertion of equivalence between PDT and Feynman–Kac theory. === 5.11 Projective dynamics === Because normalized dilation is invariant under multiplication of the unnormalized transformed state by a positive scalar, it naturally has a projective character. For example, :<math> T_{cM}(p) = T_M(p) </math> for every <math>c>0</math> for which the transformation is defined. Thus the normalized state depends on the ray determined by <math>Mp</math>, rather than its magnitude. Positive projective geometry and projective metrics, including Hilbert-type metrics, are established tools in the study of positive operators and their contraction properties. These methods provide natural mathematical machinery for analyzing normalized positive transformations, particularly in convergence problems. === 5.12 What the PDT framework contributes === The preceding comparisons show that the principal operations used in normalized probability dilation have substantial established precedents. The proposed contribution of the framework is therefore not the isolated operation :'''multiply or transform, then normalize'''. Rather, the framework provides a common notation and organizational viewpoint connecting: * finite diagonal reweighting; * nonnegative matrix transformations; * normalized positive iteration; * weighted change of measure; * exponential probability trajectories; * simplex dynamics; * information geometry. This synthesis is useful only insofar as it clarifies relationships, generates mathematically precise questions, or produces results that are not merely restatements of known theory. For that reason, the remainder of this paper concentrates on a narrower geometric problem. === 5.13 Transition to the geometric question === Every exponential dilation trajectory of the form :<math> p_i(\theta) = \frac{p_i^{(0)}e^{\theta\phi_i}} {Z(\theta)} </math> is an exponential-family trajectory and hence is naturally straight with respect to the e-connection. It does not follow that the same trajectory is a Levi-Civita geodesic of the Fisher–Rao metric. This leads to the central question considered in the remainder of the paper: :''Under what conditions is an exponential dilation trajectory simultaneously an e-geodesic and, up to reparameterization, a Fisher–Rao Levi-Civita geodesic?'' The next section develops the geometric representation required to answer this question. == 6. Exponential Dilation and Fisher–Rao Geometry == This section develops the geometric representation of exponential dilation required for the main characterization theorem. The central object is the one-parameter exponential family :<math> p_i(\theta) = \frac{p_i^{(0)}e^{\theta\phi_i}} {Z(\theta)}, </math> where :<math> Z(\theta) = \sum_{j=1}^{n}p_j^{(0)}e^{\theta\phi_j}. </math> Throughout this section, assume :<math> p_i^{(0)}>0 </math> for all <math>i</math>, and let :<math> \phi=(\phi_1,\ldots,\phi_n) </math> be a real-valued generator. === 6.1 Exponential dilation trajectory === Let :<math> p^{(0)} \in \Delta_{+}^{n-1}. </math> For a real parameter <math>\theta</math>, define :<math> p_i(\theta) = \frac{p_i^{(0)}e^{\theta\phi_i}} {\sum_{j=1}^{n}p_j^{(0)}e^{\theta\phi_j}}. </math> Since every initial component is strictly positive and the exponential function is positive, :<math> p_i(\theta)>0 </math> for every finite <math>\theta</math>. Therefore the trajectory remains in the interior of the probability simplex. The normalization factor satisfies :<math> Z(\theta)>0. </math> Hence the trajectory is well defined for every finite <math>\theta</math> in the finite-dimensional setting. === 6.2 Logarithmic form === Taking logarithms gives :<math> \log p_i(\theta) = \log p_i^{(0)} + \theta\phi_i - \log Z(\theta). </math> Differentiating with respect to <math>\theta</math> gives :<math> \frac{d}{d\theta}\log p_i(\theta) = \phi_i - \frac{d}{d\theta}\log Z(\theta). </math> Now :<math> \frac{dZ}{d\theta} = \sum_j p_j^{(0)} \phi_j e^{\theta\phi_j}. </math> Therefore :<math> \frac{d}{d\theta}\log Z(\theta) = \sum_jp_j(\theta)\phi_j. </math> Define the expectation of the generator by :<math> \mu(\theta) = \mathbb{E}_{p(\theta)}[\phi] = \sum_jp_j(\theta)\phi_j. </math> Then :<math> \frac{d}{d\theta}\log p_i(\theta) = \phi_i-\mu(\theta). </math> === 6.3 Tangent vector === Multiplying the logarithmic derivative by <math>p_i(\theta)</math> gives :<math> \frac{dp_i}{d\theta} = p_i(\theta) \left( \phi_i-\mu(\theta) \right). </math> Define the centered generator :<math> h_i(\theta) = \phi_i-\mu(\theta). </math> Then :<math> \frac{dp_i}{d\theta} = p_i(\theta)h_i(\theta). </math> Because :<math> \sum_i p_i(\theta)h_i(\theta) = 0, </math> we obtain :<math> \sum_i \frac{dp_i}{d\theta} = 0. </math> Thus the velocity vector is tangent to the probability simplex. === 6.4 Fisher information and speed === The Fisher–Rao metric on the simplex interior is :<math> g_p(u,v) = \sum_i \frac{u_iv_i}{p_i}, </math> for tangent vectors <math>u</math> and <math>v</math>. For the exponential dilation trajectory, :<math> \frac{dp_i}{d\theta} = p_i h_i. </math> Its squared Fisher–Rao speed is therefore :<math> v_{\mathrm{FR}}(\theta)^2 = \sum_i \frac{1}{p_i} \left( \frac{dp_i}{d\theta} \right)^2. </math> Substitution gives :<math> v_{\mathrm{FR}}(\theta)^2 = \sum_i p_i(\theta)h_i(\theta)^2. </math> Hence :<math> v_{\mathrm{FR}}(\theta)^2 = \operatorname{Var}_{p(\theta)}(\phi). </math> Therefore :<math> v_{\mathrm{FR}}(\theta) = \sqrt{ \operatorname{Var}_{p(\theta)}(\phi) }. </math> This is the standard Fisher-information identity for a one-parameter exponential family. === 6.5 Square-root representation === Define the square-root map :<math> \Psi: \Delta_{+}^{n-1} \rightarrow \mathbb{R}^{n} </math> by :<math> \Psi(p) = 2(\sqrt{p_1},\ldots,\sqrt{p_n}). </math> Write :<math> q(\theta) = \Psi(p(\theta)). </math> Then :<math> q_i(\theta) = 2\sqrt{p_i(\theta)}. </math> Because :<math> \sum_i p_i(\theta)=1, </math> we have :<math> \sum_iq_i(\theta)^2 = 4. </math> Thus :<math> q(\theta) </math> lies on the positive orthant of the sphere of radius <math>2</math> in <math>\mathbb{R}^{n}</math>. === 6.6 Isometry of the square-root representation === Let <math>u</math> be a tangent vector to the simplex. Differentiating :<math> q_i=2\sqrt{p_i} </math> gives :<math> dq_i = \frac{dp_i}{\sqrt{p_i}}. </math> Therefore the Euclidean squared length of the corresponding tangent displacement on the sphere is :<math> \sum_i(dq_i)^2 = \sum_i \frac{(dp_i)^2}{p_i}. </math> This is precisely the Fisher–Rao line element. Thus the square-root map identifies the Fisher–Rao metric on the simplex interior with the Euclidean metric induced on the positive orthant of the radius-<math>2</math> sphere. Consequently, Fisher–Rao Levi-Civita geodesics correspond locally to great-circle arcs on this sphere. === 6.7 Square-root form of exponential dilation === Substituting the exponential dilation family into the square-root representation gives :<math> q_i(\theta) = \frac{ 2\sqrt{p_i^{(0)}}e^{\theta\phi_i/2} } {\sqrt{Z(\theta)}}. </math> Define the unnormalized square-root vector :<math> r_i(\theta) = \sqrt{p_i^{(0)}}e^{\theta\phi_i/2}. </math> Then :<math> q(\theta) = \frac{2r(\theta)} {\sqrt{Z(\theta)}}. </math> Also, :<math> \|r(\theta)\|^2 = Z(\theta). </math> Hence :<math> q(\theta) = \frac{2r(\theta)} {\|r(\theta)\|}. </math> The normalized square-root trajectory and the unnormalized vector <math>r(\theta)</math> therefore determine the same ray through the origin. This observation allows the Fisher–Rao geodesic question to be reduced to a linear-subspace question in <math>\mathbb{R}^{n}</math>. === 6.8 Distinct generator levels === Suppose the generator <math>\phi</math> assumes exactly <math>m</math> distinct values :<math> a_1,\ldots,a_m. </math> Define the level sets :<math> A_{\ell} = \{i:\phi_i=a_{\ell}\}, </math> for :<math> \ell=1,\ldots,m. </math> For each level, define a vector <math>u_{\ell}</math> by :<math> (u_{\ell})_i = \begin{cases} \sqrt{p_i^{(0)}} & \text{if } i\in A_{\ell},\\ 0 & \text{otherwise}. \end{cases} </math> Because the level sets are disjoint, the vectors :<math> u_1,\ldots,u_m </math> have disjoint supports and are therefore mutually orthogonal. In particular, they are linearly independent. The unnormalized square-root trajectory can now be written as :<math> r(\theta) = \sum_{\ell=1}^{m} e^{a_{\ell}\theta/2} u_{\ell}. </math> This decomposition is central to the geometric characterization developed in the next section. === 6.9 The one-level case === If <math>m=1</math>, then every component of <math>\phi</math> has the same value <math>a</math>. Thus :<math> r(\theta) = e^{a\theta/2}u_1. </math> After normalization, the scalar exponential factor cancels. Therefore :<math> p(\theta)=p^{(0)} </math> for all <math>\theta</math>. The trajectory is constant. This is the degenerate case of exponential dilation. === 6.10 The two-level case === Suppose <math>\phi</math> assumes exactly two distinct values :<math> a </math> and :<math> b, </math> with <math>a\neq b</math>. Then :<math> r(\theta) = e^{a\theta/2}u + e^{b\theta/2}v, </math> where <math>u</math> and <math>v</math> are nonzero orthogonal vectors associated with the two generator levels. Consequently, :<math> r(\theta) \in \operatorname{span}\{u,v\} </math> for every <math>\theta</math>. Since <math>q(\theta)</math> is obtained from <math>r(\theta)</math> by positive scalar normalization, :<math> q(\theta) \in \operatorname{span}\{u,v\} </math> as well. The intersection of a two-dimensional linear subspace through the origin with the radius-<math>2</math> sphere is a great circle. Thus the two-level case naturally produces a Fisher–Rao great-circle trajectory. The formal statement and converse are given in Section 7. === 6.11 Three or more generator levels === If the generator assumes three or more distinct values, then :<math> r(\theta) = \sum_{\ell=1}^{m} e^{a_{\ell}\theta/2}u_{\ell}, </math> with :<math> m\geq3. </math> The vectors <math>u_{\ell}</math> are linearly independent, but this fact alone is not sufficient to conclude that the trajectory spans all <math>m</math> directions. The required result follows from the linear independence of the distinct exponential rates. In Section 7, derivatives of <math>r(\theta)</math> are evaluated at a fixed parameter value. The resulting coefficient matrix is of Vandermonde type and is invertible when the generator levels <math>a_{\ell}</math> are distinct. This shows that a trajectory with <math>m</math> distinct active generator levels spans an <math>m</math>-dimensional linear subspace. Consequently, when <math>m\geq3</math>, the square-root trajectory cannot lie in a two-dimensional great-circle plane. === 6.12 e-geodesic versus Fisher–Rao geodesic === The exponential dilation trajectory is an exponential-family path. In natural coordinates, the parameter <math>\theta</math> enters linearly through :<math> \theta\phi_i. </math> Accordingly, the trajectory is naturally an e-geodesic in the exponential connection of information geometry. The Fisher–Rao Levi-Civita geodesic condition is different. Under the square-root representation, it requires the image of the trajectory to lie on a great-circle arc. Thus the central geometric distinction is: :'''e-geodesic: linearity in exponential-family natural coordinates''' versus :'''Fisher–Rao Levi-Civita geodesic: great-circle geometry under the square-root representation''' The two notions coincide only under additional conditions. === 6.13 Geometric question in linear form === The original probability-geometric question can now be reformulated. Given :<math> r(\theta) = \sum_{\ell=1}^{m} e^{a_{\ell}\theta/2}u_{\ell}, </math> when does the normalized curve :<math> q(\theta) = \frac{2r(\theta)} {\|r(\theta)\|} </math> remain in a fixed two-dimensional linear subspace? If it does, its image lies on a great circle and is therefore a Fisher–Rao Levi-Civita geodesic up to reparameterization. If it does not, the exponential trajectory remains an e-geodesic but is not a Fisher–Rao Levi-Civita geodesic. The next section gives an exact finite-dimensional characterization. == 7. Fisher–Rao Geodesic Characterization == This section gives the principal geometric result of the paper. The question is whether the image of a finite-dimensional exponential dilation trajectory is contained in a Fisher–Rao Levi-Civita geodesic. The parameter <math>\theta</math> itself is not required to be an affine or arclength parameter for that geodesic. === 7.1 Setting and assumptions === Let :<math> p^{(0)} = (p_1^{(0)},\ldots,p_n^{(0)})^{\mathsf{T}} \in \Delta_{+}^{n-1}, </math> so that :<math> p_i^{(0)}>0 </math> for every <math>i</math>. Let :<math> \phi = (\phi_1,\ldots,\phi_n) \in \mathbb{R}^{n}. </math> Define the exponential dilation trajectory :<math> p_i(\theta) = \frac{ p_i^{(0)}e^{\theta\phi_i} } { \sum_{j=1}^{n} p_j^{(0)}e^{\theta\phi_j} }, </math> for :<math> \theta\in\mathbb{R}. </math> Let <math>m</math> denote the number of distinct values assumed by the generator components :<math> \phi_1,\ldots,\phi_n. </math> === 7.2 Theorem 1: two-level Fisher–Rao characterization === '''Theorem 1.''' Under the assumptions above, the image of the exponential dilation trajectory <math>p(\theta)</math> is contained in a Fisher–Rao Levi-Civita geodesic if and only if :<math> m\leq2. </math> Equivalently, the generator <math>\phi</math> must assume at most two distinct values. When <math>m=1</math>, the trajectory is constant. When <math>m=2</math>, the trajectory is nonconstant and its square-root image lies on a great-circle arc. === 7.3 Proof: square-root representation === Define :<math> q_i(\theta) = 2\sqrt{p_i(\theta)}. </math> As shown in Section 6, :<math> q(\theta) </math> lies on the sphere :<math> \sum_iq_i^2=4. </math> The square-root representation is an isometric representation of the Fisher–Rao simplex interior. Therefore the image of <math>p(\theta)</math> is contained in a Fisher–Rao Levi-Civita geodesic if and only if the image of <math>q(\theta)</math> is contained in a great circle of the radius-<math>2</math> sphere. A great circle is the intersection of the sphere with a two-dimensional linear subspace through the origin. === 7.4 Grouping equal generator values === Let the distinct values of <math>\phi</math> be :<math> a_1,\ldots,a_m. </math> For each <math>\ell</math>, define :<math> A_{\ell} = \{i:\phi_i=a_{\ell}\}. </math> Define <math>u_{\ell}\in\mathbb{R}^{n}</math> by :<math> (u_{\ell})_i = \begin{cases} \sqrt{p_i^{(0)}} & \text{if }i\in A_{\ell},\\ 0 & \text{otherwise}. \end{cases} </math> Because the sets <math>A_{\ell}</math> are disjoint and every initial component is strictly positive, the vectors :<math> u_1,\ldots,u_m </math> are nonzero and mutually orthogonal. Hence they are linearly independent. Define the unnormalized square-root trajectory :<math> r(\theta) = \sum_{\ell=1}^{m} e^{a_{\ell}\theta/2} u_{\ell}. </math> Then :<math> q(\theta) = \frac{2r(\theta)} {\|r(\theta)\|}. </math> Since normalization multiplies <math>r(\theta)</math> only by a positive scalar, <math>q(\theta)</math> and <math>r(\theta)</math> lie on the same ray through the origin. === 7.5 Sufficiency: one or two generator levels === Suppose first that :<math> m=1. </math> Then :<math> r(\theta) = e^{a_1\theta/2}u_1. </math> Normalization removes the scalar exponential factor, so :<math> q(\theta) </math> and therefore <math>p(\theta)</math> are constant. A constant trajectory is the degenerate case. Now suppose :<math> m=2. </math> Then :<math> r(\theta) = e^{a_1\theta/2}u_1 + e^{a_2\theta/2}u_2. </math> Therefore :<math> r(\theta) \in \operatorname{span}\{u_1,u_2\} </math> for every <math>\theta</math>. Since <math>q(\theta)</math> differs from <math>r(\theta)</math> only by scalar normalization, :<math> q(\theta) \in \operatorname{span}\{u_1,u_2\}. </math> The vectors <math>u_1</math> and <math>u_2</math> are nonzero and orthogonal, so their span is a two-dimensional linear subspace through the origin. Its intersection with the radius-<math>2</math> sphere is a great circle. Thus the image of the two-level exponential dilation trajectory lies on a Fisher–Rao Levi-Civita geodesic. This proves sufficiency. === 7.6 Necessity: derivative span === Now suppose the generator assumes :<math> m\geq3 </math> distinct values. Differentiate the unnormalized square-root trajectory: :<math> r(\theta) = \sum_{\ell=1}^{m} e^{a_{\ell}\theta/2} u_{\ell}. </math> For every nonnegative integer <math>k</math>, :<math> r^{(k)}(\theta) = \sum_{\ell=1}^{m} \left( \frac{a_{\ell}}{2} \right)^k e^{a_{\ell}\theta/2} u_{\ell}. </math> Fix any :<math> \theta_0\in\mathbb{R}. </math> Consider the vectors :<math> r(\theta_0), r^{(1)}(\theta_0), \ldots, r^{(m-1)}(\theta_0). </math> Their coefficients relative to the basis :<math> u_1,\ldots,u_m </math> form the matrix :<math> C_{k\ell} = \left( \frac{a_{\ell}}{2} \right)^k e^{a_{\ell}\theta_0/2}, </math> where :<math> k=0,\ldots,m-1 </math> and :<math> \ell=1,\ldots,m. </math> === 7.7 Vandermonde argument === Factor the nonzero quantity :<math> e^{a_{\ell}\theta_0/2} </math> from column <math>\ell</math> of the coefficient matrix. The remaining matrix has entries :<math> V_{k\ell} = \left( \frac{a_{\ell}}{2} \right)^k. </math> This is a Vandermonde matrix. Its determinant is nonzero because :<math> a_1,\ldots,a_m </math> are distinct. Therefore the coefficient matrix <math>C</math> is invertible. It follows that :<math> r(\theta_0), r^{(1)}(\theta_0), \ldots, r^{(m-1)}(\theta_0) </math> are linearly independent. Consequently, the linear span generated by the trajectory <math>r(\theta)</math> has dimension at least <math>m</math>. On the other hand, the representation :<math> r(\theta) = \sum_{\ell=1}^{m} e^{a_{\ell}\theta/2}u_{\ell} </math> shows that the trajectory is contained in :<math> \operatorname{span} \{u_1,\ldots,u_m\}, </math> which has dimension <math>m</math>. Hence :<math> \dim \operatorname{span} \{r(\theta):\theta\in\mathbb{R}\} = m. </math> === 7.8 Exclusion of three or more levels === If the square-root trajectory <math>q(\theta)</math> were contained in a great circle, then there would exist a two-dimensional linear subspace <math>W</math> through the origin such that :<math> q(\theta)\in W </math> for every <math>\theta</math>. Since :<math> r(\theta) = \frac{\|r(\theta)\|}{2} q(\theta), </math> the same subspace would contain :<math> r(\theta) </math> for every <math>\theta</math>. Therefore :<math> \dim \operatorname{span} \{r(\theta):\theta\in\mathbb{R}\} \leq2. </math> But Section 7.7 gives :<math> \dim \operatorname{span} \{r(\theta):\theta\in\mathbb{R}\} = m. </math> Thus a great-circle trajectory requires :<math> m\leq2. </math> For :<math> m\geq3, </math> the exponential dilation trajectory cannot be contained in a Fisher–Rao Levi-Civita geodesic. This proves necessity. === 7.9 Conclusion of the proof === Combining Sections 7.5 and 7.8 gives :<math> m\leq2 </math> if and only if the image of the exponential dilation trajectory is contained in a Fisher–Rao Levi-Civita geodesic. Therefore the generator <math>\phi</math> must assume at most two distinct values. This completes the proof. === 7.10 Corollary 1: dimension of the square-root trajectory === '''Corollary 1.''' Under the assumptions of Theorem 1, if the generator <math>\phi</math> assumes exactly <math>m</math> distinct values, then :<math> \dim \operatorname{span} \{r(\theta):\theta\in\mathbb{R}\} = m. </math> Thus the number of distinct generator levels is exactly the dimension of the linear subspace generated by the unnormalized square-root exponential trajectory. '''Proof.''' The vectors <math>u_1,\ldots,u_m</math> are linearly independent, and Section 7.7 shows through the Vandermonde argument that the trajectory spans all of these directions. Therefore its span has dimension <math>m</math>. === 7.11 Corollary 2: three-level obstruction === '''Corollary 2.''' If a strictly positive finite exponential dilation trajectory has a generator assuming three or more distinct values, then its image is not contained in a Fisher–Rao Levi-Civita geodesic. This follows immediately from Theorem 1. The result is exact under the stated hypotheses; it is not merely a generic non-geodesicity statement. === 7.12 Parameterization versus geodesic image === Theorem 1 concerns the image of the trajectory. Even in the two-level case, the exponential parameter <math>\theta</math> is generally not proportional to Fisher–Rao arclength. Thus :<math> p(\theta) </math> traces a Fisher–Rao geodesic path but generally does so with nonconstant Fisher–Rao speed. From Section 6, :<math> \frac{ds}{d\theta} = \sqrt{ \operatorname{Var}_{p(\theta)}(\phi) }. </math> Section 8 derives the exact change of parameter from <math>\theta</math> to Fisher–Rao arclength in the nondegenerate two-level case. === 7.13 Geometric interpretation === The theorem can be understood through the square-root sphere. A generator with one distinct value produces no probability motion. A generator with two distinct values produces two independent exponential directions, :<math> e^{a\theta/2}u </math> and :<math> e^{b\theta/2}v. </math> Their normalized sum remains in a fixed two-dimensional plane through the origin, so its spherical image follows a great circle. With three or more distinct generator values, the trajectory necessarily spans three or more independent linear directions. It therefore cannot remain in any two-dimensional great-circle plane. The distinction between the two-level and multilevel cases is consequently a dimensional property of the exponential rates under the square-root representation. === 7.14 Relation to information-geometric straightness === Theorem 1 does not state that exponential trajectories with three or more levels cease to be e-geodesics. They remain exponential-family trajectories and retain their standard information-geometric interpretation with respect to the e-connection. Rather, the theorem characterizes when this e-geodesic image also coincides with a geodesic image of the Levi-Civita connection associated with the Fisher–Rao metric. Thus the result concerns the coincidence of two distinct notions of geometric straightness. === 7.15 Status of the characterization === The proof above uses established ingredients: * the exponential-family representation; * the Fisher–Rao square-root embedding; * the great-circle characterization of spherical geodesics; * linear independence of vectors with disjoint support; * the Vandermonde determinant. The particular characterization obtained by combining these ingredients is presented here as a result of the present analysis. At this draft stage, no claim of historical priority is made. A complete literature review and independent mathematical scrutiny remain appropriate before describing the characterization as novel. The next section derives an explicit Fisher–Rao arclength parameterization for the nondegenerate two-level case. == 8. Fisher–Rao Arclength in the Two-Level Case == Theorem 1 shows that a nonconstant exponential dilation trajectory is contained in a Fisher–Rao Levi-Civita geodesic precisely when its generator assumes exactly two distinct values. This section derives an explicit Fisher–Rao arclength parameterization for that case. === 8.1 Two generator classes === Suppose the generator <math>\phi</math> assumes exactly two distinct values :<math> a\neq b. </math> Define the corresponding index sets :<math> A= \{i:\phi_i=a\} </math> and :<math> B= \{i:\phi_i=b\}. </math> Let the initial probability masses of the two classes be :<math> r_0 = \sum_{i\in A}p_i^{(0)} </math> and :<math> 1-r_0 = \sum_{i\in B}p_i^{(0)}. </math> Because the initial probability vector is strictly positive and both classes are nonempty, :<math> 0<r_0<1. </math> === 8.2 Evolution of the class probabilities === Let :<math> r(\theta) = \sum_{i\in A}p_i(\theta) </math> denote the total probability assigned to class <math>A</math>. Since every state in <math>A</math> has generator value <math>a</math> and every state in <math>B</math> has generator value <math>b</math>, :<math> r(\theta) = \frac{ r_0e^{a\theta} } { r_0e^{a\theta} + (1-r_0)e^{b\theta} }. </math> Similarly, :<math> 1-r(\theta) = \frac{ (1-r_0)e^{b\theta} } { r_0e^{a\theta} + (1-r_0)e^{b\theta} }. </math> Therefore the class odds satisfy :<math> \frac{r(\theta)} {1-r(\theta)} = \frac{r_0} {1-r_0} e^{(a-b)\theta}. </math> Thus the two-level exponential dilation reduces at the class level to a logistic probability trajectory. === 8.3 Preservation of within-class proportions === For two indices <math>i,j\in A</math>, :<math> \frac{p_i(\theta)} {p_j(\theta)} = \frac{p_i^{(0)}} {p_j^{(0)}}. </math> The same relation holds for indices within <math>B</math>. Therefore exponential dilation changes only the total probability assigned to the two generator classes; it does not change relative probabilities within either class. Define normalized class vectors <math>\widehat{u}</math> and <math>\widehat{v}</math> by :<math> \widehat{u}_i = \begin{cases} \sqrt{p_i^{(0)}/r_0} & \text{if }i\in A,\\ 0 & \text{otherwise}, \end{cases} </math> and :<math> \widehat{v}_i = \begin{cases} \sqrt{p_i^{(0)}/(1-r_0)} & \text{if }i\in B,\\ 0 & \text{otherwise}. \end{cases} </math> These vectors satisfy :<math> \|\widehat{u}\|=1, \qquad \|\widehat{v}\|=1, </math> and :<math> \widehat{u}^{\mathsf{T}}\widehat{v}=0. </math> === 8.4 Great-circle representation === Under the square-root map, :<math> q(\theta) = 2(\sqrt{p_1(\theta)},\ldots,\sqrt{p_n(\theta)}). </math> Using the class decomposition, :<math> q(\theta) = 2 \left( \sqrt{r(\theta)}\,\widehat{u} + \sqrt{1-r(\theta)}\,\widehat{v} \right). </math> Introduce an angular coordinate <math>\alpha(\theta)</math> by :<math> \sqrt{r(\theta)} = \cos\alpha(\theta) </math> and :<math> \sqrt{1-r(\theta)} = \sin\alpha(\theta), </math> with :<math> 0<\alpha(\theta)<\frac{\pi}{2}. </math> Then :<math> q(\theta) = 2 \left( \cos\alpha(\theta)\widehat{u} + \sin\alpha(\theta)\widehat{v} \right). </math> This is the standard angular parameterization of a great circle on a sphere of radius <math>2</math>. === 8.5 Angular coordinate === From the definitions above, :<math> \tan\alpha(\theta) = \sqrt{ \frac{1-r(\theta)} {r(\theta)} }. </math> Using the odds relation, :<math> \frac{1-r(\theta)} {r(\theta)} = \frac{1-r_0} {r_0} e^{(b-a)\theta}. </math> Therefore :<math> \tan\alpha(\theta) = \sqrt{ \frac{1-r_0} {r_0} } e^{(b-a)\theta/2}. </math> Hence :<math> \alpha(\theta) = \arctan \left( \sqrt{ \frac{1-r_0} {r_0} } e^{(b-a)\theta/2} \right). </math> Equivalently, :<math> \alpha(\theta) = \arccos\sqrt{r(\theta)}. </math> === 8.6 Corollary 3: exact Fisher–Rao arclength parameterization === '''Corollary 3.''' Under the hypotheses of Theorem 1, suppose the generator assumes exactly two distinct values <math>a\neq b</math>. Let :<math> r(\theta) </math> denote the total probability assigned to the class with generator value <math>a</math>. Then a signed Fisher–Rao arclength coordinate along the trajectory satisfies :<math> s(\theta)-s(\theta_0) = 2 \left( \alpha(\theta)-\alpha(\theta_0) \right), </math> where :<math> \alpha(\theta) = \arccos\sqrt{r(\theta)}. </math> Thus :<math> s(\theta)-s(\theta_0) = 2 \left( \arccos\sqrt{r(\theta)} - \arccos\sqrt{r(\theta_0)} \right). </math> Equivalently, :<math> s(\theta)-s(\theta_0) = 2 \left[ \arctan \left( \sqrt{ \frac{1-r_0}{r_0} } e^{(b-a)\theta/2} \right) - \arctan \left( \sqrt{ \frac{1-r_0}{r_0} } e^{(b-a)\theta_0/2} \right) \right]. </math> The Fisher–Rao distance traveled between the two parameter values is the absolute value :<math> d_{\mathrm{FR}} = |s(\theta)-s(\theta_0)|. </math> === 8.7 Proof of Corollary 3 === The square-root image is :<math> q(\theta) = 2 \left( \cos\alpha(\theta)\widehat{u} + \sin\alpha(\theta)\widehat{v} \right). </math> Differentiate with respect to <math>\alpha</math>: :<math> \frac{dq}{d\alpha} = 2 \left( -\sin\alpha\,\widehat{u} + \cos\alpha\,\widehat{v} \right). </math> Because <math>\widehat{u}</math> and <math>\widehat{v}</math> are orthonormal, :<math> \left\| \frac{dq}{d\alpha} \right\| = 2. </math> Therefore the spherical arclength element is :<math> ds = 2\,|d\alpha|. </math> For a chosen orientation, signed arclength satisfies :<math> ds=2\,d\alpha. </math> Integrating from <math>\theta_0</math> to <math>\theta</math> gives :<math> s(\theta)-s(\theta_0) = 2 \left( \alpha(\theta)-\alpha(\theta_0) \right). </math> Substituting the expressions for <math>\alpha(\theta)</math> gives the stated formulas. === 8.8 Fisher–Rao speed === Differentiating the angular expression gives :<math> \frac{d\alpha}{d\theta} = \frac{b-a}{2} \sqrt{ r(\theta) \left( 1-r(\theta) \right) }. </math> Therefore the unsigned Fisher–Rao speed is :<math> \left| \frac{ds}{d\theta} \right| = |a-b| \sqrt{ r(\theta) \left( 1-r(\theta) \right) }. </math> This agrees with the variance formula derived in Section 6. Indeed, because <math>\phi</math> takes only the values <math>a</math> and <math>b</math>, :<math> \operatorname{Var}_{p(\theta)}(\phi) = (a-b)^2 r(\theta) \left( 1-r(\theta) \right). </math> Hence :<math> v_{\mathrm{FR}}(\theta) = \sqrt{ \operatorname{Var}_{p(\theta)}(\phi) } = |a-b| \sqrt{ r(\theta) \left( 1-r(\theta) \right) }. </math> The geometric and information-theoretic calculations therefore agree. === 8.9 Nonuniform speed in the exponential parameter === Although the trajectory lies on a Fisher–Rao geodesic, the parameter <math>\theta</math> does not generally move along that geodesic at constant speed. The speed is largest when :<math> r(\theta)=\frac{1}{2}, </math> because the product :<math> r(\theta)(1-r(\theta)) </math> is maximal there. As the trajectory approaches either endpoint, :<math> r(\theta)\rightarrow0 </math> or :<math> r(\theta)\rightarrow1, </math> the Fisher–Rao speed with respect to <math>\theta</math> approaches zero. Thus the exponential parameter stretches the ends of the geodesic trajectory. === 8.10 Limiting behavior === Assume :<math> a>b. </math> Then as :<math> \theta\rightarrow+\infty, </math> we have :<math> r(\theta)\rightarrow1. </math> As :<math> \theta\rightarrow-\infty, </math> we have :<math> r(\theta)\rightarrow0. </math> Therefore :<math> \alpha(\theta)\rightarrow0 </math> as <math>\theta\rightarrow+\infty</math>, while :<math> \alpha(\theta)\rightarrow\frac{\pi}{2} </math> as <math>\theta\rightarrow-\infty</math>. The full two-level trajectory therefore approaches the two boundary class distributions at opposite ends of a quarter of the radius-<math>2</math> great circle. The total Fisher–Rao length between these limiting boundary points is :<math> 2 \left( \frac{\pi}{2} \right) = \pi. </math> The endpoints themselves lie on the boundary of the simplex and are approached only in the infinite-parameter limit. === 8.11 Example === Consider a three-state probability vector :<math> p^{(0)} = \left( \frac{1}{4}, \frac{1}{4}, \frac{1}{2} \right)^{\mathsf{T}} </math> and generator :<math> \phi = (1,1,0). </math> There are two generator classes: :<math> A=\{1,2\}, \qquad B=\{3\}. </math> The initial class mass is :<math> r_0 = \frac{1}{2}. </math> The class probability evolves as :<math> r(\theta) = \frac{e^{\theta}} {e^{\theta}+1}. </math> The individual probabilities are :<math> p_1(\theta) = \frac{1}{2}r(\theta), </math> :<math> p_2(\theta) = \frac{1}{2}r(\theta), </math> and :<math> p_3(\theta) = 1-r(\theta). </math> The angular coordinate is :<math> \alpha(\theta) = \arctan \left( e^{-\theta/2} \right). </math> Thus the trajectory is an exponential-family e-geodesic whose image is simultaneously a Fisher–Rao Levi-Civita geodesic. Its exponential parameterization is nonuniform, while <math>2\alpha</math> provides a signed Fisher–Rao arclength coordinate up to an additive constant and choice of orientation. === 8.12 Interpretation === The two-level result separates the '''path''' from the '''parameterization'''. The exponential parameter <math>\theta</math> generates the probability trajectory through normalized exponential weighting. The Fisher–Rao geometry identifies the same trajectory as a great-circle path. The transformation :<math> \theta \longmapsto \alpha(\theta) \longmapsto s(\theta) </math> provides the exact reparameterization needed to express that path in Fisher–Rao arclength. This provides a concrete example in which exponential-family straightness and Fisher–Rao Levi-Civita straightness describe the same geometric image while using different natural parameters. == 9. Discussion, Limitations, and Open Problems == The preceding sections developed normalized probability dilation as a common framework for positive transformation followed by normalization, and then considered a specific geometric question for exponential dilation. This section summarizes the mathematical interpretation of those results, identifies their limitations, and outlines several directions requiring further investigation. === 9.1 Scope of the framework === The normalized-dilation framework contains the basic operation :'''positive transformation → normalization → probability state'''. In finite dimensions this includes :<math> p \longmapsto \frac{Dp} {\mathbf{1}^{\mathsf{T}}Dp} </math> and :<math> p \longmapsto \frac{Mp} {\mathbf{1}^{\mathsf{T}}Mp}. </math> For probability measures it includes :<math> dP \longmapsto \frac{D\,dP} {\int_XD\,dP}. </math> These operations overlap substantially with established mathematical constructions. Accordingly, the value of the framework should not be judged by whether transformation followed by normalization is itself new. Rather, its usefulness depends on whether a common formulation clarifies relationships among existing constructions, suggests useful questions, or leads to additional mathematical results. === 9.2 Established mathematics and the PDT formulation === Several central components of the paper belong directly to established theory. These include: * normalized weighted probability measures; * Radon–Nikodym change of measure; * exponential tilting; * exponential families; * positive matrix iteration; * Perron–Frobenius theory; * normalized power iteration; * Markov operators; * replicator-type equations; * Fisher information; * Fisher–Rao geometry; * the square-root representation of the probability simplex. The PDT formulation does not replace these theories. Instead, it organizes them around a recurring transformation-and-normalization structure. This distinction is important when assessing both the mathematical contribution and the appropriate claims of the paper. === 9.3 The geometric characterization === The principal result developed in Section 7 concerns the exponential dilation family :<math> p_i(\theta) = \frac{ p_i^{(0)}e^{\theta\phi_i} } { \sum_jp_j^{(0)}e^{\theta\phi_j} }. </math> Under the finite-dimensional strict-positivity assumptions used in the theorem, the image of this trajectory is contained in a Fisher–Rao Levi-Civita geodesic if and only if the generator <math>\phi</math> assumes at most two distinct values. The proof uses the square-root representation :<math> q_i(\theta) = 2\sqrt{p_i(\theta)} </math> and the unnormalized trajectory :<math> r(\theta) = \sum_{\ell=1}^{m} e^{a_{\ell}\theta/2}u_{\ell}. </math> The Vandermonde argument shows that if the generator assumes exactly <math>m</math> distinct active values, then :<math> \dim \operatorname{span} \{r(\theta):\theta\in\mathbb{R}\} = m. </math> A Fisher–Rao geodesic requires the square-root image to lie in a two-dimensional linear subspace through the origin. This yields the two-level characterization. === 9.4 What the theorem does not claim === Theorem 1 should be interpreted narrowly. It does not claim that exponential trajectories with three or more generator levels are geometrically uninteresting. It does not claim that such trajectories cease to be e-geodesics. It does not claim that the exponential parameter <math>\theta</math> is an affine Fisher–Rao geodesic parameter in the two-level case. It does not characterize arbitrary curves on the probability simplex. It does not characterize arbitrary state-dependent dilation fields. It does not establish an analogous result for infinite-dimensional statistical manifolds. The theorem concerns a specific finite-dimensional exponential family and the coincidence of its trajectory image with a Fisher–Rao Levi-Civita geodesic. === 9.5 Boundary behavior === The main theorem assumes :<math> p_i^{(0)}>0 </math> for every state. This places the trajectory in the interior of the probability simplex for every finite <math>\theta</math>. The square-root representation remains meaningful at the boundary, but the usual coordinate expression of the Fisher–Rao metric becomes singular when one or more probabilities vanish. Boundary points therefore require separate care. In the two-level case, the exponential trajectory approaches boundary distributions only asymptotically as :<math> |\theta|\rightarrow\infty. </math> A systematic treatment of trajectories beginning on, reaching, or moving between lower-dimensional faces of the simplex is outside the scope of the present paper. === 9.6 Zero initial probabilities === If some initial components satisfy :<math> p_i^{(0)}=0, </math> then exponential dilation preserves those zeros: :<math> p_i(\theta)=0. </math> The effective trajectory then lies in a lower-dimensional face of the simplex. In such a case, the number of relevant generator levels should be counted only among states with positive initial probability. The theorem can therefore be expected to admit a support-restricted formulation, but the present statement uses strict positivity to avoid unnecessary boundary qualifications. === 9.7 Fixed versus state-dependent dilation === Much of the analysis in this paper concerns a fixed positive matrix, a fixed weighting field, or a fixed generator. More general transformations may depend on the current probability state: :<math> p^{(k+1)} = \frac{ M(p^{(k)})p^{(k)} } { \mathbf{1}^{\mathsf{T}} M(p^{(k)})p^{(k)} }. </math> Similarly, a continuous generator may depend on <math>p</math> or on the evolution parameter. Such systems may display behavior not reducible to ordinary fixed-matrix spectral theory or fixed-generator exponential tilting. Their study would require tools from nonlinear dynamical systems, nonlinear positive operators, differential geometry, and related fields. No general convergence claim for state-dependent dilation is made here. === 9.8 Entropy === Normalized dilation can either increase or decrease Shannon entropy depending on the transformation and the initial state. For :<math> H(p) = -\sum_i p_i\log p_i, </math> there is no general principle requiring :<math> H(T_M(p)) \leq H(p) </math> or the reverse inequality for arbitrary nonnegative matrices. In repeated diagonal dilation with a unique dominant weight, probability concentration generally drives the limiting distribution toward a point mass and therefore toward zero Shannon entropy. However, this special concentration behavior should not be generalized to arbitrary matrix or state-dependent dilation. A useful open problem is to identify classes of dilation operators for which entropy, relative entropy, or another information functional is monotone. === 9.9 Projective metrics and contraction === Because normalized positive transformations are invariant under positive scalar multiplication, projective geometry provides a natural language for their analysis. For positive matrices and positive operators, Hilbert-type projective metrics and contraction theorems may provide convergence estimates stronger than those obtained from elementary normalization arguments. A systematic comparison between normalized matrix dilation and established projective contraction theory would clarify which convergence properties follow immediately from known results and which, if any, require additional hypotheses. This is an important direction for further study. === 9.10 Curvature beyond the two-level case === Theorem 1 distinguishes exactly between the two-level geodesic case and trajectories generated by three or more distinct levels. The next geometric question is quantitative rather than binary. For :<math> m\geq3, </math> one may ask how far the exponential trajectory departs from a Fisher–Rao Levi-Civita geodesic. Possible quantities include: * geodesic curvature; * covariant acceleration; * deviation from the great-circle plane; * Fisher–Rao distance from an appropriate comparison geodesic; * integrated curvature along the trajectory. Such quantities could provide a graded measure of geometric departure rather than the yes-or-no characterization of Theorem 1. === 9.11 Relation between generator levels and geometric dimension === Corollary 1 gives :<math> \dim \operatorname{span} \{r(\theta)\} = m, </math> where <math>m</math> is the number of distinct active generator values. This suggests a direct relationship between the algebraic complexity of the generator and the linear dimension required to contain its square-root trajectory. The two-level Fisher–Rao result is the first consequence of this dimensional relation. Further work could investigate whether analogous dimension-counting principles arise for multiparameter exponential families or other normalized positive flows. === 9.12 Multiparameter exponential dilation === A natural extension is :<math> p_i(\theta_1,\ldots,\theta_k) = \frac{ p_i^{(0)} \exp \left( \sum_{r=1}^{k}\theta_r\phi_i^{(r)} \right) } { Z(\theta_1,\ldots,\theta_k) }. </math> This defines a multiparameter exponential family. Questions then arise concerning the dimension and curvature of its square-root image and the conditions under which particular parameter curves or submanifolds are totally geodesic with respect to the Fisher–Rao Levi-Civita connection. The one-parameter theorem in this paper does not answer these questions. === 9.13 Infinite-dimensional extension === The measure-theoretic formulation suggests possible extensions beyond finite probability simplices. For a reference probability measure <math>P_0</math>, consider :<math> dP_{\theta} = \frac{ e^{\theta\phi} } { \int e^{\theta\phi}\,dP_0 } dP_0. </math> This is the natural measure-theoretic analogue of finite exponential dilation. An infinite-dimensional version of the geodesic characterization would require careful specification of the statistical manifold, admissible tangent spaces, regularity conditions, and the appropriate Fisher–Rao geometry. The finite-dimensional Vandermonde argument does not by itself establish such a result. === 9.14 Numerical verification === The analytical results in Sections 7 and 8 can be supplemented by numerical experiments. For two generator levels, numerical calculations should verify that the square-root trajectory remains in a fixed two-dimensional plane to numerical precision. For three or more distinct levels, rank calculations can verify the predicted increase in the dimension of the trajectory span. Numerical differentiation can also compare :<math> \left| \frac{ds}{d\theta} \right| </math> with :<math> \sqrt{ \operatorname{Var}_{p(\theta)}(\phi) }. </math> Such computations do not replace proof, but they provide useful checks against algebraic or implementation errors. === 9.15 Literature and priority limitations === The mathematical ingredients used in this paper draw from established areas with extensive literatures. A literature search performed during development has identified substantial prior theory surrounding exponential families, Fisher–Rao geometry, positive operators, normalized matrix iteration, replicator dynamics, and related constructions. At the present draft stage, the exact two-level characterization proved in Section 7 has not been identified by the author in the literature in the same form. This absence should not be interpreted as proof of novelty. Equivalent results may exist under different terminology or as consequences of more general theorems. Accordingly, no claim of historical priority is made. Further literature review and expert scrutiny are required before any stronger novelty statement would be appropriate. === 9.16 Open problems === The framework suggests several specific open questions: # Can the finite-dimensional characterization be formulated cleanly for probability vectors with restricted support? # Is there an established information-geometric theorem equivalent to the two-level characterization? # What is the Fisher–Rao geodesic curvature of an exponential dilation trajectory with three distinct generator levels? # Can that curvature be expressed directly in terms of moments or cumulants of the generator <math>\phi</math>? # Which normalized matrix transformations are contractions in a natural projective or information-geometric metric? # Under what conditions is Shannon entropy monotone under repeated dilation? # What aspects of the framework survive for nonlinear state-dependent operators? # Is there a useful infinite-dimensional analogue of the generator-level dimension result? # How does the characterization generalize to multiparameter exponential families? These questions provide possible directions for extending the present work while maintaining a clear distinction between established theory and additional results. === 9.17 Summary of the discussion === The normalized-dilation viewpoint provides a common structural language for several familiar probability transformations. Its mathematical usefulness depends on what can be learned from that organization rather than on the normalization operation itself. Within the finite-dimensional exponential setting, the Fisher–Rao analysis leads to a precise characterization: the exponential trajectory has a Fisher–Rao geodesic image exactly in the one-level or two-level cases under the stated assumptions. The two-level case additionally admits an explicit Fisher–Rao arclength parameterization. These results motivate further study of curvature, dimensional structure, nonlinear dilation, and measure-theoretic extensions while leaving their broader significance open to mathematical evaluation. == 10. Conclusion == This paper has developed '''normalized probability dilation''' as a common framework for probability transformations having the form :'''positive transformation → normalization → probability state'''. In finite dimensions, the framework includes diagonal reweighting :<math> p_i' = \frac{d_ip_i} {\sum_jd_jp_j}, </math> and normalized nonnegative matrix transformations :<math> T_M(p) = \frac{Mp} {\mathbf{1}^{\mathsf{T}}Mp}. </math> At the level of probability measures, the corresponding construction is :<math> dP_D = \frac{D\,dP} {\int_XD\,dP}. </math> These constructions have direct relationships with established mathematics, including change of measure, exponential tilting, positive matrix theory, Perron–Frobenius theory, normalized power iteration, Markov operators, replicator-type dynamics, Feynman–Kac constructions, exponential families, and Fisher–Rao information geometry. The purpose of the PDT framework is therefore not to claim these established operations as new, but to place them within a common transformation-and-normalization language and to use that organization to formulate precise mathematical questions. === 10.1 Principal geometric result === For the finite-dimensional exponential dilation family :<math> p_i(\theta) = \frac{ p_i^{(0)}e^{\theta\phi_i} } { \sum_jp_j^{(0)}e^{\theta\phi_j} }, </math> the square-root representation :<math> q_i(\theta) = 2\sqrt{p_i(\theta)} </math> converts the Fisher–Rao geometry of the probability simplex into spherical geometry. Grouping equal generator values gives the unnormalized square-root trajectory :<math> r(\theta) = \sum_{\ell=1}^{m} e^{a_{\ell}\theta/2}u_{\ell}, </math> where <math>a_1,\ldots,a_m</math> are the distinct generator levels. The Vandermonde argument developed in Section 7 gives :<math> \dim \operatorname{span} \{r(\theta):\theta\in\mathbb{R}\} = m. </math> Because a spherical great circle lies in a two-dimensional linear subspace through the origin, the exponential dilation trajectory has a Fisher–Rao Levi-Civita geodesic image if and only if :<math> m\leq2. </math> Thus, under the finite-dimensional strict-positivity assumptions of the theorem, the generator must assume at most two distinct values. === 10.2 Two-level arclength === For the nondegenerate two-level case, the trajectory can be written in square-root coordinates as :<math> q(\theta) = 2 \left( \cos\alpha(\theta)\widehat{u} + \sin\alpha(\theta)\widehat{v} \right), </math> where :<math> \alpha(\theta) = \arctan \left( \sqrt{ \frac{1-r_0}{r_0} } e^{(b-a)\theta/2} \right). </math> A signed Fisher–Rao arclength coordinate therefore satisfies :<math> s(\theta)-s(\theta_0) = 2 \left( \alpha(\theta)-\alpha(\theta_0) \right). </math> This makes explicit the distinction between the exponential parameter <math>\theta</math> and Fisher–Rao arclength. The exponential trajectory may follow the correct Fisher–Rao geodesic image without moving along it at constant Fisher–Rao speed. === 10.3 Final perspective === The results illustrate a broader methodological point. A common mathematical framework is most useful when it does more than rename existing constructions. It should clarify relationships among established theories, expose structural distinctions, or lead to questions that can be answered precisely. For normalized probability dilation, the distinction between exponential-family straightness and Fisher–Rao Levi-Civita straightness provides one such question. The resulting two-level characterization and arclength formula provide a concrete starting point for further investigation. Important directions remain open, including curvature of multilevel exponential trajectories, projective contraction properties, entropy conditions, nonlinear state-dependent dilation, multiparameter families, and possible infinite-dimensional extensions. The present manuscript should therefore be regarded as a mathematical framework and initial geometric analysis rather than a completed general theory. The characterization developed here remains subject to further literature review, independent proof checking, and external mathematical evaluation before any claim of historical priority or novelty is made. == 11. Historical Development and Relationship to Probability Dilation Theory == The mathematical framework developed in this paper arose from a broader exploratory project now called '''Probability Dilation Theory (PDT)'''. The present paper should be understood as a mathematical development within that project rather than as a continuation of its earlier physical interpretations. === 11.1 Early geometric-probability motivation === The initial motivation arose from geometric probability, particularly the observation that geometric information can sometimes be inferred from repeated probabilistic sampling. Buffon-type experiments provided an intuitive starting point because they connect a random sampling procedure with geometric quantities through measurable intersection probabilities. Early exploratory work investigated whether ratios derived from such probability experiments might provide a useful language for comparing geometric or scaling effects. These investigations were heuristic and preceded the measure-theoretic formulation developed later. They should therefore be regarded as historical motivation rather than as mathematical evidence for the results proved in this paper. === 11.2 Einstein–Buffon stage === An early version of the project was informally described as the '''Einstein Buffon Process'''. At that stage, the emphasis was on possible analogies between geometric probability, scaling, and physical transformations. The terminology reflected the historical route by which the problem was approached rather than a claim of a new physical theory. As the work developed, it became increasingly clear that the mathematically tractable object was not the proposed physical analogy itself, but the transformation of probability distributions produced by positive weighting followed by normalization. This shift changed the central question from :'''Can a probabilistic sampling ratio represent a physical scaling effect?''' to the more mathematical question :'''What properties follow from normalized positive transformations of probability measures?''' === 11.3 Transition to probability-measure dilation === The resulting abstraction led to the transformation :<math> dP_D = \frac{D\,dP} {\int_XD\,dP}, </math> where <math>P</math> is a probability measure and <math>D</math> is a positive or nonnegative weighting field satisfying the required normalization conditions. This formulation separated the mathematical operation from any particular physical interpretation. It also made clear that the construction has direct relationships with established change-of-measure theory, weighted probability measures, exponential tilting, and related probabilistic methods. The term '''Probability Dilation Theory''' was subsequently adopted for the broader research framework concerned with such normalized probability transformations and their iteration. === 11.4 Development of matrix dilation operators === The finite-dimensional version of the framework naturally suggested replacing scalar componentwise weights by matrix transformations. For a nonnegative matrix <math>M</math>, this gives :<math> T_M(p) = \frac{Mp} {\mathbf{1}^{\mathsf{T}}Mp}. </math> This matrix formulation made the relationship with positive linear algebra substantially clearer. Diagonal dilation became a special case, while off-diagonal matrix elements allowed coupling among probability components. Analysis of fixed points and repeated iteration then connected the framework with eigenvectors, Perron–Frobenius theory, normalized power iteration, and projective dynamics. This stage was important in clarifying which properties of matrix dilation follow from established mathematics and which questions require additional analysis. === 11.5 Development toward information geometry === A further simplification occurs for exponential dilation fields. In finite dimensions, :<math> p_i(\theta) = \frac{ p_i^{(0)}e^{\theta\phi_i} } { \sum_jp_j^{(0)}e^{\theta\phi_j} }. </math> This expression identifies the trajectory directly with a one-parameter exponential family. The connection shifted the investigation toward information geometry. In particular, it raised a precise question that was not apparent in the original geometric-probability formulation: :''When is an exponential dilation trajectory simultaneously an e-geodesic and, up to reparameterization, a Fisher–Rao Levi-Civita geodesic?'' The analysis of that question led to the generator-level characterization proved in Section 7. === 11.6 Conceptual progression === The historical development of the project can therefore be summarized schematically as: :'''geometric probability and Buffon-type sampling''' :'''↓''' :'''exploratory scaling and Einstein–Buffon analogies''' :'''↓''' :'''positive probability reweighting''' :'''↓''' :'''normalized probability-measure transformation''' :'''↓''' :'''matrix dilation operators''' :'''↓''' :'''exponential dilation''' :'''↓''' :'''Fisher–Rao and information-geometric analysis''' This progression should not be interpreted as a derivation of the later mathematics from the earlier physical analogies. Rather, the early investigations provided motivation from which a progressively more abstract and mathematically conventional problem emerged. === 11.7 Relationship to the broader PDT project === The present manuscript focuses on only one part of the broader Probability Dilation Theory research program. The wider PDT project investigates normalized positive transformations of probability measures, their composition, iteration, fixed points, matrix representations, and possible geometric properties. The present paper narrows that scope substantially. Its primary purpose is to: * define a unified normalized-dilation notation; * identify its relationships with established mathematics; * develop the exponential-dilation formulation; * analyze its Fisher–Rao geometry; * prove the finite-dimensional generator-level characterization; * derive the explicit two-level Fisher–Rao arclength formula. Other exploratory PDT topics are not required for the mathematical results of this paper. In particular, speculative applications to physics or cosmology should be regarded as separate research questions and are not assumptions of the theorem proved here. === 11.8 Research provenance and status === The broader PDT project has been developed openly through successive research notes, computational experiments, and Wikiversity pages. Earlier formulations document the evolution of the terminology and ideas, while the present manuscript represents an attempt to isolate a cleaner mathematical core suitable for independent examination. Historical provenance does not establish mathematical novelty. The results presented in this manuscript must instead be evaluated through proof checking, comparison with the existing literature, and independent mathematical review. Accordingly, the earlier stages of the PDT project are relevant to the history of the work but are not used as authority for the mathematical claims of this paper. === 11.9 Relationship between the manuscript and the research project === The distinction between the two levels of presentation is therefore: :'''Probability Dilation Theory (PDT)''' — the broader evolving research framework. :'''This manuscript''' — a focused mathematical investigation of normalized dilation, exponential trajectories, and their Fisher–Rao geometry. The broader project may continue to develop additional models and conjectures independently of this paper. Conversely, the mathematical results of this paper can be assessed without accepting any speculative interpretation associated with earlier stages of PDT. This separation is intended to make the principal definitions, theorem, proof, and limitations accessible to independent mathematical scrutiny. == Relationship to the Probability Dilation Theory project == This manuscript is part of the broader [[Probability Dilation Theory]] research project on Wikiversity. Technical and exploratory material related to the manuscript is developed on associated PDT subpages, including: * [[Probability Dilation Theory/Measure-Theoretic Foundations|Measure-Theoretic Foundations]] * [[Probability Dilation Theory/Matrix Dilation Operators|Matrix Dilation Operators]] * [[Probability Dilation Theory/Dilation Vector Field|Dilation Vector Field]] * [[Probability Dilation Theory/Dilation Flows|Dilation Flows]] * [[Probability Dilation Theory/Convergence and Fixed Points|Convergence and Fixed Points]] * [[Probability Dilation Theory/Fisher Geometry and Dilation Flows|Fisher Geometry and Dilation Flows]] The present page is intended to develop a concise, standalone manuscript rather than reproduce the complete exploratory PDT project. == Draft status and research note == This manuscript is a work in progress. Some constructions discussed in the paper have direct counterparts in established mathematical literature. These relationships are identified explicitly wherever possible. Results developed specifically within the present formulation are being subjected to continuing literature review, proof checking, numerical verification, and independent mathematical scrutiny before any claim of novelty is made. Readers are encouraged to identify relevant prior literature, mathematical errors, counterexamples, alternative proofs, or useful extensions. == See also == * [[Probability Dilation Theory]] * [[Probability Dilation Theory/Matrix Dilation Operators]] * [[Probability Dilation Theory/Measure-Theoretic Foundations]] * [[Probability Dilation Theory/Fisher Geometry and Dilation Flows]] == Copyright and licensing == Text and original figures © Howard Richardson. Licensed under the [https://creativecommons.org/licenses/by/4.0/ Creative Commons Attribution 4.0 International License (CC BY 4.0)]. Reuse permitted with attribution. mg5xawa08d1vaul0btfsp451vzzuyur 2823789 2823788 2026-08-21T01:56:23Z Howie2024 2995240 /* 11.9 Relationship between the manuscript and the research project */ Inserting references. 2823789 wikitext text/x-wiki {{Research project}} '''Research manuscript — Draft Version 1.0''' ''This page develops a standalone research manuscript arising from the [[Probability Dilation Theory]] project. It is a work in progress and should not be regarded as a peer-reviewed publication.'' = Normalized Probability Dilation: A Unified Framework and Its Fisher–Rao Geometry = '''Howard Richardson''' ''Draft Version 1.0 — August 2026'' == Abstract == This paper develops a unified framework for normalized positive transformations of probability distributions, referred to here as '''Probability Dilation Theory (PDT)'''. The central construction consists of applying a positive transformation to a probability state and subsequently renormalizing the result. In finite dimensions this includes diagonal reweighting, :<math> p_i'= \frac{d_i p_i} {\sum_j d_jp_j}, </math> and the matrix transformation :<math> T_M(p)= \frac{Mp} {\mathbf{1}^{\mathsf T}Mp}, </math> for suitable nonnegative matrices <math>M</math>. A corresponding measure-theoretic formulation is :<math> P_D(A)= \frac{\int_A D\,dP} {\int_X D\,dP}. </math> These constructions are compared explicitly with established mathematical structures including change of measure, normalized positive operators, Perron–Frobenius iteration, Markov operators, replicator-type dynamics, and normalized Feynman–Kac transformations. The purpose of the framework is therefore not to claim these established constructions as new, but to investigate their common dilation-normalization structure and the geometry of the resulting probability trajectories. Particular attention is given to the exponential dilation family :<math> p_i(\theta)= \frac{p_i^{(0)}e^{\theta\phi_i}} {\sum_j p_j^{(0)}e^{\theta\phi_j}}. </math> Using the square-root representation of the Fisher–Rao simplex, we establish that, under finite-dimensional strict-positivity assumptions, the image of this exponential-dilation trajectory is contained in a Fisher–Rao Levi-Civita geodesic, up to reparameterization, if and only if the generator <math>\phi</math> assumes at most two distinct values. An explicit Fisher–Rao arclength parameterization is then obtained for the nondegenerate two-level case. The framework provides a common language for normalized probability transformations while separating results inherited from established theory from geometric properties arising from the particular dilation formulation. == 1. Introduction == Probability distributions are frequently transformed by operations having a common mathematical structure: nonnegative weights are modified by a positive transformation and subsequently normalized so that total probability remains unity. Such constructions occur in numerous areas of probability, statistics, dynamical systems, numerical linear algebra, and mathematical physics. The simplest finite-dimensional example takes a probability vector :<math> p=(p_1,\ldots,p_n)^{\mathsf T}, \qquad p_i\geq 0, \qquad \sum_{i=1}^{n}p_i=1, </math> assigns positive weights <math>d_i</math>, and defines :<math> p_i'= \frac{d_i p_i} {\sum_{j=1}^{n}d_jp_j}. </math> The transformation changes the relative probability assigned to individual states while normalization returns the resulting vector to the probability simplex. This paper uses the term '''probability dilation''' for this general transformation-and-normalization structure and examines a hierarchy of related constructions. In finite dimensions, diagonal dilation extends naturally to the action of a nonnegative matrix, :<math> T_M(p)= \frac{Mp} {\mathbf{1}^{\mathsf T}Mp}, </math> whenever the denominator is positive. At the level of probability measures, multiplication by a positive measurable function <math>D</math> gives :<math> P_D(A)= \frac{\displaystyle\int_A D(x)\,dP(x)} {\displaystyle\int_X D(x)\,dP(x)}. </math> These expressions have substantial connections with existing mathematics. Normalized matrix iteration is closely related to the power method and Perron–Frobenius theory; positive weighting of measures belongs to established change-of-measure constructions; stochastic matrices provide the familiar Markov special case; and normalized potential-weighted measures occur in Feynman–Kac models. Accordingly, the objective of PDT as developed here is '''not''' to rename these established mathematical theories or to assert novelty for normalization itself. Instead, the objective is to examine them through the common structural sequence :<math> \text{positive transformation} \longrightarrow \text{normalization} \longrightarrow \text{iteration} \longrightarrow \text{probability dynamics} \longrightarrow \text{geometry}. </math> This viewpoint leads naturally to questions concerning fixed points, convergence, entropy, state-dependent transformations, and the geometry of trajectories on the probability simplex. === 1.1 Exponential dilation === A particularly useful example is obtained from exponential dilation. Given an initial strictly positive probability vector <math>p^{(0)}</math> and a real-valued generator <math>\phi</math>, define :<math> p_i(\theta)= \frac{p_i^{(0)}e^{\theta\phi_i}} {Z(\theta)}, </math> where :<math> Z(\theta)= \sum_j p_j^{(0)}e^{\theta\phi_j}. </math> This is an exponential-family construction and therefore belongs to well-established information geometry. The question considered here is more specific: :''When is this exponential trajectory also a Levi-Civita geodesic of the Fisher–Rao metric?'' The Fisher–Rao geometry of a finite probability simplex admits a square-root representation on a sphere. Under the mapping :<math> p\longmapsto 2(\sqrt{p_1},\ldots,\sqrt{p_n}), </math> Fisher–Rao geodesics correspond to spherical great-circle arcs. This representation permits a direct characterization of exponential dilation trajectories that are simultaneously Fisher–Rao geodesic. === 1.2 Principal geometric result === The principal geometric result developed below is that, for a strictly positive finite probability vector, an exponential dilation trajectory lies on a Fisher–Rao geodesic, up to reparameterization, precisely when its generator assumes no more than two distinct values. The proof reduces the problem to the dimension of the linear span generated by distinct exponential rates and uses a Vandermonde argument for the converse. The resulting two-level trajectory also admits an explicit Fisher–Rao arclength parameterization. At the present draft stage, this characterization is treated conservatively. Its constituent mathematical ingredients are established results from information geometry and linear algebra. The exact characterization developed here remains subject to further literature review and independent mathematical scrutiny. === 1.3 Organization of the paper === The remainder of the paper is organized as follows: * '''Section 2''' introduces the normalized-dilation framework and notation. * '''Section 3''' develops diagonal and matrix formulations. * '''Section 4''' develops the measure-theoretic formulation. * '''Section 5''' compares the framework explicitly with established mathematics. * '''Section 6''' introduces exponential dilation and its information-geometric representation. * '''Section 7''' states and proves the Fisher–Rao geodesic characterization theorem. * '''Section 8''' derives the two-level Fisher–Rao arclength corollary and illustrative examples. * '''Section 9''' discusses limitations, possible extensions, and open problems. * '''Section 10''' summarizes the principal conclusions. == 2. Normalized-Dilation Framework == This section introduces the common mathematical structure used throughout the paper. The essential operation consists of applying a positive transformation to a probability state and then normalizing the transformed object so that it again represents a probability distribution. === 2.1 Probability simplex === For a finite state space with <math>n</math> states, define the probability simplex :<math> \Delta^{n-1} = \left\{ p\in\mathbb{R}^{n}: p_i\geq 0,\; \sum_{i=1}^{n}p_i=1 \right\}. </math> A probability state is represented by a column vector :<math> p= (p_1,\ldots,p_n)^{\mathsf{T}} \in\Delta^{n-1}. </math> Its components satisfy :<math> p_i\geq 0 </math> and :<math> \mathbf{1}^{\mathsf{T}}p=1, </math> where :<math> \mathbf{1} = (1,\ldots,1)^{\mathsf{T}}. </math> The interior of the simplex is :<math> \Delta_{+}^{n-1} = \left\{ p\in\Delta^{n-1}:p_i>0 \text{ for all }i \right\}. </math> The distinction between the simplex and its interior becomes important later when Fisher–Rao geometry is considered. === 2.2 Positive transformations === Let <math>\mathcal{L}</math> denote a transformation acting on probability states such that :<math> p\geq 0 \quad\Longrightarrow\quad \mathcal{L}(p)\geq 0. </math> The transformed object <math>\mathcal{L}(p)</math> need not itself be normalized. Define its total mass by :<math> \mathcal{N}[\mathcal{L}(p)] = \mathbf{1}^{\mathsf{T}}\mathcal{L}(p). </math> Whenever :<math> 0< \mathcal{N}[\mathcal{L}(p)] < \infty, </math> the normalized transformation is defined by :<math> \mathcal{T}_{\mathcal{L}}(p) = \frac{\mathcal{L}(p)} {\mathcal{N}[\mathcal{L}(p)]}. </math> Equivalently, in the finite-dimensional setting, :<math> \mathcal{T}_{\mathcal{L}}(p) = \frac{\mathcal{L}(p)} {\mathbf{1}^{\mathsf{T}}\mathcal{L}(p)}. </math> By construction, :<math> \mathbf{1}^{\mathsf{T}} \mathcal{T}_{\mathcal{L}}(p) = 1, </math> so :<math> \mathcal{T}_{\mathcal{L}}(p) \in \Delta^{n-1}. </math> This positive-transformation-plus-normalization operation is the basic structure referred to in this paper as '''normalized probability dilation'''. === 2.3 Normalization as projectivization === An immediate property of the normalized transformation is invariance under multiplication by a positive scalar. If <math>c>0</math>, then :<math> \frac{c\mathcal{L}(p)} {\mathbf{1}^{\mathsf{T}}c\mathcal{L}(p)} = \frac{\mathcal{L}(p)} {\mathbf{1}^{\mathsf{T}}\mathcal{L}(p)}. </math> Hence :<math> \mathcal{T}_{c\mathcal{L}}(p) = \mathcal{T}_{\mathcal{L}}(p). </math> The normalized transformation therefore depends on the relative components of <math>\mathcal{L}(p)</math>, rather than on its overall positive scale. This projective feature connects normalized dilation with established theories of positive operators and projective dynamics. No claim of novelty is attached to the normalization or projectivization operation itself. === 2.4 Diagonal dilation === Let :<math> D= \operatorname{diag}(d_1,\ldots,d_n), \qquad d_i>0. </math> Applying <math>D</math> to <math>p</math> gives :<math> Dp= (d_1p_1,\ldots,d_np_n)^{\mathsf{T}}. </math> Normalization produces :<math> T_D(p) = \frac{Dp} {\mathbf{1}^{\mathsf{T}}Dp}. </math> Componentwise, :<math> T_D(p)_i = \frac{d_ip_i} {\sum_{j=1}^{n}d_jp_j}. </math> This is the basic finite-dimensional dilation operation from which the broader PDT formulation developed. The factors <math>d_i</math> alter the relative weights of the probability states, while the denominator restores unit total probability. === 2.5 Matrix dilation === The diagonal transformation can be generalized to a nonnegative matrix :<math> M\in\mathbb{R}^{n\times n}, \qquad M_{ij}\geq 0. </math> For any probability vector <math>p</math> satisfying :<math> \mathbf{1}^{\mathsf{T}}Mp>0, </math> define :<math> T_M(p) = \frac{Mp} {\mathbf{1}^{\mathsf{T}}Mp}. </math> The diagonal case is recovered when :<math> M=D. </math> Off-diagonal entries permit components of the input probability vector to contribute to different output components before normalization. The matrix formulation therefore extends independent componentwise reweighting to coupled positive transformations. The mathematical behavior of this construction is closely related to established positive-matrix theory, normalized power iteration, and Perron–Frobenius theory. These relationships are discussed explicitly in Section 5. === 2.6 Measure-theoretic dilation === The same normalization principle extends naturally from finite probability vectors to probability measures. Let <math>(X,\mathcal{F},P)</math> be a probability space, and let :<math> D:X\rightarrow[0,\infty) </math> be measurable with :<math> 0< \int_X D(x)\,dP(x) < \infty. </math> Define a new probability measure <math>P_D</math> by :<math> P_D(A) = \frac{\displaystyle\int_A D(x)\,dP(x)} {\displaystyle\int_X D(x)\,dP(x)}, \qquad A\in\mathcal{F}. </math> Equivalently, the Radon–Nikodym derivative of <math>P_D</math> with respect to <math>P</math> is :<math> \frac{dP_D}{dP} = \frac{D} {\displaystyle\int_X D\,dP}. </math> Thus the finite-dimensional rule :<math> p_i \longmapsto \frac{d_ip_i} {\sum_jd_jp_j} </math> and the measure-theoretic rule :<math> dP \longmapsto \frac{D\,dP} {\int_XD\,dP} </math> share the same normalized positive-reweighting structure. This construction has direct connections with established change-of-measure and weighted-measure theory. The PDT terminology is used here as an organizing framework rather than as a claim that normalized change of measure is itself new. === 2.7 Iterated dilation === A normalized dilation operator can be iterated. Given an initial state :<math> p^{(0)}\in\Delta^{n-1}, </math> define :<math> p^{(k+1)} = \mathcal{T}_{\mathcal{L}}\left(p^{(k)}\right). </math> This generates an orbit :<math> p^{(0)} \longmapsto p^{(1)} \longmapsto p^{(2)} \longmapsto \cdots </math> on the probability simplex. For a fixed matrix <math>M</math>, :<math> p^{(k+1)} = \frac{Mp^{(k)}} {\mathbf{1}^{\mathsf{T}}Mp^{(k)}}. </math> When all required denominators are positive, repeated normalization gives :<math> p^{(k)} = \frac{M^k p^{(0)}} {\mathbf{1}^{\mathsf{T}}M^k p^{(0)}}. </math> The long-term behavior of this iteration is governed in important cases by established spectral and Perron–Frobenius theory. More general formulations may allow the transformation itself to depend on the iteration index or the current probability state, for example :<math> p^{(k+1)} = \frac{M_kp^{(k)}} {\mathbf{1}^{\mathsf{T}}M_kp^{(k)}} </math> or :<math> p^{(k+1)} = \frac{M(p^{(k)})p^{(k)}} {\mathbf{1}^{\mathsf{T}}M(p^{(k)})p^{(k)}}. </math> These state-dependent and iteration-dependent forms are treated as possible extensions rather than necessary components of the basic framework. === 2.8 Hierarchy of normalized dilation === The constructions above can be summarized by the following hierarchy: :'''diagonal reweighting → matrix transformation → positive operator → measure transformation''' At each level the essential operation is: :'''positive transformation + normalization''' The framework is deliberately broad. Its purpose is not to imply that all normalized positive transformations constitute a new mathematical theory, but to provide a common notation and viewpoint from which their dynamics and geometry can be compared. The following sections specialize this framework before examining its relationship to established mathematical constructions. == 3. Finite-Dimensional and Matrix Dilation == This section develops the finite-dimensional forms of normalized probability dilation in greater detail. The emphasis is on the relationship between diagonal reweighting and nonnegative matrix transformations, together with the basic structural properties required later in the paper. === 3.1 Finite probability states === Let :<math> p=(p_1,\ldots,p_n)^{\mathsf{T}} \in\Delta^{n-1}. </math> A positive weighting vector is written :<math> d=(d_1,\ldots,d_n)^{\mathsf{T}}, \qquad d_i>0. </math> The associated diagonal matrix is :<math> D= \operatorname{diag}(d_1,\ldots,d_n). </math> Applying the weighting gives :<math> Dp= (d_1p_1,\ldots,d_np_n)^{\mathsf{T}}. </math> Its total mass is :<math> Z(p,D) = \mathbf{1}^{\mathsf{T}}Dp = \sum_{i=1}^{n}d_ip_i. </math> Since <math>d_i>0</math> and <math>p</math> is a probability vector, :<math> Z(p,D)>0. </math> The normalized diagonal dilation operator is therefore :<math> T_D(p) = \frac{Dp}{Z(p,D)}. </math> Equivalently, :<math> T_D(p)_i = \frac{d_ip_i} {\sum_{j=1}^{n}d_jp_j}. </math> === 3.2 Relative probability transformation === Diagonal dilation has a simple effect on probability ratios. For any states <math>i</math> and <math>j</math> with <math>p_i>0</math> and <math>p_j>0</math>, :<math> \frac{T_D(p)_i}{T_D(p)_j} = \frac{d_i}{d_j} \frac{p_i}{p_j}. </math> Thus normalization does not alter the relative dilation introduced by the factors <math>d_i</math> and <math>d_j</math>. If :<math> d_i>d_j, </math> then the odds of state <math>i</math> relative to state <math>j</math> increase by the factor :<math> \frac{d_i}{d_j}. </math> This ratio form makes clear that diagonal dilation is fundamentally a relative reweighting operation. === 3.3 Scale invariance === Multiplying every dilation factor by the same positive constant does not change the normalized state. Let :<math> c>0. </math> Then :<math> T_{cD}(p) = \frac{cDp} {\mathbf{1}^{\mathsf{T}}cDp} = \frac{Dp} {\mathbf{1}^{\mathsf{T}}Dp} = T_D(p). </math> Therefore only the relative values of the dilation factors affect the transformed probability distribution. This scale invariance is a basic projective property of normalized positive transformations. === 3.4 Repeated diagonal dilation === Suppose the same diagonal operator <math>D</math> is applied repeatedly. Starting from <math>p^{(0)}</math>, define :<math> p^{(k+1)} = T_D(p^{(k)}). </math> Then :<math> p^{(k)} = \frac{D^k p^{(0)}} {\mathbf{1}^{\mathsf{T}}D^k p^{(0)}}. </math> Since :<math> D^k = \operatorname{diag}(d_1^k,\ldots,d_n^k), </math> the individual components are :<math> p_i^{(k)} = \frac{d_i^k p_i^{(0)}} {\sum_{j=1}^{n}d_j^k p_j^{(0)}}. </math> Consequently, for two initially positive components, :<math> \frac{p_i^{(k)}}{p_j^{(k)}} = \left(\frac{d_i}{d_j}\right)^k \frac{p_i^{(0)}}{p_j^{(0)}}. </math> This expression describes the concentration mechanism directly. If one dilation factor is strictly larger than all others and its corresponding initial probability is positive, repeated dilation concentrates probability on that state. If several states share the maximal dilation factor, probability concentrates on that maximal set while preserving the initial relative proportions within that set. This behavior is a direct consequence of normalized repeated weighting and is not specific to PDT terminology. === 3.5 General nonnegative matrix transformation === Let :<math> M=(M_{ij}) \in\mathbb{R}^{n\times n}, \qquad M_{ij}\geq0. </math> For <math>p\in\Delta^{n-1}</math>, define :<math> q=Mp. </math> Because <math>M</math> and <math>p</math> are nonnegative, :<math> q_i\geq0. </math> Whenever :<math> \mathbf{1}^{\mathsf{T}}Mp>0, </math> the normalized matrix dilation operator is :<math> T_M(p) = \frac{Mp} {\mathbf{1}^{\mathsf{T}}Mp}. </math> Its components are :<math> T_M(p)_i = \frac{\sum_{j=1}^{n}M_{ij}p_j} {\sum_{r=1}^{n}\sum_{j=1}^{n}M_{rj}p_j}. </math> By construction, :<math> \sum_{i=1}^{n}T_M(p)_i=1. </math> Hence :<math> T_M(p)\in\Delta^{n-1}. </math> === 3.6 Diagonal dilation as a special case === If :<math> M=D = \operatorname{diag}(d_1,\ldots,d_n), </math> then :<math> Mp=Dp, </math> and therefore :<math> T_M(p)=T_D(p). </math> Diagonal dilation is thus a special case of normalized matrix dilation. The distinction is structural. For a diagonal matrix, each output component depends only on the corresponding input component: :<math> (Dp)_i=d_ip_i. </math> For a general matrix, :<math> (Mp)_i = \sum_{j=1}^{n}M_{ij}p_j, </math> so multiple input states may contribute to a single output state before normalization. This permits coupled probability evolution. === 3.7 When normalization is unnecessary === There is an important special case. Suppose <math>M</math> satisfies :<math> \mathbf{1}^{\mathsf{T}}M = \mathbf{1}^{\mathsf{T}}. </math> Then for every probability vector <math>p</math>, :<math> \mathbf{1}^{\mathsf{T}}Mp = \mathbf{1}^{\mathsf{T}}p = 1. </math> Consequently, :<math> T_M(p)=Mp. </math> With the column-vector convention used in this paper, the condition :<math> \mathbf{1}^{\mathsf{T}}M = \mathbf{1}^{\mathsf{T}} </math> means that the columns of <math>M</math> sum to one. Thus an ordinary probability-preserving linear transition is contained as a special case of the normalized matrix framework. When <math>M</math> does not preserve total mass, normalization supplies the additional step required to return <math>Mp</math> to the simplex. === 3.8 Fixed points and eigenvectors === Suppose <math>p^{*}</math> is a fixed point of the normalized matrix operator: :<math> T_M(p^{*})=p^{*}. </math> Then :<math> \frac{Mp^{*}} {\mathbf{1}^{\mathsf{T}}Mp^{*}} = p^{*}. </math> Multiplying by the denominator gives :<math> Mp^{*} = \lambda p^{*}, </math> where :<math> \lambda = \mathbf{1}^{\mathsf{T}}Mp^{*}. </math> Therefore every fixed point of the normalized matrix transformation is a nonnegative eigenvector of <math>M</math>, normalized to have unit total mass. Conversely, if <math>v\geq0</math> is a nonzero eigenvector satisfying :<math> Mv=\lambda v, \qquad \lambda>0, </math> then :<math> p^{*} = \frac{v} {\mathbf{1}^{\mathsf{T}}v} </math> is a fixed point of <math>T_M</math>. Thus normalized fixed points and positive eigenvectors are directly related. === 3.9 Repeated matrix dilation === For a fixed nonnegative matrix <math>M</math>, define :<math> p^{(k+1)} = T_M(p^{(k)}). </math> Whenever the required denominators remain positive, :<math> p^{(k)} = \frac{M^k p^{(0)}} {\mathbf{1}^{\mathsf{T}}M^k p^{(0)}}. </math> This identity follows because the scalar normalization introduced at each intermediate step cancels under the next normalization. The iteration is therefore closely related to normalized power iteration. Under suitable positivity or primitivity assumptions, Perron–Frobenius theory describes the dominant eigenvalue and positive eigenvector governing the long-term behavior. Accordingly, convergence of the fixed-matrix case should be understood primarily through established positive-matrix and spectral theory rather than as a separate PDT convergence mechanism. === 3.10 Primitive positive matrices === A particularly important case occurs when <math>M</math> is primitive; that is, some positive integer power of <math>M</math> has strictly positive entries. Perron–Frobenius theory then provides a dominant real eigenvalue :<math> \rho(M)>0 </math> with a corresponding strictly positive eigenvector <math>v</math>. After normalization, :<math> p^{*} = \frac{v} {\mathbf{1}^{\mathsf{T}}v}, </math> this eigenvector gives the distinguished interior fixed point of the normalized matrix transformation. For suitable initial probability vectors, :<math> T_M^{k}(p^{(0)}) </math> converges toward <math>p^{*}</math>. This convergence is an established consequence of Perron–Frobenius theory and normalized power iteration. Its role here is to locate matrix dilation within known mathematics. === 3.11 Interpretation of off-diagonal terms === The off-diagonal entries of <math>M</math> distinguish matrix dilation from independent diagonal reweighting. For :<math> i\neq j, </math> a term :<math> M_{ij}p_j </math> represents a contribution from input state <math>j</math> to output component <math>i</math> before normalization. The matrix therefore combines two operations: * positive redistribution or coupling through <math>M</math>; * restoration of unit total probability through normalization. This interpretation is useful for organizing the framework, but the underlying linear transformation remains standard matrix mathematics. === 3.12 Scope of the matrix formulation === The matrix formulation substantially enlarges the class of transformations expressible within the normalized-dilation notation, but that enlargement should not be confused with mathematical novelty. For a fixed matrix <math>M</math>, the central objects :<math> Mp, \qquad M^kp, \qquad \rho(M), </math> and the associated eigenvectors and convergence properties belong to established linear algebra and positive-operator theory. The role of the PDT framework is to place diagonal reweighting, matrix transformation, iteration, and later measure-theoretic and geometric constructions within a common normalized-probability notation. This distinction between '''framework''' and '''new mathematical result''' will be maintained throughout the paper. == 4. Measure-Theoretic Dilation == The finite-dimensional dilation rule extends naturally to probability measures. In this setting, componentwise multiplication by positive weights is replaced by multiplication of a probability measure by a nonnegative measurable function followed by normalization. This formulation places finite probability dilation within the standard language of measure theory and makes its relationship to change of measure explicit. === 4.1 Probability-space formulation === Let :<math> (X,\mathcal{F},P) </math> be a probability space. Let :<math> D:X\rightarrow[0,\infty) </math> be a measurable function satisfying :<math> 0< \int_X D(x)\,dP(x) < \infty. </math> Define the normalization factor :<math> Z(P,D) = \int_X D(x)\,dP(x). </math> For every measurable set :<math> A\in\mathcal{F}, </math> define :<math> P_D(A) = \frac{\displaystyle\int_A D(x)\,dP(x)} {Z(P,D)}. </math> Equivalently, :<math> P_D(A) = \frac{\displaystyle\int_A D(x)\,dP(x)} {\displaystyle\int_X D(x)\,dP(x)}. </math> The function <math>D</math> acts as a nonnegative weighting or dilation field over the probability space. === 4.2 Normalization === The transformed measure has total mass one because :<math> P_D(X) = \frac{\displaystyle\int_X D(x)\,dP(x)} {\displaystyle\int_X D(x)\,dP(x)} = 1. </math> Also, because <math>D</math> is nonnegative, :<math> P_D(A)\geq0 </math> for every <math>A\in\mathcal{F}</math>. Countable additivity follows from the countable additivity of integration with respect to <math>P</math>. Therefore <math>P_D</math> is a probability measure. === 4.3 Radon–Nikodym representation === The transformed measure <math>P_D</math> is absolutely continuous with respect to <math>P</math>. Its Radon–Nikodym derivative is :<math> \frac{dP_D}{dP}(x) = \frac{D(x)} {\displaystyle\int_X D(y)\,dP(y)}. </math> Thus normalized measure dilation can be written formally as :<math> dP_D(x) = \frac{D(x)\,dP(x)} {\displaystyle\int_X D(y)\,dP(y)}. </math> This expression makes clear that the construction is a normalized change of measure. The Radon–Nikodym framework is established measure theory. The terminology of dilation is used here to emphasize the common transformation-and-normalization structure shared with the finite-dimensional formulation. === 4.4 Scale invariance === As in the finite-dimensional case, multiplication of the dilation field by a positive constant does not change the normalized measure. Let :<math> c>0. </math> Then :<math> P_{cD}(A) = \frac{\displaystyle\int_A cD\,dP} {\displaystyle\int_X cD\,dP}. </math> The common factor cancels, giving :<math> P_{cD}(A)=P_D(A). </math> Hence the transformed probability measure depends only on the relative values of the dilation field <math>D</math>, not on its overall positive scale. === 4.5 Finite probability spaces as a special case === Consider a finite state space :<math> X=\{1,\ldots,n\}. </math> Let :<math> P(\{i\})=p_i </math> and define :<math> D(i)=d_i. </math> Then :<math> \int_X D\,dP = \sum_{j=1}^{n}d_jp_j. </math> For the singleton event <math>\{i\}</math>, :<math> P_D(\{i\}) = \frac{d_ip_i} {\sum_{j=1}^{n}d_jp_j}. </math> Thus the finite diagonal dilation rule :<math> p_i' = \frac{d_ip_i} {\sum_jd_jp_j} </math> is recovered exactly from the measure-theoretic construction. The discrete and measure-theoretic formulations are therefore instances of the same normalized positive-reweighting operation. === 4.6 Expectations under dilation === Let :<math> f:X\rightarrow\mathbb{R} </math> be measurable and integrable with respect to the transformed measure. Then :<math> \mathbb{E}_{P_D}[f] = \int_X f(x)\,dP_D(x). </math> Using the Radon–Nikodym representation, :<math> \mathbb{E}_{P_D}[f] = \frac{\displaystyle\int_X f(x)D(x)\,dP(x)} {\displaystyle\int_X D(x)\,dP(x)}. </math> Equivalently, :<math> \mathbb{E}_{P_D}[f] = \frac{\mathbb{E}_{P}[fD]} {\mathbb{E}_{P}[D]}, </math> provided the required expectations exist. This identity is a standard weighted-expectation formula and will later be useful for exponential dilation. === 4.7 Composition of dilation fields === Suppose a first dilation field <math>D_1</math> transforms <math>P</math> into <math>P_{D_1}</math>, and a second field <math>D_2</math> is then applied. The first transformation gives :<math> dP_{D_1} = \frac{D_1\,dP} {\int_XD_1\,dP}. </math> Applying <math>D_2</math> gives :<math> d(P_{D_1})_{D_2} = \frac{D_2\,dP_{D_1}} {\int_XD_2\,dP_{D_1}}. </math> Substituting the first transformation and simplifying yields :<math> d(P_{D_1})_{D_2} = \frac{D_1D_2\,dP} {\int_XD_1D_2\,dP}, </math> whenever the required integrals are finite and positive. Therefore :<math> (P_{D_1})_{D_2} = P_{D_1D_2}. </math> Sequential scalar dilation fields thus combine multiplicatively before normalization. This composition property is the measure-theoretic analogue of repeated diagonal reweighting. === 4.8 Iterated fixed dilation === If the same dilation field <math>D</math> is applied repeatedly, then after <math>k</math> iterations, :<math> dP^{(k)} = \frac{D^k\,dP^{(0)}} {\displaystyle\int_XD^k\,dP^{(0)}}. </math> Equivalently, for any measurable event <math>A</math>, :<math> P^{(k)}(A) = \frac{\displaystyle\int_A D(x)^k\,dP^{(0)}(x)} {\displaystyle\int_X D(x)^k\,dP^{(0)}(x)}. </math> This is the direct measure-theoretic counterpart of :<math> p_i^{(k)} = \frac{d_i^kp_i^{(0)}} {\sum_jd_j^kp_j^{(0)}}. </math> Regions where <math>D</math> is relatively large receive increasing relative weight under repeated application. The precise limiting behavior depends on the structure of <math>D</math> and the initial measure. === 4.9 Exponential dilation fields === A particularly important family is obtained by choosing :<math> D_{\theta}(x) = e^{\theta\phi(x)}, </math> where <math>\phi:X\rightarrow\mathbb{R}</math> is measurable and <math>\theta</math> is a real parameter for which the normalization integral is finite. Define :<math> Z(\theta) = \int_X e^{\theta\phi(x)}\,dP_0(x). </math> Then :<math> dP_{\theta}(x) = \frac{e^{\theta\phi(x)}} {Z(\theta)} dP_0(x). </math> In a finite state space this becomes :<math> p_i(\theta) = \frac{p_i^{(0)}e^{\theta\phi_i}} {\sum_jp_j^{(0)}e^{\theta\phi_j}}. </math> This is a standard exponential tilting construction and is closely related to exponential families, cumulant-generating functions, and information geometry. Its importance for the present paper is that it provides a continuous one-parameter dilation trajectory whose Fisher–Rao geometry can be studied explicitly. === 4.10 Infinitesimal evolution of exponential dilation === For the finite-dimensional exponential family, :<math> p_i(\theta) = \frac{p_i^{(0)}e^{\theta\phi_i}} {Z(\theta)}, </math> differentiate with respect to <math>\theta</math>. The logarithmic derivative is :<math> \frac{d}{d\theta}\log p_i(\theta) = \phi_i - \frac{d}{d\theta}\log Z(\theta). </math> Since :<math> \frac{d}{d\theta}\log Z(\theta) = \sum_jp_j(\theta)\phi_j, </math> define :<math> \overline{\phi}_{\theta} = \sum_jp_j(\theta)\phi_j. </math> Then :<math> \frac{dp_i}{d\theta} = p_i(\theta) \left( \phi_i-\overline{\phi}_{\theta} \right). </math> This equation has the form of a replicator-type evolution equation with a fixed state-dependent generator <math>\phi_i</math>. The relationship to established replicator dynamics is discussed in Section 5. === 4.11 Conservation of total probability === Summing the infinitesimal evolution equation gives :<math> \sum_i \frac{dp_i}{d\theta} = \sum_i p_i(\theta) \left( \phi_i-\overline{\phi}_{\theta} \right). </math> Since :<math> \sum_ip_i(\theta)\phi_i = \overline{\phi}_{\theta} </math> and :<math> \sum_ip_i(\theta)=1, </math> it follows that :<math> \sum_i \frac{dp_i}{d\theta} = 0. </math> Thus the vector field is tangent to the probability simplex. Normalization is therefore reflected infinitesimally by conservation of total probability. === 4.12 Scope of the measure-theoretic formulation === The measure-theoretic formulation shows that normalized probability dilation is not restricted to finite vectors or matrices. The same structural operation appears as :'''weight → normalize → obtain a new probability measure''' and, for exponential fields, :'''exponential weight → normalize → continuous probability trajectory'''. These constructions overlap directly with established change-of-measure theory, exponential tilting, weighted probability measures, and related probabilistic methods. Their role in the present framework is to connect the finite dilation notation to continuous probability spaces and to provide the bridge to the information-geometric analysis developed later in the paper. The next section therefore compares the normalized-dilation framework systematically with established mathematical constructions before any additional geometric results are introduced. == 5. Relation to Established Mathematics == The normalized-dilation framework overlaps with several established areas of mathematics. This section identifies those relationships explicitly. The purpose is twofold: first, to place the notation used in this paper within its appropriate mathematical context; and second, to distinguish established constructions from the particular synthesis and geometric questions developed later in the paper. The term '''probability dilation''' is therefore used as an organizing description of a transformation-and-normalization structure, not as a claim that the underlying operations of reweighting, normalization, positive matrix iteration, or change of measure are themselves new. === 5.1 Weighted probability and change of measure === The measure-theoretic transformation :<math> dP_D = \frac{D\,dP} {\int_XD\,dP} </math> is a standard normalized change of measure. Its Radon–Nikodym derivative with respect to <math>P</math> is :<math> \frac{dP_D}{dP} = \frac{D} {\int_XD\,dP}. </math> Consequently, for an integrable observable <math>f</math>, :<math> \mathbb{E}_{P_D}[f] = \frac{\mathbb{E}_{P}[fD]} {\mathbb{E}_{P}[D]}. </math> These expressions belong to established measure-theoretic probability. Within the present framework, their role is to show that finite diagonal dilation and continuous weighted change of measure share the same normalized reweighting structure. === 5.2 Bayesian reweighting === A closely related normalization structure occurs in Bayesian inference. If <math>\pi(x)</math> is a prior density and <math>L(y\mid x)</math> is a likelihood for observed data <math>y</math>, Bayes' rule gives :<math> \pi(x\mid y) = \frac{L(y\mid x)\pi(x)} {\int L(y\mid z)\pi(z)\,dz}, </math> when the denominator is finite and nonzero. Structurally, this has the same form as :<math> dP_D = \frac{D\,dP} {\int D\,dP}, </math> with the likelihood acting as a positive weighting function. The statistical interpretation is different: Bayesian updating has a specific inferential meaning associated with conditioning on data. The comparison here concerns only the common mathematical normalization structure. === 5.3 Importance weighting and exponential tilting === Weighted probability measures also arise in importance sampling, exponential tilting, large-deviation methods, and related statistical constructions. For a generator <math>\phi</math>, exponential tilting takes the form :<math> dP_{\theta}(x) = \frac{e^{\theta\phi(x)}} {Z(\theta)} dP_0(x), </math> where :<math> Z(\theta) = \int_Xe^{\theta\phi(x)}\,dP_0(x). </math> This is an established exponential-family construction. The corresponding finite-dimensional expression, :<math> p_i(\theta) = \frac{p_i^{(0)}e^{\theta\phi_i}} {\sum_jp_j^{(0)}e^{\theta\phi_j}}, </math> will be the principal object of the Fisher–Rao analysis in Sections 6 through 8. The geometric analysis developed later concerns this established exponential-tilt family under a particular question about coincidence of information-geometric and Fisher–Rao geodesics. === 5.4 Positive matrices and Perron–Frobenius theory === For a fixed nonnegative matrix <math>M</math>, the normalized transformation :<math> T_M(p) = \frac{Mp} {\mathbf{1}^{\mathsf{T}}Mp} </math> is closely related to classical positive-matrix theory. If <math>M</math> is primitive, Perron–Frobenius theory provides a dominant positive eigenvalue :<math> \rho(M)>0 </math> and a corresponding strictly positive eigenvector. Repeated normalized iteration, :<math> p^{(k)} = \frac{M^kp^{(0)}} {\mathbf{1}^{\mathsf{T}}M^kp^{(0)}}, </math> is therefore closely related to normalized power iteration. Under appropriate hypotheses, its asymptotic direction is governed by the Perron eigenvector. These spectral and convergence results are established mathematics and are not presented here as new consequences of PDT. === 5.5 Markov operators === Suppose <math>M</math> is nonnegative and satisfies :<math> \mathbf{1}^{\mathsf{T}}M = \mathbf{1}^{\mathsf{T}}. </math> With the column-vector convention used in this paper, :<math> \mathbf{1}^{\mathsf{T}}Mp = 1 </math> for every probability vector <math>p</math>. Thus :<math> T_M(p)=Mp. </math> In this mass-preserving case, the normalization step is unnecessary. Accordingly, ordinary finite-state Markov evolution is contained as a special mass-preserving case of the broader positive-transformation framework. This observation is structural. It does not imply that normalized dilation provides a replacement for Markov-chain theory. === 5.6 Replicator-type dynamics === The exponential dilation family satisfies :<math> \frac{dp_i}{d\theta} = p_i \left( \phi_i-\overline{\phi}_{\theta} \right), </math> where :<math> \overline{\phi}_{\theta} = \sum_jp_j(\theta)\phi_j. </math> The standard replicator equation has the form :<math> \frac{dp_i}{dt} = p_i \left( f_i(p)-\overline{f}(p) \right). </math> Thus exponential dilation with fixed generator values <math>\phi_i</math> has the same algebraic structure as a replicator equation with state-independent fitness values. The mean-subtraction term guarantees :<math> \sum_i\frac{dp_i}{d\theta}=0, </math> so the flow remains tangent to the probability simplex. Replicator dynamics and their geometric interpretations are established subjects. The present paper uses this connection to relate normalized dilation to known simplex dynamics. === 5.7 Fisher–Rao and Shahshahani geometry === The interior of the probability simplex carries the Fisher–Rao metric. For tangent vectors <math>u</math> and <math>v</math> satisfying :<math> \sum_i u_i = \sum_i v_i = 0, </math> the finite-dimensional Fisher–Rao metric can be written as :<math> g_p(u,v) = \sum_{i=1}^{n} \frac{u_iv_i}{p_i}. </math> Closely related forms of this metric appear in evolutionary dynamics under the name Shahshahani metric. The square-root mapping :<math> \Psi(p) = 2(\sqrt{p_1},\ldots,\sqrt{p_n}) </math> satisfies :<math> \sum_i\Psi_i(p)^2=4. </math> Thus the simplex interior is represented in the positive orthant of a sphere of radius <math>2</math>. Under this representation, the Fisher–Rao metric becomes the metric induced by the ambient Euclidean space, and Levi-Civita Fisher–Rao geodesics correspond locally to great-circle arcs. This established spherical representation will be the principal geometric tool used in Section 7. === 5.8 Exponential families and the e-connection === The exponential dilation path :<math> p_i(\theta) = \frac{p_i^{(0)}e^{\theta\phi_i}} {Z(\theta)} </math> is a one-parameter exponential family. Taking logarithms gives :<math> \log p_i(\theta) = \log p_i^{(0)} + \theta\phi_i - \log Z(\theta). </math> The natural parameter varies linearly with <math>\theta</math>. In information geometry, exponential families are naturally associated with the exponential, or '''e''', connection. A path linear in natural parameters is an e-geodesic. This notion of geodesic is distinct from a Levi-Civita geodesic of the Fisher–Rao metric. Consequently, an exponential dilation trajectory may be straight with respect to the e-connection while being curved with respect to the Fisher–Rao Levi-Civita connection. This distinction is central to the geometric question investigated later in the paper. === 5.9 Fisher information and variance === For the exponential dilation family, :<math> \frac{d}{d\theta} \log p_i(\theta) = \phi_i-\overline{\phi}_{\theta}. </math> The Fisher information associated with the parameter <math>\theta</math> is therefore :<math> I(\theta) = \sum_i p_i(\theta) \left( \phi_i-\overline{\phi}_{\theta} \right)^2. </math> Hence :<math> I(\theta) = \operatorname{Var}_{p(\theta)}(\phi). </math> The Fisher–Rao speed of the trajectory is :<math> v_{\mathrm{FR}}(\theta) = \sqrt{I(\theta)} = \sqrt{\operatorname{Var}_{p(\theta)}(\phi)}. </math> This variance identity is a standard property of one-parameter exponential families. It will be used later when deriving the arclength parameterization of the two-level case. === 5.10 Normalized Feynman–Kac transformations === Another closely related structure occurs in Feynman–Kac models. At an abstract level, a positive measure may first be weighted by a nonnegative potential and then propagated through a positive or Markov operator, followed by normalization. Schematically, such an evolution has the form :'''weight → propagate → normalize'''. The matrix expression :<math> T_M(p) = \frac{Mp} {\mathbf{1}^{\mathsf{T}}Mp} </math> and the measure expression :<math> dP_D = \frac{D\,dP} {\int D\,dP} </math> therefore have structural analogues within normalized Feynman–Kac theory. The exact interpretation and assumptions differ among applications. The comparison made here is structural rather than an assertion of equivalence between PDT and Feynman–Kac theory. === 5.11 Projective dynamics === Because normalized dilation is invariant under multiplication of the unnormalized transformed state by a positive scalar, it naturally has a projective character. For example, :<math> T_{cM}(p) = T_M(p) </math> for every <math>c>0</math> for which the transformation is defined. Thus the normalized state depends on the ray determined by <math>Mp</math>, rather than its magnitude. Positive projective geometry and projective metrics, including Hilbert-type metrics, are established tools in the study of positive operators and their contraction properties. These methods provide natural mathematical machinery for analyzing normalized positive transformations, particularly in convergence problems. === 5.12 What the PDT framework contributes === The preceding comparisons show that the principal operations used in normalized probability dilation have substantial established precedents. The proposed contribution of the framework is therefore not the isolated operation :'''multiply or transform, then normalize'''. Rather, the framework provides a common notation and organizational viewpoint connecting: * finite diagonal reweighting; * nonnegative matrix transformations; * normalized positive iteration; * weighted change of measure; * exponential probability trajectories; * simplex dynamics; * information geometry. This synthesis is useful only insofar as it clarifies relationships, generates mathematically precise questions, or produces results that are not merely restatements of known theory. For that reason, the remainder of this paper concentrates on a narrower geometric problem. === 5.13 Transition to the geometric question === Every exponential dilation trajectory of the form :<math> p_i(\theta) = \frac{p_i^{(0)}e^{\theta\phi_i}} {Z(\theta)} </math> is an exponential-family trajectory and hence is naturally straight with respect to the e-connection. It does not follow that the same trajectory is a Levi-Civita geodesic of the Fisher–Rao metric. This leads to the central question considered in the remainder of the paper: :''Under what conditions is an exponential dilation trajectory simultaneously an e-geodesic and, up to reparameterization, a Fisher–Rao Levi-Civita geodesic?'' The next section develops the geometric representation required to answer this question. == 6. Exponential Dilation and Fisher–Rao Geometry == This section develops the geometric representation of exponential dilation required for the main characterization theorem. The central object is the one-parameter exponential family :<math> p_i(\theta) = \frac{p_i^{(0)}e^{\theta\phi_i}} {Z(\theta)}, </math> where :<math> Z(\theta) = \sum_{j=1}^{n}p_j^{(0)}e^{\theta\phi_j}. </math> Throughout this section, assume :<math> p_i^{(0)}>0 </math> for all <math>i</math>, and let :<math> \phi=(\phi_1,\ldots,\phi_n) </math> be a real-valued generator. === 6.1 Exponential dilation trajectory === Let :<math> p^{(0)} \in \Delta_{+}^{n-1}. </math> For a real parameter <math>\theta</math>, define :<math> p_i(\theta) = \frac{p_i^{(0)}e^{\theta\phi_i}} {\sum_{j=1}^{n}p_j^{(0)}e^{\theta\phi_j}}. </math> Since every initial component is strictly positive and the exponential function is positive, :<math> p_i(\theta)>0 </math> for every finite <math>\theta</math>. Therefore the trajectory remains in the interior of the probability simplex. The normalization factor satisfies :<math> Z(\theta)>0. </math> Hence the trajectory is well defined for every finite <math>\theta</math> in the finite-dimensional setting. === 6.2 Logarithmic form === Taking logarithms gives :<math> \log p_i(\theta) = \log p_i^{(0)} + \theta\phi_i - \log Z(\theta). </math> Differentiating with respect to <math>\theta</math> gives :<math> \frac{d}{d\theta}\log p_i(\theta) = \phi_i - \frac{d}{d\theta}\log Z(\theta). </math> Now :<math> \frac{dZ}{d\theta} = \sum_j p_j^{(0)} \phi_j e^{\theta\phi_j}. </math> Therefore :<math> \frac{d}{d\theta}\log Z(\theta) = \sum_jp_j(\theta)\phi_j. </math> Define the expectation of the generator by :<math> \mu(\theta) = \mathbb{E}_{p(\theta)}[\phi] = \sum_jp_j(\theta)\phi_j. </math> Then :<math> \frac{d}{d\theta}\log p_i(\theta) = \phi_i-\mu(\theta). </math> === 6.3 Tangent vector === Multiplying the logarithmic derivative by <math>p_i(\theta)</math> gives :<math> \frac{dp_i}{d\theta} = p_i(\theta) \left( \phi_i-\mu(\theta) \right). </math> Define the centered generator :<math> h_i(\theta) = \phi_i-\mu(\theta). </math> Then :<math> \frac{dp_i}{d\theta} = p_i(\theta)h_i(\theta). </math> Because :<math> \sum_i p_i(\theta)h_i(\theta) = 0, </math> we obtain :<math> \sum_i \frac{dp_i}{d\theta} = 0. </math> Thus the velocity vector is tangent to the probability simplex. === 6.4 Fisher information and speed === The Fisher–Rao metric on the simplex interior is :<math> g_p(u,v) = \sum_i \frac{u_iv_i}{p_i}, </math> for tangent vectors <math>u</math> and <math>v</math>. For the exponential dilation trajectory, :<math> \frac{dp_i}{d\theta} = p_i h_i. </math> Its squared Fisher–Rao speed is therefore :<math> v_{\mathrm{FR}}(\theta)^2 = \sum_i \frac{1}{p_i} \left( \frac{dp_i}{d\theta} \right)^2. </math> Substitution gives :<math> v_{\mathrm{FR}}(\theta)^2 = \sum_i p_i(\theta)h_i(\theta)^2. </math> Hence :<math> v_{\mathrm{FR}}(\theta)^2 = \operatorname{Var}_{p(\theta)}(\phi). </math> Therefore :<math> v_{\mathrm{FR}}(\theta) = \sqrt{ \operatorname{Var}_{p(\theta)}(\phi) }. </math> This is the standard Fisher-information identity for a one-parameter exponential family. === 6.5 Square-root representation === Define the square-root map :<math> \Psi: \Delta_{+}^{n-1} \rightarrow \mathbb{R}^{n} </math> by :<math> \Psi(p) = 2(\sqrt{p_1},\ldots,\sqrt{p_n}). </math> Write :<math> q(\theta) = \Psi(p(\theta)). </math> Then :<math> q_i(\theta) = 2\sqrt{p_i(\theta)}. </math> Because :<math> \sum_i p_i(\theta)=1, </math> we have :<math> \sum_iq_i(\theta)^2 = 4. </math> Thus :<math> q(\theta) </math> lies on the positive orthant of the sphere of radius <math>2</math> in <math>\mathbb{R}^{n}</math>. === 6.6 Isometry of the square-root representation === Let <math>u</math> be a tangent vector to the simplex. Differentiating :<math> q_i=2\sqrt{p_i} </math> gives :<math> dq_i = \frac{dp_i}{\sqrt{p_i}}. </math> Therefore the Euclidean squared length of the corresponding tangent displacement on the sphere is :<math> \sum_i(dq_i)^2 = \sum_i \frac{(dp_i)^2}{p_i}. </math> This is precisely the Fisher–Rao line element. Thus the square-root map identifies the Fisher–Rao metric on the simplex interior with the Euclidean metric induced on the positive orthant of the radius-<math>2</math> sphere. Consequently, Fisher–Rao Levi-Civita geodesics correspond locally to great-circle arcs on this sphere. === 6.7 Square-root form of exponential dilation === Substituting the exponential dilation family into the square-root representation gives :<math> q_i(\theta) = \frac{ 2\sqrt{p_i^{(0)}}e^{\theta\phi_i/2} } {\sqrt{Z(\theta)}}. </math> Define the unnormalized square-root vector :<math> r_i(\theta) = \sqrt{p_i^{(0)}}e^{\theta\phi_i/2}. </math> Then :<math> q(\theta) = \frac{2r(\theta)} {\sqrt{Z(\theta)}}. </math> Also, :<math> \|r(\theta)\|^2 = Z(\theta). </math> Hence :<math> q(\theta) = \frac{2r(\theta)} {\|r(\theta)\|}. </math> The normalized square-root trajectory and the unnormalized vector <math>r(\theta)</math> therefore determine the same ray through the origin. This observation allows the Fisher–Rao geodesic question to be reduced to a linear-subspace question in <math>\mathbb{R}^{n}</math>. === 6.8 Distinct generator levels === Suppose the generator <math>\phi</math> assumes exactly <math>m</math> distinct values :<math> a_1,\ldots,a_m. </math> Define the level sets :<math> A_{\ell} = \{i:\phi_i=a_{\ell}\}, </math> for :<math> \ell=1,\ldots,m. </math> For each level, define a vector <math>u_{\ell}</math> by :<math> (u_{\ell})_i = \begin{cases} \sqrt{p_i^{(0)}} & \text{if } i\in A_{\ell},\\ 0 & \text{otherwise}. \end{cases} </math> Because the level sets are disjoint, the vectors :<math> u_1,\ldots,u_m </math> have disjoint supports and are therefore mutually orthogonal. In particular, they are linearly independent. The unnormalized square-root trajectory can now be written as :<math> r(\theta) = \sum_{\ell=1}^{m} e^{a_{\ell}\theta/2} u_{\ell}. </math> This decomposition is central to the geometric characterization developed in the next section. === 6.9 The one-level case === If <math>m=1</math>, then every component of <math>\phi</math> has the same value <math>a</math>. Thus :<math> r(\theta) = e^{a\theta/2}u_1. </math> After normalization, the scalar exponential factor cancels. Therefore :<math> p(\theta)=p^{(0)} </math> for all <math>\theta</math>. The trajectory is constant. This is the degenerate case of exponential dilation. === 6.10 The two-level case === Suppose <math>\phi</math> assumes exactly two distinct values :<math> a </math> and :<math> b, </math> with <math>a\neq b</math>. Then :<math> r(\theta) = e^{a\theta/2}u + e^{b\theta/2}v, </math> where <math>u</math> and <math>v</math> are nonzero orthogonal vectors associated with the two generator levels. Consequently, :<math> r(\theta) \in \operatorname{span}\{u,v\} </math> for every <math>\theta</math>. Since <math>q(\theta)</math> is obtained from <math>r(\theta)</math> by positive scalar normalization, :<math> q(\theta) \in \operatorname{span}\{u,v\} </math> as well. The intersection of a two-dimensional linear subspace through the origin with the radius-<math>2</math> sphere is a great circle. Thus the two-level case naturally produces a Fisher–Rao great-circle trajectory. The formal statement and converse are given in Section 7. === 6.11 Three or more generator levels === If the generator assumes three or more distinct values, then :<math> r(\theta) = \sum_{\ell=1}^{m} e^{a_{\ell}\theta/2}u_{\ell}, </math> with :<math> m\geq3. </math> The vectors <math>u_{\ell}</math> are linearly independent, but this fact alone is not sufficient to conclude that the trajectory spans all <math>m</math> directions. The required result follows from the linear independence of the distinct exponential rates. In Section 7, derivatives of <math>r(\theta)</math> are evaluated at a fixed parameter value. The resulting coefficient matrix is of Vandermonde type and is invertible when the generator levels <math>a_{\ell}</math> are distinct. This shows that a trajectory with <math>m</math> distinct active generator levels spans an <math>m</math>-dimensional linear subspace. Consequently, when <math>m\geq3</math>, the square-root trajectory cannot lie in a two-dimensional great-circle plane. === 6.12 e-geodesic versus Fisher–Rao geodesic === The exponential dilation trajectory is an exponential-family path. In natural coordinates, the parameter <math>\theta</math> enters linearly through :<math> \theta\phi_i. </math> Accordingly, the trajectory is naturally an e-geodesic in the exponential connection of information geometry. The Fisher–Rao Levi-Civita geodesic condition is different. Under the square-root representation, it requires the image of the trajectory to lie on a great-circle arc. Thus the central geometric distinction is: :'''e-geodesic: linearity in exponential-family natural coordinates''' versus :'''Fisher–Rao Levi-Civita geodesic: great-circle geometry under the square-root representation''' The two notions coincide only under additional conditions. === 6.13 Geometric question in linear form === The original probability-geometric question can now be reformulated. Given :<math> r(\theta) = \sum_{\ell=1}^{m} e^{a_{\ell}\theta/2}u_{\ell}, </math> when does the normalized curve :<math> q(\theta) = \frac{2r(\theta)} {\|r(\theta)\|} </math> remain in a fixed two-dimensional linear subspace? If it does, its image lies on a great circle and is therefore a Fisher–Rao Levi-Civita geodesic up to reparameterization. If it does not, the exponential trajectory remains an e-geodesic but is not a Fisher–Rao Levi-Civita geodesic. The next section gives an exact finite-dimensional characterization. == 7. Fisher–Rao Geodesic Characterization == This section gives the principal geometric result of the paper. The question is whether the image of a finite-dimensional exponential dilation trajectory is contained in a Fisher–Rao Levi-Civita geodesic. The parameter <math>\theta</math> itself is not required to be an affine or arclength parameter for that geodesic. === 7.1 Setting and assumptions === Let :<math> p^{(0)} = (p_1^{(0)},\ldots,p_n^{(0)})^{\mathsf{T}} \in \Delta_{+}^{n-1}, </math> so that :<math> p_i^{(0)}>0 </math> for every <math>i</math>. Let :<math> \phi = (\phi_1,\ldots,\phi_n) \in \mathbb{R}^{n}. </math> Define the exponential dilation trajectory :<math> p_i(\theta) = \frac{ p_i^{(0)}e^{\theta\phi_i} } { \sum_{j=1}^{n} p_j^{(0)}e^{\theta\phi_j} }, </math> for :<math> \theta\in\mathbb{R}. </math> Let <math>m</math> denote the number of distinct values assumed by the generator components :<math> \phi_1,\ldots,\phi_n. </math> === 7.2 Theorem 1: two-level Fisher–Rao characterization === '''Theorem 1.''' Under the assumptions above, the image of the exponential dilation trajectory <math>p(\theta)</math> is contained in a Fisher–Rao Levi-Civita geodesic if and only if :<math> m\leq2. </math> Equivalently, the generator <math>\phi</math> must assume at most two distinct values. When <math>m=1</math>, the trajectory is constant. When <math>m=2</math>, the trajectory is nonconstant and its square-root image lies on a great-circle arc. === 7.3 Proof: square-root representation === Define :<math> q_i(\theta) = 2\sqrt{p_i(\theta)}. </math> As shown in Section 6, :<math> q(\theta) </math> lies on the sphere :<math> \sum_iq_i^2=4. </math> The square-root representation is an isometric representation of the Fisher–Rao simplex interior. Therefore the image of <math>p(\theta)</math> is contained in a Fisher–Rao Levi-Civita geodesic if and only if the image of <math>q(\theta)</math> is contained in a great circle of the radius-<math>2</math> sphere. A great circle is the intersection of the sphere with a two-dimensional linear subspace through the origin. === 7.4 Grouping equal generator values === Let the distinct values of <math>\phi</math> be :<math> a_1,\ldots,a_m. </math> For each <math>\ell</math>, define :<math> A_{\ell} = \{i:\phi_i=a_{\ell}\}. </math> Define <math>u_{\ell}\in\mathbb{R}^{n}</math> by :<math> (u_{\ell})_i = \begin{cases} \sqrt{p_i^{(0)}} & \text{if }i\in A_{\ell},\\ 0 & \text{otherwise}. \end{cases} </math> Because the sets <math>A_{\ell}</math> are disjoint and every initial component is strictly positive, the vectors :<math> u_1,\ldots,u_m </math> are nonzero and mutually orthogonal. Hence they are linearly independent. Define the unnormalized square-root trajectory :<math> r(\theta) = \sum_{\ell=1}^{m} e^{a_{\ell}\theta/2} u_{\ell}. </math> Then :<math> q(\theta) = \frac{2r(\theta)} {\|r(\theta)\|}. </math> Since normalization multiplies <math>r(\theta)</math> only by a positive scalar, <math>q(\theta)</math> and <math>r(\theta)</math> lie on the same ray through the origin. === 7.5 Sufficiency: one or two generator levels === Suppose first that :<math> m=1. </math> Then :<math> r(\theta) = e^{a_1\theta/2}u_1. </math> Normalization removes the scalar exponential factor, so :<math> q(\theta) </math> and therefore <math>p(\theta)</math> are constant. A constant trajectory is the degenerate case. Now suppose :<math> m=2. </math> Then :<math> r(\theta) = e^{a_1\theta/2}u_1 + e^{a_2\theta/2}u_2. </math> Therefore :<math> r(\theta) \in \operatorname{span}\{u_1,u_2\} </math> for every <math>\theta</math>. Since <math>q(\theta)</math> differs from <math>r(\theta)</math> only by scalar normalization, :<math> q(\theta) \in \operatorname{span}\{u_1,u_2\}. </math> The vectors <math>u_1</math> and <math>u_2</math> are nonzero and orthogonal, so their span is a two-dimensional linear subspace through the origin. Its intersection with the radius-<math>2</math> sphere is a great circle. Thus the image of the two-level exponential dilation trajectory lies on a Fisher–Rao Levi-Civita geodesic. This proves sufficiency. === 7.6 Necessity: derivative span === Now suppose the generator assumes :<math> m\geq3 </math> distinct values. Differentiate the unnormalized square-root trajectory: :<math> r(\theta) = \sum_{\ell=1}^{m} e^{a_{\ell}\theta/2} u_{\ell}. </math> For every nonnegative integer <math>k</math>, :<math> r^{(k)}(\theta) = \sum_{\ell=1}^{m} \left( \frac{a_{\ell}}{2} \right)^k e^{a_{\ell}\theta/2} u_{\ell}. </math> Fix any :<math> \theta_0\in\mathbb{R}. </math> Consider the vectors :<math> r(\theta_0), r^{(1)}(\theta_0), \ldots, r^{(m-1)}(\theta_0). </math> Their coefficients relative to the basis :<math> u_1,\ldots,u_m </math> form the matrix :<math> C_{k\ell} = \left( \frac{a_{\ell}}{2} \right)^k e^{a_{\ell}\theta_0/2}, </math> where :<math> k=0,\ldots,m-1 </math> and :<math> \ell=1,\ldots,m. </math> === 7.7 Vandermonde argument === Factor the nonzero quantity :<math> e^{a_{\ell}\theta_0/2} </math> from column <math>\ell</math> of the coefficient matrix. The remaining matrix has entries :<math> V_{k\ell} = \left( \frac{a_{\ell}}{2} \right)^k. </math> This is a Vandermonde matrix. Its determinant is nonzero because :<math> a_1,\ldots,a_m </math> are distinct. Therefore the coefficient matrix <math>C</math> is invertible. It follows that :<math> r(\theta_0), r^{(1)}(\theta_0), \ldots, r^{(m-1)}(\theta_0) </math> are linearly independent. Consequently, the linear span generated by the trajectory <math>r(\theta)</math> has dimension at least <math>m</math>. On the other hand, the representation :<math> r(\theta) = \sum_{\ell=1}^{m} e^{a_{\ell}\theta/2}u_{\ell} </math> shows that the trajectory is contained in :<math> \operatorname{span} \{u_1,\ldots,u_m\}, </math> which has dimension <math>m</math>. Hence :<math> \dim \operatorname{span} \{r(\theta):\theta\in\mathbb{R}\} = m. </math> === 7.8 Exclusion of three or more levels === If the square-root trajectory <math>q(\theta)</math> were contained in a great circle, then there would exist a two-dimensional linear subspace <math>W</math> through the origin such that :<math> q(\theta)\in W </math> for every <math>\theta</math>. Since :<math> r(\theta) = \frac{\|r(\theta)\|}{2} q(\theta), </math> the same subspace would contain :<math> r(\theta) </math> for every <math>\theta</math>. Therefore :<math> \dim \operatorname{span} \{r(\theta):\theta\in\mathbb{R}\} \leq2. </math> But Section 7.7 gives :<math> \dim \operatorname{span} \{r(\theta):\theta\in\mathbb{R}\} = m. </math> Thus a great-circle trajectory requires :<math> m\leq2. </math> For :<math> m\geq3, </math> the exponential dilation trajectory cannot be contained in a Fisher–Rao Levi-Civita geodesic. This proves necessity. === 7.9 Conclusion of the proof === Combining Sections 7.5 and 7.8 gives :<math> m\leq2 </math> if and only if the image of the exponential dilation trajectory is contained in a Fisher–Rao Levi-Civita geodesic. Therefore the generator <math>\phi</math> must assume at most two distinct values. This completes the proof. === 7.10 Corollary 1: dimension of the square-root trajectory === '''Corollary 1.''' Under the assumptions of Theorem 1, if the generator <math>\phi</math> assumes exactly <math>m</math> distinct values, then :<math> \dim \operatorname{span} \{r(\theta):\theta\in\mathbb{R}\} = m. </math> Thus the number of distinct generator levels is exactly the dimension of the linear subspace generated by the unnormalized square-root exponential trajectory. '''Proof.''' The vectors <math>u_1,\ldots,u_m</math> are linearly independent, and Section 7.7 shows through the Vandermonde argument that the trajectory spans all of these directions. Therefore its span has dimension <math>m</math>. === 7.11 Corollary 2: three-level obstruction === '''Corollary 2.''' If a strictly positive finite exponential dilation trajectory has a generator assuming three or more distinct values, then its image is not contained in a Fisher–Rao Levi-Civita geodesic. This follows immediately from Theorem 1. The result is exact under the stated hypotheses; it is not merely a generic non-geodesicity statement. === 7.12 Parameterization versus geodesic image === Theorem 1 concerns the image of the trajectory. Even in the two-level case, the exponential parameter <math>\theta</math> is generally not proportional to Fisher–Rao arclength. Thus :<math> p(\theta) </math> traces a Fisher–Rao geodesic path but generally does so with nonconstant Fisher–Rao speed. From Section 6, :<math> \frac{ds}{d\theta} = \sqrt{ \operatorname{Var}_{p(\theta)}(\phi) }. </math> Section 8 derives the exact change of parameter from <math>\theta</math> to Fisher–Rao arclength in the nondegenerate two-level case. === 7.13 Geometric interpretation === The theorem can be understood through the square-root sphere. A generator with one distinct value produces no probability motion. A generator with two distinct values produces two independent exponential directions, :<math> e^{a\theta/2}u </math> and :<math> e^{b\theta/2}v. </math> Their normalized sum remains in a fixed two-dimensional plane through the origin, so its spherical image follows a great circle. With three or more distinct generator values, the trajectory necessarily spans three or more independent linear directions. It therefore cannot remain in any two-dimensional great-circle plane. The distinction between the two-level and multilevel cases is consequently a dimensional property of the exponential rates under the square-root representation. === 7.14 Relation to information-geometric straightness === Theorem 1 does not state that exponential trajectories with three or more levels cease to be e-geodesics. They remain exponential-family trajectories and retain their standard information-geometric interpretation with respect to the e-connection. Rather, the theorem characterizes when this e-geodesic image also coincides with a geodesic image of the Levi-Civita connection associated with the Fisher–Rao metric. Thus the result concerns the coincidence of two distinct notions of geometric straightness. === 7.15 Status of the characterization === The proof above uses established ingredients: * the exponential-family representation; * the Fisher–Rao square-root embedding; * the great-circle characterization of spherical geodesics; * linear independence of vectors with disjoint support; * the Vandermonde determinant. The particular characterization obtained by combining these ingredients is presented here as a result of the present analysis. At this draft stage, no claim of historical priority is made. A complete literature review and independent mathematical scrutiny remain appropriate before describing the characterization as novel. The next section derives an explicit Fisher–Rao arclength parameterization for the nondegenerate two-level case. == 8. Fisher–Rao Arclength in the Two-Level Case == Theorem 1 shows that a nonconstant exponential dilation trajectory is contained in a Fisher–Rao Levi-Civita geodesic precisely when its generator assumes exactly two distinct values. This section derives an explicit Fisher–Rao arclength parameterization for that case. === 8.1 Two generator classes === Suppose the generator <math>\phi</math> assumes exactly two distinct values :<math> a\neq b. </math> Define the corresponding index sets :<math> A= \{i:\phi_i=a\} </math> and :<math> B= \{i:\phi_i=b\}. </math> Let the initial probability masses of the two classes be :<math> r_0 = \sum_{i\in A}p_i^{(0)} </math> and :<math> 1-r_0 = \sum_{i\in B}p_i^{(0)}. </math> Because the initial probability vector is strictly positive and both classes are nonempty, :<math> 0<r_0<1. </math> === 8.2 Evolution of the class probabilities === Let :<math> r(\theta) = \sum_{i\in A}p_i(\theta) </math> denote the total probability assigned to class <math>A</math>. Since every state in <math>A</math> has generator value <math>a</math> and every state in <math>B</math> has generator value <math>b</math>, :<math> r(\theta) = \frac{ r_0e^{a\theta} } { r_0e^{a\theta} + (1-r_0)e^{b\theta} }. </math> Similarly, :<math> 1-r(\theta) = \frac{ (1-r_0)e^{b\theta} } { r_0e^{a\theta} + (1-r_0)e^{b\theta} }. </math> Therefore the class odds satisfy :<math> \frac{r(\theta)} {1-r(\theta)} = \frac{r_0} {1-r_0} e^{(a-b)\theta}. </math> Thus the two-level exponential dilation reduces at the class level to a logistic probability trajectory. === 8.3 Preservation of within-class proportions === For two indices <math>i,j\in A</math>, :<math> \frac{p_i(\theta)} {p_j(\theta)} = \frac{p_i^{(0)}} {p_j^{(0)}}. </math> The same relation holds for indices within <math>B</math>. Therefore exponential dilation changes only the total probability assigned to the two generator classes; it does not change relative probabilities within either class. Define normalized class vectors <math>\widehat{u}</math> and <math>\widehat{v}</math> by :<math> \widehat{u}_i = \begin{cases} \sqrt{p_i^{(0)}/r_0} & \text{if }i\in A,\\ 0 & \text{otherwise}, \end{cases} </math> and :<math> \widehat{v}_i = \begin{cases} \sqrt{p_i^{(0)}/(1-r_0)} & \text{if }i\in B,\\ 0 & \text{otherwise}. \end{cases} </math> These vectors satisfy :<math> \|\widehat{u}\|=1, \qquad \|\widehat{v}\|=1, </math> and :<math> \widehat{u}^{\mathsf{T}}\widehat{v}=0. </math> === 8.4 Great-circle representation === Under the square-root map, :<math> q(\theta) = 2(\sqrt{p_1(\theta)},\ldots,\sqrt{p_n(\theta)}). </math> Using the class decomposition, :<math> q(\theta) = 2 \left( \sqrt{r(\theta)}\,\widehat{u} + \sqrt{1-r(\theta)}\,\widehat{v} \right). </math> Introduce an angular coordinate <math>\alpha(\theta)</math> by :<math> \sqrt{r(\theta)} = \cos\alpha(\theta) </math> and :<math> \sqrt{1-r(\theta)} = \sin\alpha(\theta), </math> with :<math> 0<\alpha(\theta)<\frac{\pi}{2}. </math> Then :<math> q(\theta) = 2 \left( \cos\alpha(\theta)\widehat{u} + \sin\alpha(\theta)\widehat{v} \right). </math> This is the standard angular parameterization of a great circle on a sphere of radius <math>2</math>. === 8.5 Angular coordinate === From the definitions above, :<math> \tan\alpha(\theta) = \sqrt{ \frac{1-r(\theta)} {r(\theta)} }. </math> Using the odds relation, :<math> \frac{1-r(\theta)} {r(\theta)} = \frac{1-r_0} {r_0} e^{(b-a)\theta}. </math> Therefore :<math> \tan\alpha(\theta) = \sqrt{ \frac{1-r_0} {r_0} } e^{(b-a)\theta/2}. </math> Hence :<math> \alpha(\theta) = \arctan \left( \sqrt{ \frac{1-r_0} {r_0} } e^{(b-a)\theta/2} \right). </math> Equivalently, :<math> \alpha(\theta) = \arccos\sqrt{r(\theta)}. </math> === 8.6 Corollary 3: exact Fisher–Rao arclength parameterization === '''Corollary 3.''' Under the hypotheses of Theorem 1, suppose the generator assumes exactly two distinct values <math>a\neq b</math>. Let :<math> r(\theta) </math> denote the total probability assigned to the class with generator value <math>a</math>. Then a signed Fisher–Rao arclength coordinate along the trajectory satisfies :<math> s(\theta)-s(\theta_0) = 2 \left( \alpha(\theta)-\alpha(\theta_0) \right), </math> where :<math> \alpha(\theta) = \arccos\sqrt{r(\theta)}. </math> Thus :<math> s(\theta)-s(\theta_0) = 2 \left( \arccos\sqrt{r(\theta)} - \arccos\sqrt{r(\theta_0)} \right). </math> Equivalently, :<math> s(\theta)-s(\theta_0) = 2 \left[ \arctan \left( \sqrt{ \frac{1-r_0}{r_0} } e^{(b-a)\theta/2} \right) - \arctan \left( \sqrt{ \frac{1-r_0}{r_0} } e^{(b-a)\theta_0/2} \right) \right]. </math> The Fisher–Rao distance traveled between the two parameter values is the absolute value :<math> d_{\mathrm{FR}} = |s(\theta)-s(\theta_0)|. </math> === 8.7 Proof of Corollary 3 === The square-root image is :<math> q(\theta) = 2 \left( \cos\alpha(\theta)\widehat{u} + \sin\alpha(\theta)\widehat{v} \right). </math> Differentiate with respect to <math>\alpha</math>: :<math> \frac{dq}{d\alpha} = 2 \left( -\sin\alpha\,\widehat{u} + \cos\alpha\,\widehat{v} \right). </math> Because <math>\widehat{u}</math> and <math>\widehat{v}</math> are orthonormal, :<math> \left\| \frac{dq}{d\alpha} \right\| = 2. </math> Therefore the spherical arclength element is :<math> ds = 2\,|d\alpha|. </math> For a chosen orientation, signed arclength satisfies :<math> ds=2\,d\alpha. </math> Integrating from <math>\theta_0</math> to <math>\theta</math> gives :<math> s(\theta)-s(\theta_0) = 2 \left( \alpha(\theta)-\alpha(\theta_0) \right). </math> Substituting the expressions for <math>\alpha(\theta)</math> gives the stated formulas. === 8.8 Fisher–Rao speed === Differentiating the angular expression gives :<math> \frac{d\alpha}{d\theta} = \frac{b-a}{2} \sqrt{ r(\theta) \left( 1-r(\theta) \right) }. </math> Therefore the unsigned Fisher–Rao speed is :<math> \left| \frac{ds}{d\theta} \right| = |a-b| \sqrt{ r(\theta) \left( 1-r(\theta) \right) }. </math> This agrees with the variance formula derived in Section 6. Indeed, because <math>\phi</math> takes only the values <math>a</math> and <math>b</math>, :<math> \operatorname{Var}_{p(\theta)}(\phi) = (a-b)^2 r(\theta) \left( 1-r(\theta) \right). </math> Hence :<math> v_{\mathrm{FR}}(\theta) = \sqrt{ \operatorname{Var}_{p(\theta)}(\phi) } = |a-b| \sqrt{ r(\theta) \left( 1-r(\theta) \right) }. </math> The geometric and information-theoretic calculations therefore agree. === 8.9 Nonuniform speed in the exponential parameter === Although the trajectory lies on a Fisher–Rao geodesic, the parameter <math>\theta</math> does not generally move along that geodesic at constant speed. The speed is largest when :<math> r(\theta)=\frac{1}{2}, </math> because the product :<math> r(\theta)(1-r(\theta)) </math> is maximal there. As the trajectory approaches either endpoint, :<math> r(\theta)\rightarrow0 </math> or :<math> r(\theta)\rightarrow1, </math> the Fisher–Rao speed with respect to <math>\theta</math> approaches zero. Thus the exponential parameter stretches the ends of the geodesic trajectory. === 8.10 Limiting behavior === Assume :<math> a>b. </math> Then as :<math> \theta\rightarrow+\infty, </math> we have :<math> r(\theta)\rightarrow1. </math> As :<math> \theta\rightarrow-\infty, </math> we have :<math> r(\theta)\rightarrow0. </math> Therefore :<math> \alpha(\theta)\rightarrow0 </math> as <math>\theta\rightarrow+\infty</math>, while :<math> \alpha(\theta)\rightarrow\frac{\pi}{2} </math> as <math>\theta\rightarrow-\infty</math>. The full two-level trajectory therefore approaches the two boundary class distributions at opposite ends of a quarter of the radius-<math>2</math> great circle. The total Fisher–Rao length between these limiting boundary points is :<math> 2 \left( \frac{\pi}{2} \right) = \pi. </math> The endpoints themselves lie on the boundary of the simplex and are approached only in the infinite-parameter limit. === 8.11 Example === Consider a three-state probability vector :<math> p^{(0)} = \left( \frac{1}{4}, \frac{1}{4}, \frac{1}{2} \right)^{\mathsf{T}} </math> and generator :<math> \phi = (1,1,0). </math> There are two generator classes: :<math> A=\{1,2\}, \qquad B=\{3\}. </math> The initial class mass is :<math> r_0 = \frac{1}{2}. </math> The class probability evolves as :<math> r(\theta) = \frac{e^{\theta}} {e^{\theta}+1}. </math> The individual probabilities are :<math> p_1(\theta) = \frac{1}{2}r(\theta), </math> :<math> p_2(\theta) = \frac{1}{2}r(\theta), </math> and :<math> p_3(\theta) = 1-r(\theta). </math> The angular coordinate is :<math> \alpha(\theta) = \arctan \left( e^{-\theta/2} \right). </math> Thus the trajectory is an exponential-family e-geodesic whose image is simultaneously a Fisher–Rao Levi-Civita geodesic. Its exponential parameterization is nonuniform, while <math>2\alpha</math> provides a signed Fisher–Rao arclength coordinate up to an additive constant and choice of orientation. === 8.12 Interpretation === The two-level result separates the '''path''' from the '''parameterization'''. The exponential parameter <math>\theta</math> generates the probability trajectory through normalized exponential weighting. The Fisher–Rao geometry identifies the same trajectory as a great-circle path. The transformation :<math> \theta \longmapsto \alpha(\theta) \longmapsto s(\theta) </math> provides the exact reparameterization needed to express that path in Fisher–Rao arclength. This provides a concrete example in which exponential-family straightness and Fisher–Rao Levi-Civita straightness describe the same geometric image while using different natural parameters. == 9. Discussion, Limitations, and Open Problems == The preceding sections developed normalized probability dilation as a common framework for positive transformation followed by normalization, and then considered a specific geometric question for exponential dilation. This section summarizes the mathematical interpretation of those results, identifies their limitations, and outlines several directions requiring further investigation. === 9.1 Scope of the framework === The normalized-dilation framework contains the basic operation :'''positive transformation → normalization → probability state'''. In finite dimensions this includes :<math> p \longmapsto \frac{Dp} {\mathbf{1}^{\mathsf{T}}Dp} </math> and :<math> p \longmapsto \frac{Mp} {\mathbf{1}^{\mathsf{T}}Mp}. </math> For probability measures it includes :<math> dP \longmapsto \frac{D\,dP} {\int_XD\,dP}. </math> These operations overlap substantially with established mathematical constructions. Accordingly, the value of the framework should not be judged by whether transformation followed by normalization is itself new. Rather, its usefulness depends on whether a common formulation clarifies relationships among existing constructions, suggests useful questions, or leads to additional mathematical results. === 9.2 Established mathematics and the PDT formulation === Several central components of the paper belong directly to established theory. These include: * normalized weighted probability measures; * Radon–Nikodym change of measure; * exponential tilting; * exponential families; * positive matrix iteration; * Perron–Frobenius theory; * normalized power iteration; * Markov operators; * replicator-type equations; * Fisher information; * Fisher–Rao geometry; * the square-root representation of the probability simplex. The PDT formulation does not replace these theories. Instead, it organizes them around a recurring transformation-and-normalization structure. This distinction is important when assessing both the mathematical contribution and the appropriate claims of the paper. === 9.3 The geometric characterization === The principal result developed in Section 7 concerns the exponential dilation family :<math> p_i(\theta) = \frac{ p_i^{(0)}e^{\theta\phi_i} } { \sum_jp_j^{(0)}e^{\theta\phi_j} }. </math> Under the finite-dimensional strict-positivity assumptions used in the theorem, the image of this trajectory is contained in a Fisher–Rao Levi-Civita geodesic if and only if the generator <math>\phi</math> assumes at most two distinct values. The proof uses the square-root representation :<math> q_i(\theta) = 2\sqrt{p_i(\theta)} </math> and the unnormalized trajectory :<math> r(\theta) = \sum_{\ell=1}^{m} e^{a_{\ell}\theta/2}u_{\ell}. </math> The Vandermonde argument shows that if the generator assumes exactly <math>m</math> distinct active values, then :<math> \dim \operatorname{span} \{r(\theta):\theta\in\mathbb{R}\} = m. </math> A Fisher–Rao geodesic requires the square-root image to lie in a two-dimensional linear subspace through the origin. This yields the two-level characterization. === 9.4 What the theorem does not claim === Theorem 1 should be interpreted narrowly. It does not claim that exponential trajectories with three or more generator levels are geometrically uninteresting. It does not claim that such trajectories cease to be e-geodesics. It does not claim that the exponential parameter <math>\theta</math> is an affine Fisher–Rao geodesic parameter in the two-level case. It does not characterize arbitrary curves on the probability simplex. It does not characterize arbitrary state-dependent dilation fields. It does not establish an analogous result for infinite-dimensional statistical manifolds. The theorem concerns a specific finite-dimensional exponential family and the coincidence of its trajectory image with a Fisher–Rao Levi-Civita geodesic. === 9.5 Boundary behavior === The main theorem assumes :<math> p_i^{(0)}>0 </math> for every state. This places the trajectory in the interior of the probability simplex for every finite <math>\theta</math>. The square-root representation remains meaningful at the boundary, but the usual coordinate expression of the Fisher–Rao metric becomes singular when one or more probabilities vanish. Boundary points therefore require separate care. In the two-level case, the exponential trajectory approaches boundary distributions only asymptotically as :<math> |\theta|\rightarrow\infty. </math> A systematic treatment of trajectories beginning on, reaching, or moving between lower-dimensional faces of the simplex is outside the scope of the present paper. === 9.6 Zero initial probabilities === If some initial components satisfy :<math> p_i^{(0)}=0, </math> then exponential dilation preserves those zeros: :<math> p_i(\theta)=0. </math> The effective trajectory then lies in a lower-dimensional face of the simplex. In such a case, the number of relevant generator levels should be counted only among states with positive initial probability. The theorem can therefore be expected to admit a support-restricted formulation, but the present statement uses strict positivity to avoid unnecessary boundary qualifications. === 9.7 Fixed versus state-dependent dilation === Much of the analysis in this paper concerns a fixed positive matrix, a fixed weighting field, or a fixed generator. More general transformations may depend on the current probability state: :<math> p^{(k+1)} = \frac{ M(p^{(k)})p^{(k)} } { \mathbf{1}^{\mathsf{T}} M(p^{(k)})p^{(k)} }. </math> Similarly, a continuous generator may depend on <math>p</math> or on the evolution parameter. Such systems may display behavior not reducible to ordinary fixed-matrix spectral theory or fixed-generator exponential tilting. Their study would require tools from nonlinear dynamical systems, nonlinear positive operators, differential geometry, and related fields. No general convergence claim for state-dependent dilation is made here. === 9.8 Entropy === Normalized dilation can either increase or decrease Shannon entropy depending on the transformation and the initial state. For :<math> H(p) = -\sum_i p_i\log p_i, </math> there is no general principle requiring :<math> H(T_M(p)) \leq H(p) </math> or the reverse inequality for arbitrary nonnegative matrices. In repeated diagonal dilation with a unique dominant weight, probability concentration generally drives the limiting distribution toward a point mass and therefore toward zero Shannon entropy. However, this special concentration behavior should not be generalized to arbitrary matrix or state-dependent dilation. A useful open problem is to identify classes of dilation operators for which entropy, relative entropy, or another information functional is monotone. === 9.9 Projective metrics and contraction === Because normalized positive transformations are invariant under positive scalar multiplication, projective geometry provides a natural language for their analysis. For positive matrices and positive operators, Hilbert-type projective metrics and contraction theorems may provide convergence estimates stronger than those obtained from elementary normalization arguments. A systematic comparison between normalized matrix dilation and established projective contraction theory would clarify which convergence properties follow immediately from known results and which, if any, require additional hypotheses. This is an important direction for further study. === 9.10 Curvature beyond the two-level case === Theorem 1 distinguishes exactly between the two-level geodesic case and trajectories generated by three or more distinct levels. The next geometric question is quantitative rather than binary. For :<math> m\geq3, </math> one may ask how far the exponential trajectory departs from a Fisher–Rao Levi-Civita geodesic. Possible quantities include: * geodesic curvature; * covariant acceleration; * deviation from the great-circle plane; * Fisher–Rao distance from an appropriate comparison geodesic; * integrated curvature along the trajectory. Such quantities could provide a graded measure of geometric departure rather than the yes-or-no characterization of Theorem 1. === 9.11 Relation between generator levels and geometric dimension === Corollary 1 gives :<math> \dim \operatorname{span} \{r(\theta)\} = m, </math> where <math>m</math> is the number of distinct active generator values. This suggests a direct relationship between the algebraic complexity of the generator and the linear dimension required to contain its square-root trajectory. The two-level Fisher–Rao result is the first consequence of this dimensional relation. Further work could investigate whether analogous dimension-counting principles arise for multiparameter exponential families or other normalized positive flows. === 9.12 Multiparameter exponential dilation === A natural extension is :<math> p_i(\theta_1,\ldots,\theta_k) = \frac{ p_i^{(0)} \exp \left( \sum_{r=1}^{k}\theta_r\phi_i^{(r)} \right) } { Z(\theta_1,\ldots,\theta_k) }. </math> This defines a multiparameter exponential family. Questions then arise concerning the dimension and curvature of its square-root image and the conditions under which particular parameter curves or submanifolds are totally geodesic with respect to the Fisher–Rao Levi-Civita connection. The one-parameter theorem in this paper does not answer these questions. === 9.13 Infinite-dimensional extension === The measure-theoretic formulation suggests possible extensions beyond finite probability simplices. For a reference probability measure <math>P_0</math>, consider :<math> dP_{\theta} = \frac{ e^{\theta\phi} } { \int e^{\theta\phi}\,dP_0 } dP_0. </math> This is the natural measure-theoretic analogue of finite exponential dilation. An infinite-dimensional version of the geodesic characterization would require careful specification of the statistical manifold, admissible tangent spaces, regularity conditions, and the appropriate Fisher–Rao geometry. The finite-dimensional Vandermonde argument does not by itself establish such a result. === 9.14 Numerical verification === The analytical results in Sections 7 and 8 can be supplemented by numerical experiments. For two generator levels, numerical calculations should verify that the square-root trajectory remains in a fixed two-dimensional plane to numerical precision. For three or more distinct levels, rank calculations can verify the predicted increase in the dimension of the trajectory span. Numerical differentiation can also compare :<math> \left| \frac{ds}{d\theta} \right| </math> with :<math> \sqrt{ \operatorname{Var}_{p(\theta)}(\phi) }. </math> Such computations do not replace proof, but they provide useful checks against algebraic or implementation errors. === 9.15 Literature and priority limitations === The mathematical ingredients used in this paper draw from established areas with extensive literatures. A literature search performed during development has identified substantial prior theory surrounding exponential families, Fisher–Rao geometry, positive operators, normalized matrix iteration, replicator dynamics, and related constructions. At the present draft stage, the exact two-level characterization proved in Section 7 has not been identified by the author in the literature in the same form. This absence should not be interpreted as proof of novelty. Equivalent results may exist under different terminology or as consequences of more general theorems. Accordingly, no claim of historical priority is made. Further literature review and expert scrutiny are required before any stronger novelty statement would be appropriate. === 9.16 Open problems === The framework suggests several specific open questions: # Can the finite-dimensional characterization be formulated cleanly for probability vectors with restricted support? # Is there an established information-geometric theorem equivalent to the two-level characterization? # What is the Fisher–Rao geodesic curvature of an exponential dilation trajectory with three distinct generator levels? # Can that curvature be expressed directly in terms of moments or cumulants of the generator <math>\phi</math>? # Which normalized matrix transformations are contractions in a natural projective or information-geometric metric? # Under what conditions is Shannon entropy monotone under repeated dilation? # What aspects of the framework survive for nonlinear state-dependent operators? # Is there a useful infinite-dimensional analogue of the generator-level dimension result? # How does the characterization generalize to multiparameter exponential families? These questions provide possible directions for extending the present work while maintaining a clear distinction between established theory and additional results. === 9.17 Summary of the discussion === The normalized-dilation viewpoint provides a common structural language for several familiar probability transformations. Its mathematical usefulness depends on what can be learned from that organization rather than on the normalization operation itself. Within the finite-dimensional exponential setting, the Fisher–Rao analysis leads to a precise characterization: the exponential trajectory has a Fisher–Rao geodesic image exactly in the one-level or two-level cases under the stated assumptions. The two-level case additionally admits an explicit Fisher–Rao arclength parameterization. These results motivate further study of curvature, dimensional structure, nonlinear dilation, and measure-theoretic extensions while leaving their broader significance open to mathematical evaluation. == 10. Conclusion == This paper has developed '''normalized probability dilation''' as a common framework for probability transformations having the form :'''positive transformation → normalization → probability state'''. In finite dimensions, the framework includes diagonal reweighting :<math> p_i' = \frac{d_ip_i} {\sum_jd_jp_j}, </math> and normalized nonnegative matrix transformations :<math> T_M(p) = \frac{Mp} {\mathbf{1}^{\mathsf{T}}Mp}. </math> At the level of probability measures, the corresponding construction is :<math> dP_D = \frac{D\,dP} {\int_XD\,dP}. </math> These constructions have direct relationships with established mathematics, including change of measure, exponential tilting, positive matrix theory, Perron–Frobenius theory, normalized power iteration, Markov operators, replicator-type dynamics, Feynman–Kac constructions, exponential families, and Fisher–Rao information geometry. The purpose of the PDT framework is therefore not to claim these established operations as new, but to place them within a common transformation-and-normalization language and to use that organization to formulate precise mathematical questions. === 10.1 Principal geometric result === For the finite-dimensional exponential dilation family :<math> p_i(\theta) = \frac{ p_i^{(0)}e^{\theta\phi_i} } { \sum_jp_j^{(0)}e^{\theta\phi_j} }, </math> the square-root representation :<math> q_i(\theta) = 2\sqrt{p_i(\theta)} </math> converts the Fisher–Rao geometry of the probability simplex into spherical geometry. Grouping equal generator values gives the unnormalized square-root trajectory :<math> r(\theta) = \sum_{\ell=1}^{m} e^{a_{\ell}\theta/2}u_{\ell}, </math> where <math>a_1,\ldots,a_m</math> are the distinct generator levels. The Vandermonde argument developed in Section 7 gives :<math> \dim \operatorname{span} \{r(\theta):\theta\in\mathbb{R}\} = m. </math> Because a spherical great circle lies in a two-dimensional linear subspace through the origin, the exponential dilation trajectory has a Fisher–Rao Levi-Civita geodesic image if and only if :<math> m\leq2. </math> Thus, under the finite-dimensional strict-positivity assumptions of the theorem, the generator must assume at most two distinct values. === 10.2 Two-level arclength === For the nondegenerate two-level case, the trajectory can be written in square-root coordinates as :<math> q(\theta) = 2 \left( \cos\alpha(\theta)\widehat{u} + \sin\alpha(\theta)\widehat{v} \right), </math> where :<math> \alpha(\theta) = \arctan \left( \sqrt{ \frac{1-r_0}{r_0} } e^{(b-a)\theta/2} \right). </math> A signed Fisher–Rao arclength coordinate therefore satisfies :<math> s(\theta)-s(\theta_0) = 2 \left( \alpha(\theta)-\alpha(\theta_0) \right). </math> This makes explicit the distinction between the exponential parameter <math>\theta</math> and Fisher–Rao arclength. The exponential trajectory may follow the correct Fisher–Rao geodesic image without moving along it at constant Fisher–Rao speed. === 10.3 Final perspective === The results illustrate a broader methodological point. A common mathematical framework is most useful when it does more than rename existing constructions. It should clarify relationships among established theories, expose structural distinctions, or lead to questions that can be answered precisely. For normalized probability dilation, the distinction between exponential-family straightness and Fisher–Rao Levi-Civita straightness provides one such question. The resulting two-level characterization and arclength formula provide a concrete starting point for further investigation. Important directions remain open, including curvature of multilevel exponential trajectories, projective contraction properties, entropy conditions, nonlinear state-dependent dilation, multiparameter families, and possible infinite-dimensional extensions. The present manuscript should therefore be regarded as a mathematical framework and initial geometric analysis rather than a completed general theory. The characterization developed here remains subject to further literature review, independent proof checking, and external mathematical evaluation before any claim of historical priority or novelty is made. == 11. Historical Development and Relationship to Probability Dilation Theory == The mathematical framework developed in this paper arose from a broader exploratory project now called '''Probability Dilation Theory (PDT)'''. The present paper should be understood as a mathematical development within that project rather than as a continuation of its earlier physical interpretations. === 11.1 Early geometric-probability motivation === The initial motivation arose from geometric probability, particularly the observation that geometric information can sometimes be inferred from repeated probabilistic sampling. Buffon-type experiments provided an intuitive starting point because they connect a random sampling procedure with geometric quantities through measurable intersection probabilities. Early exploratory work investigated whether ratios derived from such probability experiments might provide a useful language for comparing geometric or scaling effects. These investigations were heuristic and preceded the measure-theoretic formulation developed later. They should therefore be regarded as historical motivation rather than as mathematical evidence for the results proved in this paper. === 11.2 Einstein–Buffon stage === An early version of the project was informally described as the '''Einstein Buffon Process'''. At that stage, the emphasis was on possible analogies between geometric probability, scaling, and physical transformations. The terminology reflected the historical route by which the problem was approached rather than a claim of a new physical theory. As the work developed, it became increasingly clear that the mathematically tractable object was not the proposed physical analogy itself, but the transformation of probability distributions produced by positive weighting followed by normalization. This shift changed the central question from :'''Can a probabilistic sampling ratio represent a physical scaling effect?''' to the more mathematical question :'''What properties follow from normalized positive transformations of probability measures?''' === 11.3 Transition to probability-measure dilation === The resulting abstraction led to the transformation :<math> dP_D = \frac{D\,dP} {\int_XD\,dP}, </math> where <math>P</math> is a probability measure and <math>D</math> is a positive or nonnegative weighting field satisfying the required normalization conditions. This formulation separated the mathematical operation from any particular physical interpretation. It also made clear that the construction has direct relationships with established change-of-measure theory, weighted probability measures, exponential tilting, and related probabilistic methods. The term '''Probability Dilation Theory''' was subsequently adopted for the broader research framework concerned with such normalized probability transformations and their iteration. === 11.4 Development of matrix dilation operators === The finite-dimensional version of the framework naturally suggested replacing scalar componentwise weights by matrix transformations. For a nonnegative matrix <math>M</math>, this gives :<math> T_M(p) = \frac{Mp} {\mathbf{1}^{\mathsf{T}}Mp}. </math> This matrix formulation made the relationship with positive linear algebra substantially clearer. Diagonal dilation became a special case, while off-diagonal matrix elements allowed coupling among probability components. Analysis of fixed points and repeated iteration then connected the framework with eigenvectors, Perron–Frobenius theory, normalized power iteration, and projective dynamics. This stage was important in clarifying which properties of matrix dilation follow from established mathematics and which questions require additional analysis. === 11.5 Development toward information geometry === A further simplification occurs for exponential dilation fields. In finite dimensions, :<math> p_i(\theta) = \frac{ p_i^{(0)}e^{\theta\phi_i} } { \sum_jp_j^{(0)}e^{\theta\phi_j} }. </math> This expression identifies the trajectory directly with a one-parameter exponential family. The connection shifted the investigation toward information geometry. In particular, it raised a precise question that was not apparent in the original geometric-probability formulation: :''When is an exponential dilation trajectory simultaneously an e-geodesic and, up to reparameterization, a Fisher–Rao Levi-Civita geodesic?'' The analysis of that question led to the generator-level characterization proved in Section 7. === 11.6 Conceptual progression === The historical development of the project can therefore be summarized schematically as: :'''geometric probability and Buffon-type sampling''' :'''↓''' :'''exploratory scaling and Einstein–Buffon analogies''' :'''↓''' :'''positive probability reweighting''' :'''↓''' :'''normalized probability-measure transformation''' :'''↓''' :'''matrix dilation operators''' :'''↓''' :'''exponential dilation''' :'''↓''' :'''Fisher–Rao and information-geometric analysis''' This progression should not be interpreted as a derivation of the later mathematics from the earlier physical analogies. Rather, the early investigations provided motivation from which a progressively more abstract and mathematically conventional problem emerged. === 11.7 Relationship to the broader PDT project === The present manuscript focuses on only one part of the broader Probability Dilation Theory research program. The wider PDT project investigates normalized positive transformations of probability measures, their composition, iteration, fixed points, matrix representations, and possible geometric properties. The present paper narrows that scope substantially. Its primary purpose is to: * define a unified normalized-dilation notation; * identify its relationships with established mathematics; * develop the exponential-dilation formulation; * analyze its Fisher–Rao geometry; * prove the finite-dimensional generator-level characterization; * derive the explicit two-level Fisher–Rao arclength formula. Other exploratory PDT topics are not required for the mathematical results of this paper. In particular, speculative applications to physics or cosmology should be regarded as separate research questions and are not assumptions of the theorem proved here. === 11.8 Research provenance and status === The broader PDT project has been developed openly through successive research notes, computational experiments, and Wikiversity pages. Earlier formulations document the evolution of the terminology and ideas, while the present manuscript represents an attempt to isolate a cleaner mathematical core suitable for independent examination. Historical provenance does not establish mathematical novelty. The results presented in this manuscript must instead be evaluated through proof checking, comparison with the existing literature, and independent mathematical review. Accordingly, the earlier stages of the PDT project are relevant to the history of the work but are not used as authority for the mathematical claims of this paper. === 11.9 Relationship between the manuscript and the research project === The distinction between the two levels of presentation is therefore: :'''Probability Dilation Theory (PDT)''' — the broader evolving research framework. :'''This manuscript''' — a focused mathematical investigation of normalized dilation, exponential trajectories, and their Fisher–Rao geometry. The broader project may continue to develop additional models and conjectures independently of this paper. Conversely, the mathematical results of this paper can be assessed without accepting any speculative interpretation associated with earlier stages of PDT. This separation is intended to make the principal definitions, theorem, proof, and limitations accessible to independent mathematical scrutiny. == References == <references /> === General probability and statistical foundations === * Fisher, R. A. (1922). ''On the Mathematical Foundations of Theoretical Statistics''. Philosophical Transactions of the Royal Society of London. Series A, 222, 309–368. doi:10.1098/rsta.1922.0009. * Rao, C. R. (1945). ''Information and Accuracy Attainable in the Estimation of Statistical Parameters''. Bulletin of the Calcutta Mathematical Society, 37, 81–91. === Information geometry === * Amari, S. and Nagaoka, H. (2000). ''Methods of Information Geometry''. Translations of Mathematical Monographs, Vol. 191. American Mathematical Society and Oxford University Press. * Amari, S. (2016). ''Information Geometry and Its Applications''. Applied Mathematical Sciences, Vol. 194. Springer. === Positive matrices, Markov chains, and projective methods === * Seneta, E. (2006). ''Non-negative Matrices and Markov Chains'', 2nd ed. Springer Series in Statistics. Springer. doi:10.1007/0-387-32792-4. * Birkhoff, G. (1957). ''Extensions of Jentzsch's Theorem''. Transactions of the American Mathematical Society, 85, 219–227. === Replicator and simplex geometry === * Shahshahani, S. (1979). ''A New Mathematical Framework for the Study of Linkage and Selection''. Memoirs of the American Mathematical Society, Vol. 17, No. 211. American Mathematical Society. doi:10.1090/memo/0211. === Feynman–Kac and normalized positive transformations === * Del Moral, P. (2004). ''Feynman-Kac Formulae: Genealogical and Interacting Particle Systems with Applications''. Probability and Its Applications. Springer. == Relationship to the Probability Dilation Theory project == This manuscript is part of the broader [[Probability Dilation Theory]] research project on Wikiversity. Technical and exploratory material related to the manuscript is developed on associated PDT subpages, including: * [[Probability Dilation Theory/Measure-Theoretic Foundations|Measure-Theoretic Foundations]] * [[Probability Dilation Theory/Matrix Dilation Operators|Matrix Dilation Operators]] * [[Probability Dilation Theory/Dilation Vector Field|Dilation Vector Field]] * [[Probability Dilation Theory/Dilation Flows|Dilation Flows]] * [[Probability Dilation Theory/Convergence and Fixed Points|Convergence and Fixed Points]] * [[Probability Dilation Theory/Fisher Geometry and Dilation Flows|Fisher Geometry and Dilation Flows]] The present page is intended to develop a concise, standalone manuscript rather than reproduce the complete exploratory PDT project. == Draft status and research note == This manuscript is a work in progress. Some constructions discussed in the paper have direct counterparts in established mathematical literature. These relationships are identified explicitly wherever possible. Results developed specifically within the present formulation are being subjected to continuing literature review, proof checking, numerical verification, and independent mathematical scrutiny before any claim of novelty is made. Readers are encouraged to identify relevant prior literature, mathematical errors, counterexamples, alternative proofs, or useful extensions. == See also == * [[Probability Dilation Theory]] * [[Probability Dilation Theory/Matrix Dilation Operators]] * [[Probability Dilation Theory/Measure-Theoretic Foundations]] * [[Probability Dilation Theory/Fisher Geometry and Dilation Flows]] == Copyright and licensing == Text and original figures © Howard Richardson. Licensed under the [https://creativecommons.org/licenses/by/4.0/ Creative Commons Attribution 4.0 International License (CC BY 4.0)]. Reuse permitted with attribution. s1uitycrs8aj7319swf67igmvirh2vn 2 331357 2823796 2026-08-21T02:58:26Z U3246286 3105520 created an about me page 2823796 wikitext text/x-wiki == About me == Hi! My name is Georgia and I am a third-year student studying at the University of Canberra. I am interested in studying psychology and hope to become a psychologist specialising in ADF and Military veterans! == Book Chapter == This is my book chapter for Motivation and Emotion 2026: [[Motivation and emotion/Book/2026/Self-determination theory and military veteran reintegration]] l8dq8er0t8rfceu5vmbj3xd7cw4ahpk 2823797 2823796 2026-08-21T03:00:16Z U3246286 3105520 2823797 wikitext text/x-wiki == About me == Hi! My name is Georgia and I am a third-year student studying at the University of Canberra. I am interested in studying psychology and hope to become a psychologist specialising in ADF and Military veterans! == Book Chapter == This is my book chapter for Motivation and Emotion 2026: [[Motivation and emotion/Book/2026/Self-determination theory and military veteran reintegration]] == Social Contributions == Contributed to discussion forum: https://uclearn.canberra.edu.au/courses/20143/discussion_topics/456558 8s9w0lovmqdhl9vy7sx9vij8cnvmhe7 0 331358 2823802 2026-08-21T03:39:09Z Gracelp 3108790 Created page with "- GraceLp" 2823802 wikitext text/x-wiki - GraceLp 8t8wfipb06gu5g7m5pu4rjli3tm6mem 0 331359 2823807 2026-08-21T04:13:30Z It-is-Truly-Meet 3089598 Created page with "== Prepositions == A ''preposition'' is a function word that typically combines with a noun phrase to form a phrase which usually expresses a modification or predication (e.g., "the cup is '''on''' the table"). The preposition together with its object is called a ''prepositional phrase''. Prepositions in Ancient Greek function similarly to English, but the object of a Greek preposition must be inflected in either the genitive (away from), dative (on, in, under), or accu..." 2823807 wikitext text/x-wiki == Prepositions == A ''preposition'' is a function word that typically combines with a noun phrase to form a phrase which usually expresses a modification or predication (e.g., "the cup is '''on''' the table"). The preposition together with its object is called a ''prepositional phrase''. Prepositions in Ancient Greek function similarly to English, but the object of a Greek preposition must be inflected in either the genitive (away from), dative (on, in, under), or accusative (into): * εἰς + acc.: into (e.g., εἰς τὸ στόμα — into the mouth) * ἐν + dat.: in (e.g., ἐν τῷ στόματι — in the mouth) * ἐκ + gen.: from, out of (e.g., ἐκ τοῦ στόματος — out of the mouth) ** ἐκ becomes ἐξ before a vowel (e.g., ἐξ αἵματος — out of blood) ===Accents, Elision, and Aspiration=== * Prepositions—with the exception of εἰς, ἐν, and ἐκ—normally have an acute accent. If the preposition has two syllables, the acute falls on the ultima ** e.g., ἀπὸ τῆς ἐλπίδος — from the hope * Prepositions frequently drop their final vowel before a word beginning with a vowel, and in such cases, the preposition has no accent—though περί and πρό don’t allow for elision ** e.g., ἀπ’ ἐλπίδος — from hope * After a preposition drops its final vowel and ends in a stop consonant, that consonant becomes aspirated if the following word begins with an aspirated (i.e., marked with a rough breathing) vowel or diphthong ** e.g., ἀφ’ αἵματος — from blood ===Accusative Prepositions=== * ἀμφί around, about * ἀνά up, through * διά because of, through * εἰς/ἐς into * ἐπί against * κατά down, along, according to * μετά after, behind * παρά to, throughout, beside * περί near, around * πρός toward * ὑπέρ above, over, beyond * ὑπό under ===Dative Prepositions=== * ἀμφί around, near * ἀνά upon * ἐν in * ἐπί on, for the purpose of, because of * παρά with, near * περί about * πρός by, in addition to * σύν with (the help of) * ὑπό under ===Genitive Prepositions=== * ἀμφί around, near * ἀνά upon * ἀπό from * ἐν in * ἐπί on, for the purpose of, because of * παρά with, near * περί about * πρός by, in addition to * σύν with (the help of) * ὑπό under ===Prefixes, Elision, and Aspiration=== Prepositions can also double as prefixes for verbs. When prefixes are attached to verbs, any final vowel drops out (elides) if the tense stem to which it is added begins with a vowel. As with prepositions, the prefixes περί and πρό are an exception to this rule, and do not elide. If a prefix drops its final vowel, the remaining consonant becomes aspirated if the tense stem begins with an aspirated vowel or diphthong (e.g., ἀφίημι (ἀπο + ἵημι) → let go, allow, forgive). When the prepositions ἐν and σύν are used as prefixes, they retain these forms when the verb begins with a vowel (e.g., ἐν + ἐργέω (work) → ἐνεργέω (be in action; be efficient; operate)). When the verb begins with a consonant, they assimilate with the consonant. * They retain their form (ἐν– and συν–) before a dental (τ, δ, θ) * They become ἐμ– and συμ– before a labial (π, β, φ, ψ, μ) ** e.g., ἐν + βάλλω (throw) → ἐμβάλλω (throw in; hand in) * They become ἐγ– and συγ– before a palatal (κ, γ, χ, ξ) συν becomes συλ– before λ. ** e.g., σύν + λαμβάνω (take) → συλλαμβάνω (collect; gather together) == Negation == Affirmation and negation are ways in which grammar encodes positive and negative polarity into clauses. An affirmative form is used to express the validity of an assertion, while a negative form expresses its falsity. In Ancient Greek, '''οὐ''', or its compound, simply denies. '''Μή''', or its compound, presents the negation as willed, or as part of an imagined or assumed case. Hence, μή is the regular negative in wishes and in subjunctive and imperative sentences. After οὐ, alone or in composition, a compound of οὐ strengthens the negation; in older English a similar doubling of the negative was common: "I will not budge for no man’s pleasure, I." (Shakespeare, Romeo and Juliet From the Folger Shakespeare 3.1.56). So also a compound of μή following μή. * '''Οὔ'''ποτε ἐρεῖ '''οὐ'''δείς (Xen. Anabasis 1.3.5). If the second negative is simple, each has its separate force: "Καὶ '''οὐ''' γράφει μὲν ταῦτα τοῖς δʼ ἔργοις '''οὐ''' ποιεῖ" (Demosthenes 9.27). Οὐ μή with the subjunctive is a strong denial referring to the future. ===Alternative Forms of οὐ=== * οὐκ — before vowel with smooth breathing * οὐχ — before vowel with rough breathing * οὔ — pausal form * οὐχῐ́ — (intensive) Attic, Epic, Ionic [[Category:Ancient Greek Language]] ilh12u5sud1wn272d2wq03phc6bqoz9 3 331360 2823817 2026-08-21T04:32:58Z Jtneill 10242 Welcome 2823817 wikitext text/x-wiki ==Welcome== {{Robelbox|theme=9|title='''[[Wikiversity:Welcome|Welcome]] to [[Wikiversity:What is Wikiversity|Wikiversity]], BellaJohnson1!'''|width=100%}} <div style="{{Robelbox/pad}}"> You can [[Wikiversity:Contact|contact us]] with [[Wikiversity:Questions|questions]] at the [[Wikiversity:Colloquium|colloquium]] or get in touch with [[User talk:Jtneill|me personally]] if you would like some [[Help:Contents|help]]. 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See you around Wikiversity! ---- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 04:32, 21 August 2026 (UTC)</div> <!-- Template:Welcome --> {{Robelbox/close}} ll0o0pcc28f3ypw6cewkg99bqtz2yg8 3 331361 2823819 2026-08-21T04:35:18Z Jtneill 10242 Welcome 2823819 wikitext text/x-wiki ==Welcome== {{Robelbox|theme=9|title='''[[Wikiversity:Welcome|Welcome]] to [[Wikiversity:What is Wikiversity|Wikiversity]], Gracelp!'''|width=100%}} <div style="{{Robelbox/pad}}"> You can [[Wikiversity:Contact|contact us]] with [[Wikiversity:Questions|questions]] at the [[Wikiversity:Colloquium|colloquium]] or get in touch with [[User talk:Jtneill|me personally]] if you would like some [[Help:Contents|help]]. Remember to [[Wikiversity:Signature#How to add your signature|sign]] your comments when [[Wikiversity:Who are Wikiversity participants?|participating]] in [[Wikiversity:Talk page|discussions]]. 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See you around Wikiversity! ---- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 04:35, 21 August 2026 (UTC)</div> <!-- Template:Welcome --> {{Robelbox/close}} dcxfti94rwy8fmulcpnxc25kf7q3g03 2823820 2823819 2026-08-21T04:36:55Z Jtneill 10242 Topic sign-up 2823820 wikitext text/x-wiki ==Welcome== {{Robelbox|theme=9|title='''[[Wikiversity:Welcome|Welcome]] to [[Wikiversity:What is Wikiversity|Wikiversity]], Gracelp!'''|width=100%}} <div style="{{Robelbox/pad}}"> You can [[Wikiversity:Contact|contact us]] with [[Wikiversity:Questions|questions]] at the [[Wikiversity:Colloquium|colloquium]] or get in touch with [[User talk:Jtneill|me personally]] if you would like some [[Help:Contents|help]]. Remember to [[Wikiversity:Signature#How to add your signature|sign]] your comments when [[Wikiversity:Who are Wikiversity participants?|participating]] in [[Wikiversity:Talk page|discussions]]. 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See you around Wikiversity! ---- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 04:35, 21 August 2026 (UTC)</div> <!-- Template:Welcome --> {{Robelbox/close}} ==Topic sign-up== To sign up to a topic, you'll need to edit this page: [[Motivation and emotion/Book/2026]] to put your user name alongside a topic. For more explanation, see [[Motivation and emotion/Assessment/Selection]]. Sincerely, James -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 04:36, 21 August 2026 (UTC) ntv19m3r8ar2hvc9ck72nalram88jpn 1 331362 2823825 2026-08-21T04:42:28Z Jtneill 10242 Heading casing 2823825 wikitext text/x-wiki == Heading casing == {| style="float: center; background:transparent;color:inherit;" |- | [[File:Crystal Clear app ktip.svg|48px|left]] | {{#if:|Hi [[User:{{{1}}}|{{{1}}}]].|}} FYI, the recommended [[Wikiversity]] heading style uses [[w:Letter case#Sentence_case|sentence casing]]. For example:<br> <big><big>Self-determination theory</big></big> rather than <big><big>Self-Determination Theory</big></big> Here's an example chapter with correct heading casing: [[Motivation and emotion/Book/2019/Growth mindset development|Growth mindset development]] -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 04:42, 21 August 2026 (UTC) |} jot00gn1rjcp9agwa6kwqqqtof6gf4e 2 331363 2823830 2026-08-21T05:03:41Z Nabal Kishore Pande 3108802 CREATED COMPLETE PAGE 2823830 wikitext text/x-wiki [[File:Portrait of Nabal Kishore Pande.jpg|250px|thumb|right|Nabal Kishore Pande]] '''Nabal Kishore Pande''' is an independent author and researcher from India. I am interested in research, decision-making, scholarship preparation, and the development of practical frameworks for organising and using knowledge. My work brings together research and writing with a focus on questions that require careful examination of evidence and preparation before action. I use Wikiversity as a place to learn from and contribute to open educational and research material. I am particularly interested in material that explains research methods, structured reasoning, and practical approaches to complex academic and professional questions. I welcome constructive discussion and corrections from other contributors. sayix3egptszthq20b0wcjusd4n3oa0 2 331364 2823836 2026-08-21T05:57:08Z U3228742 3005570 introduction of self on user page 2823836 wikitext text/x-wiki I am a student studying an undergraduate Bachelor of Science in Psychology. My interests and area of focus is social psychology, emotional intelligence, and the understanding people's motivations. I am a life learner who has studied other health modalities and would love to practice clinical psychology. My hobbies are painting, reading and my latest obsession is making sourdough. 92atjr4hgeg2q18163az1td37ftfwkv 2823837 2823836 2026-08-21T06:00:49Z U3228742 3005570 added link to dark empathy chapter in the book 2026 2823837 wikitext text/x-wiki I am a student studying an undergraduate Bachelor of Science in Psychology. My interests and area of focus is social psychology, emotional intelligence, and the understanding people's motivations. I am a life learner who has studied other health modalities and would love to practice clinical psychology. My hobbies are painting, reading and my latest obsession is making sourdough. Created a chapter on [[Motivation and emotion/Book/2026/Dark empathy|Dark Empathy]] in the [[Motivation and emotion/Book/2026|Motivation and emotion book 2026]] 1gep8acsuso80restuo9fhc5cqc8hd7 2 331365 2823839 2026-08-21T06:07:22Z It-is-Truly-Meet 3089598 Created page with "Hello, I am '''It-is-Truly-Meet''', a student that is studying Western philosophy and Attic Greek. I have experience in calculus, calculus-based physics, and computer science." 2823839 wikitext text/x-wiki Hello, I am '''It-is-Truly-Meet''', a student that is studying Western philosophy and Attic Greek. I have experience in calculus, calculus-based physics, and computer science. qxt6j8vw9hrctxl31w8p6bosnqcq21a 3 331366 2823844 2026-08-21T06:58:21Z Atcovi 276019 /* Welcome */ new section 2823844 wikitext text/x-wiki ==Welcome== {{Robelbox|theme=9|title='''[[Wikiversity:Welcome|Welcome]] to [[Wikiversity:What is Wikiversity|Wikiversity]], It-is-Truly-Meet!'''|width=100%}} <div style="{{Robelbox/pad}}"> You can [[Wikiversity:Contact|contact us]] with [[Wikiversity:Questions|questions]] at the [[Wikiversity:Colloquium|colloquium]] or get in touch with [[User talk:Atcovi|me personally]] if you would like some [[Help:Contents|help]]. Remember to [[Wikiversity:Signature#How to add your signature|sign]] your comments when [[Wikiversity:Who are Wikiversity participants?|participating]] in [[Wikiversity:Talk page|discussions]]. Using the signature icon [[File:OOjs UI icon signature-ltr.svg]] makes it simple. We invite you to [[Wikiversity:Be bold|be bold]] and [[Wikiversity|assume good faith]]. Please abide by our [[Wikiversity:Civility|civility]], [[Wikiversity:Privacy policy|privacy]], and [[Foundation:Terms of Use|terms of use]] policies. To find your way around, check out: <!-- The Left column --> <div style="width:50.0%; float:left"> * [[Wikiversity:Introduction|Introduction to Wikiversity]] * [[Help:Guides|Take a guided tour]] and learn [[Help:Editing|how to edit]] * [[Wikiversity:Browse|Browse]] or visit an educational level portal:<br>[[Portal:Pre-school Education|pre-school]] | [[Portal:Primary Education|primary]] | [[Portal:Secondary Education|secondary]] | [[Portal:Tertiary Education|tertiary]] | [[Portal:Non-formal Education|non-formal]] * [[Wikiversity:Introduction explore|Explore]] links in left-hand navigation menu </div> <!-- The Right column --> <div style="width:50.0%; float:left"> * Read an [[Wikiversity:Wikiversity teachers|introduction for teachers]] * Learn [[Help:How to write an educational resource|how to write an educational resource]] * Find out about [[Wikiversity:Research|research]] activities * Give [[Wikiversity:Feedback|feedback]] about your observations * Discuss issues or ask questions at the [[Wikiversity:Colloquium|colloquium]] </div> <br clear="both"/> To get started, experiment in the [[wikiversity:sandbox|sandbox]] or on [[special:mypage|your userpage]]. See you around Wikiversity! --—[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 06:58, 21 August 2026 (UTC)</div> <!-- Template:Welcome --> {{Robelbox/close}} dfs50dbijs67t076onvboc0vhsb2c37 2 331367 2823857 2026-08-21T10:28:59Z U3263365 3104938 Started page 2823857 wikitext text/x-wiki Hi, I am a third year student and I am currently studying Psychology and Law at the University of Canberra. 8irpkfmnufobmy8jjbi3ahbfm65q8d5 2823858 2823857 2026-08-21T10:32:31Z U3263365 3104938 Headings and hobbies 2823858 wikitext text/x-wiki == About me == Hi, I am a third year student and I am currently studying Psychology and Law at the University of Canberra. == Hobbies == * Hockey *# Field *# Indoor * Karaoke * Kickbxing == Book Chapter == == Social Contributions == 4yydiktaj88gr7q7as6seghj029kjrl 2823859 2823858 2026-08-21T10:33:13Z U3263365 3104938 /* Hobbies */ spelling 2823859 wikitext text/x-wiki == About me == Hi, I am a third year student and I am currently studying Psychology and Law at the University of Canberra. == Hobbies == * Hockey *# Field *# Indoor * Karaoke * Kickboxing == Book Chapter == == Social Contributions == dy2kdrupd26gxfn8qczovmj9lukrbyp 2823860 2823859 2026-08-21T10:40:04Z U3263365 3104938 /* About me */ added links 2823860 wikitext text/x-wiki == About me == Hi, I am a third year student and I am currently studying Psychology and Law at the [https://www.canberra.edu.au/ University of Canberra]. This semester I am completing the unit [[motivation and emotion]]. == Hobbies == * Hockey *# [[w:Field_hockey|Field]] *# [[w:Indoor_hockey|Indoor]] * Karaoke * Kickboxing == Book Chapter == == Social Contributions == m68bo547rp55kmk1nwac7g2l2742pu7 2823861 2823860 2026-08-21T10:43:04Z U3263365 3104938 /* Book Chapter */ added link 2823861 wikitext text/x-wiki == About me == Hi, I am a third year student and I am currently studying Psychology and Law at the [https://www.canberra.edu.au/ University of Canberra]. This semester I am completing the unit [[motivation and emotion]]. == Hobbies == * Hockey *# [[w:Field_hockey|Field]] *# [[w:Indoor_hockey|Indoor]] * Karaoke * Kickboxing == Book Chapter == [[Motivation and emotion/Book/2026/Moral emotions and ethical behaviour|Moral emotions and ethical behaviour]] == Social Contributions == aifk8w2f7osmvguaa1pu0ap54v5eq4x 2823863 2823861 2026-08-21T11:04:14Z U3263365 3104938 Added image 2823863 wikitext text/x-wiki == About me == Hi, I am a third year student and I am currently studying Psychology and Law at the [https://www.canberra.edu.au/ University of Canberra]. This semester I am completing the unit [[motivation and emotion]]. == Hobbies == [[File:Sulphur-crested cockatoos on a gum tree.jpg|thumb|'''Figure 1.''' Nature walks are a perfect way to experience native flora and fauna|200x200px]] * Hockey *# [[w:Field_hockey|Field]] *# [[w:Indoor_hockey|Indoor]] * Karaoke * Nature Walking == Book Chapter == [[Motivation and emotion/Book/2026/Moral emotions and ethical behaviour|Moral emotions and ethical behaviour]] == Social Contributions == dmj49qckijk5mscugu0dcchgpr422ii